chap7习题答案

合集下载

信号与系统奥本海姆英文版课后答案chapter7

137Chapter 7 Answers7.1 From the Nyquist sampling theorem , we know that only if X (j w)=0 for |w| > w s /2 will be signal be recoverable from its samples. Therefore, X(jw)>5000л.7.2 From the Nyquist theorem ,we know that the sampling frequency in this case must be at least w s =2000п.In other words ,the sampling period should be at most T=2п/ (w s )=1＊10-3.Clearly ,only (a) and (e) satisfy this condition.7.3 (a) We can easily show that X(j w)=0 for |w| >4000п.Therefore, the Nyquist rate for this signal is w N =2(4000п)=8000п.(b)From the Tables 4.1 and 4.2 we know that X(j w) is a rectangular pulse for which X(j w)=0 for |w| > 4000п.Therefore, the Nyquist rate for this signal is w N =2(4000п)=800п.(c) From the Tables 4.1 and 4.2 we know that X(j w) is the convolution of two rectangular pulses each of which is zero for |w| > 4000п.Therefore ,X(j w)=0 for |w| >8000пand the Nyquist rate for this signal is w N =2(8000п)=16000п.7.4 If the signal x(t) has a Nyquist rate of w o ,then its Fourier transform X (j w)=0 for |w| > w o /2. (a) From chapter 4,y(t) = x (t) + x (t-1) −→←FTY (jw) = X (jw) + e -jwt X (jw).Clearly, we can only guarantee that Y (jw) =0 for |w| > w o /2. Therefore, the Nyquist rate for y(t) is also w o . (b) From chapter 4,y(t) = dtt dx )( −→←FTY (jw)= jw X(jw).Clearly, we can only guarantee that Y (jw) =0 for |w| > w o /2. Therefore, the Nyquist rate for y(t) is also w o . (c) From chapter 4,y(t) =x 2(t) −→←FTY (jw)= (1/2п)[X(jw)*X(jw)]Clearly, we can only guarantee that Y (jw) =0 for |w| > w o . Therefore, the Nyquist rate for y(t) is also 2w o . (d) From chapter 4,y(t)=x(t)cos (w o t) −→←FTY (jw)= (1/2)X(j(w- w o )) +(1/2)X(j(w+ w o )).Clearly, we can guarantee that Y (jw) =0 for |w| > w o + w o /2. Therefore, the Nyquist rate for y(t) is 3w o. 7.5 Using Table 4.2,p(t) −→←FT Tπ2∑∞-∞=-K T K )/2(πωδFrom Table 4.1 p(t-1) −→←FT Tπ2 e -jw T jk k eTk ππωδ2)2(-∞-∞=∑-. Since y(t)=x(t)p(t-1),we haveY (jw)= (1/2п)[X(jw)*FT{P(t-1)}]=(1/T)T jk K e Tk j X ππω2))2((-∞-∞=∑-Therefore, Y(j ω) consists of replicates of X(j ω) shifted by k2π/T and added to earth other (see Figure⎩⎨⎧≤=otherwiseT j H c ,0||,)(ωωωWhere (2/0ω)<c ω<(2π/T) - (2/0ω).7.6 Consider the signal w(t)=x 1(t)x 2(t).The Fourier transform W(j ω) of w(t) is given by W(j ω)=π21[])(*)(21ωωj X j X .Since 0)(1=ωj X for |ω|≥1ωand X 2(j ω)=0 for |ω|≥2ω, we may conclude that W(j ω)=0 for |ω|≥1ω+2ω.Consequently ，the Nyquist rate for w(t) iss ω=2(1ω+2ω).Therefore ,the maximum sampling138period which would still allow w(t) to be recovered is T=2π/(s ω)=π/(1ω+2ω). 7.7 We note thatx 1(t) =h 1(t)*{∑∞-∞=-n nT t nT x )()(δ}Form Figure 7.7 in the book ,we know that the output of the zero-order hold may be written as x 0(t)=h 0(t)* {∑∞-∞=-n nT t nT x )()(δ}where h 0(t) is as shown in Figure S7.7 By taking the Fourier transform of the two above equations, we have X 1(j ω)=H 1( j ω)X p ( j ω)X 0(j ω)=H 0( j ω) X p ( j ω)We now need to determine a frequency response H d ( j ω) for a filter which produces x 1(t) at its output when x 0(t) is its input. Therefore, we needX 0(j ω) H d ( j ω)= X 1(j ω)The triangular function h 1(t) may be obtained by convolving two rectangular pulses as shown in Figure S7.7Therefore,h 1(t)={(1/T ) h 0(t+T/2)}*{( 1/T ) h 0(t+T/2)} Taking the Fourier transform of both sides of the above equation, H 1( j ω)=T1e T j ω H 0( j ω) H 0( j ω) ThereforeX 1(j ω)= H 1( j ω) X p ( j ω)=T 1e T j ω H 0( j ω) H 0( j ω) X p ( j ω) =T1e Tj ω H 0( j ω) X 0(j ω)ThereforeH d ( j ω)=T1eTj ω H 0( j ω)=e2/jwT TT ωω)2/sin(2 7.8 (a) Yes, aliasing does occur in this case .This may be easily shown by considering the sinusoidal term of x(t) for k=5. This term is a signal of the form y(t)=(1/2)5sin(5πt).If x(t) is sampled as T=0.2, then we will always be sampling y(t) at exactly its zero-crossings (This is similar to the idea presented in Figure 7.17 of your textbook). Therefore ,the signal y(t) appears to be identical to the signal (1/2)5sin(0πt) for frequency 5π is a liased into a sinusoid of frequency 0 in the sampled signal.(b) The lowpass filter performs band limited interpolation on the signal ∧x(t).But since aliasing has alreadyresulted in the loss of the sinusoid (1/2)5sin(5πt),the output will be of the formx γ(t)=k k )21(40∑= sin(k πt)The Fourier series representation of this signal is of the form139x γ(t)=∑-=44k k a e )/(t k j π-Where a k =-j(1/2)1+kj(1/2)1+-k7.9 The Fourier transform X(jWe know from the results on impulse-train sampling thatG(jw)=∑∞∞--ωωk j X T ((1s )),Where T=2π/s ω=1/75.therefore,G(jw) is as shown in Figure S7.9 .Clearly, G(jw)=(1/T)X(j ω)=75 X(j ω) for |ω|≤50π.7.10 (a) We know that x(t) is not a band-limited signal. Therefore, it cannot undergo impulse-train sampling without aliasing.(b) Form the given X(j ω) it is clear that the signal x(t) which is bandlimited. That is, X(j ω)=0 for |ω|>0ω.Therefore, it must be possible to perform impulse-train sampling on this signal without experiencing aliasing. The minimum sampling rate required would bes ω=20ω,This implies that thesampling period can at most be T=2π/s ω=π/0ω(c) When x(t) undergoes impulse train sampling with T=2π/0ω,we would obtain the signal g(t) with Fourier transformG(jw)= T1∑∞-∞=-k T k j X ))/2((πωFigure S7.10It is clear from the figure that no aliasing occurs, and that X(jw) can be recovered by using a filter with frequency response T 0≤ωω≤0 H(jw)= 0 otherwiseTherefore, the given statement is true. 7.11 We know from Section 7.4 thatX d (ωj e )= T1∑∞-∞=-k cT k j X ))/2((πω(a) Since X d (ωj e) is just formed by shifting and summing replicas of X(jw),we may argue that ifX d (ωj e ) is real , then X(jw) must also be real(b) X d (ωj e) consists of replicas of X(jw) which are scaled by 1/T,Therefore,if X d (ωj e) has amaximum of 1, then X(jw) must also be real.(c) The region πωπ≤≤||4/3in the discrete-time domain corresponds to the regionT T /||)4/(3πωπ≤≤ in the discrete-time domain. Therefore ,if X d (ωj e )=0 forπωπ≤≤||4/3,then X(jw)=0 for πωπ2000||1500≤≤,But since we already have X(jw)=0 for140πω2000||≥,we have X(jw)=0 for πω1500||≥(d) In this case, sinceπ in discrete-time frequency domain corresponds to 2000π in the continuous-time frequency domain, this condition translates to X(jw)=(j(ω-2000π))7.12 Form Section 7.4 ,we know that the discrete and continuous-time frequencies Ω and ω are related by Ω=ω.Therefore, in this case for Ω=43π,we find the corresponding value of ω toω=43πT1=3000π/4=7500π7.13 For this problem ,we use an approach similar to the one used in Example 7.2 .we assume thatx c (t)=tT t ππ)/sin(The overall output isy c (t)= x c (t-2T)= )2()]2)(/sin[(T t T t T --ππForm x c (t). We obtain the corresponding discrete-time signal x d [n] to be x d [n]= x c (nT)= T1][n δalso, we obtain from y c (t),the corresponding discrete-time signal y d [n] to be y d [n]= y c (nT) =)2()]2(sin[(--n T n ππWe note that the right-hand side of the above equation is always zero when n ≠2.When n=2 ,wemay evaluate the value of ratio using L ,Hospital ,s rule to be 1/T ,Thereforey d [n]= T1]2[-n δWe conclude that the impulse response of the filter is h d [n]= ]2[-n δ7.14 For this problem ,we use an approach similar to the one used in Example 7.2.We assume that x c (t)= tT t ππ)]/sin[(The overall output isy c (t)=)2(T t x dt d c -=)2/()]2/()/[()/(T t T t T COS T ---πππ-2))2/(()]2/)(/sin[(T t T t T --πππForm x c (t) , we obtain the corresponding discrete-time signal x d [n] to be x d [n]= x c (nT)= T1][n δAlso, we obtain from yc(t),the corresponding discrete-time signal y d [n] to beY d [n]=y c (nT)=)2/1()]2/1(cos[)/(--n T n T πππ- )2/1()]2/1(sin[--n T n ππThe first term in rig πht-hang side of the above equation is always zero because cos[π(n-1/2)]=0, therefore, y d [n]= )2/1()]2/1(sin[--n T n ππWe conclude that the impulse response of the filter is h d [n]= )2/1()]2/1(sin[--n T n ππ7.15. in this problem we are interested in the lowest rate which x[n] may be sampled without the possibility of aliasing, we use the approach used in Example 7.4 to solve this problem. To find the lowest rate at which x[n] may be sampled while avoiding the possibility of aliasing, we must find an N such that (22≥Nπ)73πN ≤7/37.16 Although the signal x 1[n]=2sin(πn/2)/( πn) satisfies the first tow conditions, it does not satisfy the thirdcondition . This is because the Flurries transform X 1(e j ω) of this signal is rectangular pulse which is zero for π/2<|ω|<π/2 We also note that the signal x[n]=4[sin(πn/2)/(πn)]2 satisfies the first tow conditions. Fromour numerous encounters with this signal, we know that its Fourier transform X(e j ω) is given by the periodic141convolution of X 1(e j ω) with itself. Therefore, X(e j ω) will be a triangular function in the range 0≤|ω|≤π. This obviously satisfies the third condition as well. T therefore, the desired signal is x[n]=4[sin(πn/2)/(πn)]2.7.17 In this problem .we wish to determine the effect of decimating the impulse response of the given filter by a factor of 2. As explained in Section 7.5.2 ,the process of decimation may be broken up into two steps. In the first step we perform impulse train sampling on h[n] to obtain H p [n]∑∞-∞=k h[2k]δ[n-2k]The decimated sequence is then obtained using h 1[n]=h[2n]=h p [2n]Using eq (7.37), we obtain the Fourier transform H p (e j ω) of h p [n] to beH 1(e j ω)=H p (e jω/2)In other words , H 1(e j ω) is H p (e j ω/2) expanded by a factor of 2. This is as shown in the figure above. Therefore, h 1[n]=h[2n] is the impulse response of an ideal lowpass filter with a passband gain of unity and a cutoff frequency of π/27.18 From Figure 7.37,it is clear interpolation by a factor of 2 results in the frequency response getting compressed by a factor of 2. Interpolation also results in a magnitude sealing by a factor of 2. Therefore, in this problem, the interpolated impulse response will correspond to an ideal lowpass filter with cutoff frequency π/ and a passband gain of 2.7.19 The Fourier transform of x[n] is given by1 |ω|≤ω1X(e j ω)= 0 otherwiseThis is as shown in Figure 7.19.(a) when ω1 ≤3π/5, the Fourier transform X 1(e j ω) of the output of the zero-insertion system is shown inFigure 7.19. The output w(e j ω) of the lowpass filter is as shown in Figure 7.19. The Fourier transform of theoutput of the decimation system Y(e j ω) is an expanded or stretched out version of W(e j ω). This is as shown in Figure 7.19.therefore, y[n]=51nn πω)3/5sin(1(b) When ω1＞3π/5, the Fourier’s transform X 1(e j ω) of the output of the zero-insertion system is as shownin Figure 7.19 The output W(e j ω142The Fourier transform of the output of the decimation system Y(e j ω) bis an expanded or stretched outversion of W(e j ω) .This is as shown in Figure S7.19. Therefore,y[n]=][51n δ7.20 Suppose that X(e j ω) is as shown in Figure S7.20, then the Fourier transform X A (e j ω) of the output of theoutput of S A , the Fourier transform X 1(e j ω) of the output of the lowpass filter , and the Fourier transform X B (e j ω) of the output of S B are all shown in the figures below. Clearly this system accomplishes the filtering task .Figure S7.20(b) Suppose that X(e j ω) is as shown in Figure S7.20 ,then the Fourier transform X B (e j ω) of the output ofS B ,the Fourier transform X 1(e j ω)of the output of the first lowpass filter ,the Fourier transfore X A (e j ω) of theoutput of S A ,the Fourier transform X 2(e j ω) of the output of the first lowpass filter are all shown in the figure below .Clearly this system does not accomplish the filtering task. 7.21(a) The Nyquist rate for the given signal is 2×5000π=10000π. Therefore in order to be able to recover x(t)from x p (t) ,the sampling period must at most be T max =2π/10000π=2×10-4 sec .Since the sampling period used is T=10-4＜T max ,x(t) can be recovered from x p (t).(b) The Nyquist rate for the given signal is 2×15000π=30000π. Therefore in order to be able to recover x(t)from x p (t) ,the sampling period must at most be T max =2π/30000π=0.66×10-4 sec .Since the sampling period used is T=10-4＞T max , x(t) can not be recovered from x p (t).(c) Here,I m {X(j ω)} is not specified. Therefore, the Nyquist rate for the signal x(t) is indeterminate. Thisimplies that one cannot guarantee that x(t) would be recoverable from x p (t).(d) Since x(t) is real,we may conclude that X(j ω)=0 for |ω|＞5000. Therefore the answer to this part isidentical to that of part (a)(e) Since x(t) is real, X(j ω)=0 for |ω|＞15000π. Therefore the answer to this part is identical to that of part(b)(f) If X(j ω)=0 for |ω|＞ω1,then X(j ω)*X(j ω)=0 for |ω|＞2ω1,Therefore in this part X(j ω)=0 for |ω|＞7500. The Nyquist rate for this signal is 2×7500π=15000π. Therefore in order to be able to recover x(t) from x p (t) ,the sampling period must at most be T max =2π/15000π=1.33×10-4 sec .Since the sampling period used is T=10-4＜T max , x(t) can be recovered from x p (t). (g)If |X(j ω)|=0 for ω＞5000π,then X(j ω)=0 for |ω|＞5000π. Therefore the answer to this part is identical to that of part (a).7.22 Using the properties of the Fourier transform, we obtain Y(j ω)=X 1(j ω)X 2(j ω).Therefore, Y(j ω)=0 for |ω|＞1000π.This implies that the Nyquist rate for y(t) is2×1000π=2000π.Therefore, the sampling period T can at most be 2π/(2000π)=10-3sec. Therefore we have to use T<10-3sec in order to be able to recover y(t) from y p (t). 7.23(a) We may express p(t) asP(t)=p 1(t)-p 1(t-△);Where p 1(t)=∑∞-∞=∆-k k t )2(δnow,143P 1(j ω)=∆π∑∞-∞=∆-k )/(πωδTherefore,P(j ω)= P 1(j ω)-e -j ω∆P 1(j )ωIs as shown in figure S7.23. Now,X p (j ω)=)](*)([21ωωπjP j XTherefore, X p (j ω) is as sketched below for △<π/(2ωM ),The corresponding Y(j ω) is also sketched in figure S7.23.(b) The system which can be used to recover x(t) from x p (t) is as shown in FigureS7.23. (c) The system which can be used to recover x(t) from x(t) is as shown in FigureS7.23.(d) We see from the figures sketched in part (a) that aliasing is avoided when ωM ≤π/△.therefore, △max =π/ωM.7.24 we may impress s(t) as s(t)=s(t)-1,where s(t) is as shown in Figure S7.24 we may easily show thats (j )ω= ∑∞-∞=-∆k T k kT k )/2()/2sin(4πωδπFrom this, we obtainS(j =-=)(2)()ωπδωωj S∑∞-∞=-∆k T k k T k )/2()/2sin(4πωδπ-2)(ωπδ Clearly, S(j ω) consists of impulses spaced every 2π/T.(a) If △=T/3, thenS(j =)ω∑∞-∞=-k T k kk )/2()3/2sin(4πωδπ-2)(ωπδNow, since w(t)=s(t)x(t),πω21)(=j W ∑∞-∞=--k X T k j X kk )(2))/2(()3/2sin(4ωππωπTherefore, W(j ω)consists of replicas of X(j ω) which are spaced 2π/T apart. Tn order to avoid aliasing,ωW should be less that π/T. Therefore, T max =2π/ωW. (b) If △=T/3, then(a)(b)()jw Figure S7.24x144S(j =)ω∑∞-∞=-k T k k k )/2()4/2sin(4πωδπ-2)(ωπδ we note that S(j ω)=0 for k=0,±2, ±4,…..This is as sketched in Figure S7.24.Therefore, the replicas of X(j ω)in W(j ω) are now spaced 4π/T apart. Tn order to avoid aliasing,ωW should be less that2π/T. Therefore, T max =2π/ωW. 7.25 Here, x T (kT) can be written asX T (kT)= ∑∞-∞=--k nT x n k n k )()()](sin[ππNote that when n ≠k,0)()](sin[=--n k n k ππAnd when n=k,1)()](sin[=--n k n k ππ Therefore,x τ(kT)=x(kT)7.26. We note thatp(j ω)=Tπ2δ(ω－k2π/T)Also, since x p (t)=x(t)p(t).X p (j ω)=12π{ x(j ω) * P(j ω)}=1Tx(j(ω－k2π/T))Figure S7.26Note that as T increase, Tπ2－ω2 approaches zero. Also, we note that there is aliasingWhen2ω1-ω2<Tπ2－ω2<ω2If 2ω1-ω2≥0(as given) then it is easy to see that aliasing does not occur when 0≤Tπ2－ω2≤2ω1－ω2For maximum T, we must choose the minimum allowable value for Tπ2－ω2 (which is zero).This implies that T max =2π/ω2. We plot x p (j ω) for this case in Figure S7.26. Therefore, A=T, ωb =2π/T, and ωa =ωb －ω11457.27.(a) Let x 1(j ω) denote the Fourier transform of the signal x 1(t) obtained by multiplyingx(t) with e -j ω0t Let x 2(j ω) be the Fourier transform of the signal x 2(t) obtained at the output of the lowpass filter. Then, x 1(j ω), x 2(j ω),and x p (j ω),are as shown in Figure S7.27(b) The Nyquist rate for the signal x 2(t) is 2×(ω2－ω1)/2=ω2－ω1.Therefore, thep 7.28. (a) The fundamental frequency of x(t) is 20π rad/sec.From Chapter 4 we know that the Fourier transform of x(t) is given byX(j ω)=2πk ∞=-∞∑a k δ(ω－20πk).This is as sketched below. The Fourier transform x c (j ω) of the signal x c (t) is also Sketched in Figure S7.28. Note thatP(j ω)=2510π⨯3(2/(510))k k δωπ∞-=-∞-⨯∑Andx p (j ω)=12π[ x c (j ω)* p(j ω)]Therefore, x p (j ω) is as shown in the Figure S7.28.Note that the impulses from adjacentReplicas of x c (j ω) add up at 200π.Now the Fourier transform x(e j Ω) of the sequence x[n] is given byx(e j Ω)= x p (j ω)|ω=ΩT. This is as shown in the Figure S7.28.Since the impulses in x(e j ω) are located at multiples of a 0.1π,the signal x[n] is146(b) The Fourier series coefficients of X[n] aT π2(12)k , k=0,±1,±2,….,±9 a k =4T π(12)10 , k=10 7.29. x p (j ω)=1T((2/))k x j k T ωπ∞=-∞-∑x(jwe ), Y(jwe ), Y p (j ω),and Y c (j ω) are as shown in Figure S7.29. 7.30. (a) Since x c (t)=δ(t),we have()c dy t dt+y c (t)= δ(t) Taking the Fourier transform we obtainj ωY(j ω)+ Y(j ω)=1 Therefore , Y c (j ω)=11j ω+, and y c (t) =e -t u(t). (b) Since y c (t) =e -tu(t) , y[n]= y c (nT)= e -nT u[n].Therefore, j ωH(e j ω)=()()j W e Y e ω=11/(1)T j e e ω---=1－e －T e －j ωTherefore,h[n]= δ[n]－e －T δ[n －1]7.31. In this problem for the sake of clarity we will use the variable Ωto denote discretefrequency. Taking the Fourier transform of both sides of the given difference equation we obtainH(j e Ω)=()()j j Y e X e ΩΩ=1112j e -Ω-Given that the sampling rate is greater than the Nyquist rate, we have147x(j eΩ)=1Tx c (j Ω/T), for －π≤Ω≤π Therefore,Y(j eΩ)=1(/)12c j x j T T e -ΩΩ-For －π≤Ω≤π.From this we getY(j ω)= Y(jw eT)= =1()12c j Tx j T e ωω--For －π/T ≤ω≤π/T. in this range, Y(j ω)= Y c (j ω).Therefore,H c (j ω)=()()c c Y j X j ωω=1/112j TT e ω--7.32. Let p[n]=[14]k n k δ∞=-∞--∑.Then from Chapter 5,p(jwe )= e -j ω24π(2/4)k k δωπ∞=-∞-∑=2π2/4(2/4)j k k k eπδωπ∞--=-∞∑Therefore, G(jw e )=()1()()2j j p e x e d πθωθπθπ--⎰=32/4(2/4)01()4j k j k k e x e πωπ--=∑jwjwFigure S7.32Clearly, in order to isolate just x(jwe ) we need to use an ideal lowpass filter with Cutoff frequency π/4 and passband gain of 4. Therefore, in the range |ω|<π, 4, |ω|<π/4H(e j ω)= 0, π/4≤|ω|≤π7.33. Let y[n]=x[n][3]k n k δ∞=-∞-∑.ThenY(e j ω)=3(2/3)1()3j k k x eωπ-=∑Note that sin(πn/3)/(πn/3) is the impulse response of an ideal lowpass filter with cutoff frequency π/3 and passband gain of 3.Therefore,we now require that y[n] when passed through this filter should yieldx[n].Therefore, the replicas of x(e j ω) contained in Y(e j ω) should not overlap with one another. This ispossible only if x(e j ω) =0 for π/3≤|ω|≤π.7.34. In order to make x(e j ω) occupy the entire region from －πto π,the signal x[n]148must be downsampled by a factor of 14/3.Since it is not possible to directly downsample by a noninteger factor, we first upsample the signal by a factor of 3. Therefore, after the upsampling we will need toreduce the sampling rate by 14/3× 3=14. Therefore, the overall system for performing the sampling rate conversion isy[n][]2nx ,n=0,±3,±6,… y[n]=p[14n] ω[n]= 0, otherwise Figure S7.34)(e xp)(ωj d e x 7.36. (a) Let us decnote the sampled signaled signal by x p (t). We have∑∞-∞=-=n pnT t nT x t x )()()(δSince the Nyquist rate for the signal x(t) is T /2π,we can reconstruct the signal from x p (t). From Section 7.2,we know that)(*)()(t h t x t x p = whereTt T t t h /)/sin()(ππ=Thereforedtt dh t x dtt dx p )(*)()(=Denoting dtt dh )( by g(t),we have∑∞-∞=-==n pnT t g nT x t g t x dtt dx )()()(*)()(Therefore,2)/sin()/cos()()(tT t T tT t dtt dh t g πππ-==(b) No.7.37. We may write p(t) asp(t)=p 1(t)+p 1(t-∆),where∑∞-∞=-=k W k t t p )/2()(1πδTherefore,)()1()(1ωωωj p e j p j ∆-+= where∑∞-∞=-=k kW w j p )()(1ωδω149Let us denote the product p(t)f(t) by g(t).Then,)()()()()()()(11t f t p t f t p t f t p t g ∆-+== This may be written as)()()(11∆-+=t bp t ap t g Therefore,)(()(1)ωωωj p be a j G j ∆-+= with )(1ωj p is specified in eq.(s7.37-1). Therefore [])()(kw be a w j G k w jk -+=∑∞-∞=∆-ωδωWe now have)()()()(1t f t p t x t y = Therefore,[])(*)(21)(1ωωπωj x j G j Y =This give us[]))((2)(1kW j x be a Wj Y wjk -+=∑∆-ωπωIn the range 0<ω<W, we may specify Y 1(j ω) as[]))(()()()(2)(1W j x be a j x b a w j Y w jk -+++=∆-ωωπωsince )()()(112ωωωj H j Y j Y =, in the range 0<ω<W we may specify Y 2(j ω) as []))(()()()(2)(2W j x be a j x b a jW j Y W j -+++=∆-ωωπωSince ),()()(3t p t x t y =in the range 0<ω<W we may specify Y 3(j ω) as []))(()1()(22)(3W j x e j x W j Y W j -++=∆-ωωπωGive that 0<W △<π,we require that )()()(32ωωωj kx j Y j Y =+ for 0<ω<W. That is[][])())(()1(2)()(2ωωπωπj kx W j x e W j x jb ja a Ww j =-++++∆-This implies that01=+++∆-∆-W j Wj jbe ja e Solving this we obtainA=1, b= -1, When W △=π/2. More generally, we also geta=sin(W △)+)tan())cos(1(∆∆+W W and )sin()cos(1∆∆+-=W W bexcept when 2/π=∆W Finally, we also get [])2/(12jb ja Wk ++=π。

特种加工chap7

第七章超声加工一、课内习题及答案1．超声加工时的进给系统有何特点？答：超声加工时的进给系统是靠重锤通过杠杆使工具轻轻压在工件上，靠轻微的压力使工具端面和磨粒与工件表面接触，工件表面去掉多少、进给多少，是悬浮式的柔性进给系统，而不是刚性的进给系统实现的，它与机械加工和电火花加工的进给系统不一样。

2．一共振频率为25kHz的磁致伸缩型超声清洗器，底面中心点的最大振幅为0.01mm，试计算该点最大速度和最大加速度。

它是重力加速度g的多少倍？如果是共振频率为50kHz的压电陶瓷型超声清洗器，底面中心点的最大振幅为0.005mm，则最大速度和加速度又是多少？答：按教材中超声振动时的最大速度υmax和最大加速度a max计算公式υmax= ωA= 2πfA= 2π×25000×0.01= 1570.8 mm/s = 1.57 m/s，a max= ω2A= 4π2×250002×0.01 = 246.74×106 mm/s2= 246740 m/s2，是地心加速度g =9.8 m/s2的25000倍。

如果共振频率增加为一倍f =50kHz,振幅减小成一半A =0.005mm,则υmax= 1.57×2/2 = 1.57 mm/s，a max= 246740×4/2 = 493480 m/s2，是地心加速度g的50000倍。

3．试判断超声加工时：（1）工具整体在作超声振动；（2）只有工具端面在作超声振动；（3）工具各个横截面都在作超声振动，单个截面同一时间的振幅并不一样；（4）工具各个横截面依次都在作“原地踏步”式的振动。

以上各点，哪种说法最确切？有无更确切的说法？答：以上说法中，（3）比较确切，超声波在工具(变幅杆)内传递时，各个横截面都在作超声振动，单个截面在同一时间的振幅不一样，有的截面振幅始终为零（如固定超声系统的驻波点），有的有时振幅最大，如工具端面的加工点。

chapter7习题答案

第七章习题答案7.1 ARM处理器有几种运行模式，处理器如何区别各种不同的运行模式？ARM处理器有7中运行模式：●用户模式（user）：ARM处理器正常的程序执行状态●快速中断模式（fiq）：处理高速中断，用于高速数据传输或通道处理●外部中断模式（irq）：用于普通的中断处理●管理模式（supervisor）：操作系统使用的保护模式，系统复位后的默认模式●中止模式（abort）：数据或指令预取中止时进入该模式●未定义模式（undefined）：处理未定义指令，用于支持硬件协处理器的软件仿真●系统模式（system）：运行特权级的操作系统任务处理器使用CPSR寄存器中的M4~M0位来指示不同的运行模式。

7.2 通用寄存器中PC、CPSR和SPSR的作用各是什么？PC：程序计数器，用于保存处理器要取的下一条指令的地址。

CPSR：当前程序状态寄存器，CPSR保存条件标志位、中断禁止位、当前处理器模式标志，以及其他一些相关的控制和状态位。

SPSR：备份程序状态寄存器，当异常发生时，SPSR用于保存CPSR的当前值，当从异常退出时，可用SPSR来恢复CPSR。

7.3 从编程的角度讲，ARM处理器的工作状态有哪两种？这两种状态之间如何转换？从编程角度讲，ARM处理器的两种工作状态为：●ARM状态（复位状态）：处理器执行32位的字对齐的ARM指令●Thumb状态：处理器执行16位的半字对齐的Thumb指令ARM指令集和Thumb指令集均有切换处理器状态的指令，并可在两种工作状态之间切换：●进入Thumb状态：当操作数寄存器的状态位（最低位）为1时，执行BX指令就可以进入Thumb状态。

如果处理器在Thumb状态时发生异常（异常处理要在ARM状态下执行），则当异常处理返回时自动切换到Thumb状态●进入ARM状态：当操作数寄存器的状态位（最低位）位0时，执行BX指令就可以进入ARM状态。

处理器进行异常处理时，把PC的值放入异常模式链接寄存器中，从异常向量地址开始执行程序，系统自动进入ARM状态7.5 哪些特征是ARM和其他RISC体系结构所共有的？ARM和其他RISC体系结构共有的三个相同特征：●Load/Store体系结构：也称为寄存器/寄存器体系结构或RR系统结构。

等级考试chap7_等级考试辅导题

等级考试辅导题一．选择题1.在VFP中，若把表单设置为子表单，应设置的属性即属性值为A．设置ShowWindow属性值为2B．设置ShowWindow属性值为0或1，设置Desktop属性值为.F.C．设置ShowWindow属性值为0或1，设置Desktop属性值为.T.D．设置ShowWindow属性值为2，设置Desktop属性值为.T.2.在运行表单时，下列有关表单事件的引发次序正确的是A．Destroy—Init—Load B. Destroy—Load—InitC. Init—Destroy—LoadD. Load—Init—Destroy3.在下列几组VFP基类中，均具有ControlSource属性的是A. ListBox、Label、OptionButtonB. ComboBox、EditBox、GridC. ComboBox、Grid、TimerD. EditBox、CheckBox、OptionButton4.下列表单的哪个属性设置为真时，表单运行时将自动居中A．AutoCenter B.AlwaysOnTop C.ShowCenter D.FormCenter5.下列控件中，在运行时一定不可见。

A．OptionButton B.Page C.OptionGroup D.Timer6.当用鼠标单击正在运行的表单中一个未被禁用的文本框对象时，文本框发生的三个事件的顺序为。

A．GotFocus—When—Click B. When—GotFocus—ClickC. Click—GotFocus—WhenD. Click—When—GotFocus7．如果ComboBox对象的RowSourceType设置为6，以一个表的字段为行数据源，则_____ A）在数据环境中添加此表，运行时用户从下拉列表中选择数据，将移动此表的记录指针B）在数据环境中添加此表，运行时可使用AddItem方法，对列表增加新项C）在数据环境中不必添加此表，ComboBox会找到表文件D）下拉列表不能使用多列方式8．如果ListBox对象的RowSourceType设置为3，则在RowSource属性中写入的SELECT语句，通常包含_____子句A） GROUP BY B）ORDER BY C）INTO TABLE D）INTO CURSOR9．如果要在列表框中一次选择多个项（行），必须设置_____属性为.t.A）MultiSelect B）ListItem C）Controlsv D）Enabled10．确定列表框内的某个条目是否被选定以及确定第几列数据和Value属性进行绑定，应使用的属性是_______A）selected ColumnCount B）selected BoundColumnC）list ColumnCount D）list BoundColumn11.如果表单中有一命令按钮组，命令按纽组包含若干命令按纽，现设定了命令按纽组的Click事件代码，但没有设定命令按纽的Click事件代码。

chap7中级宏观经济学答案华中科技大学

Microeconomics, 4e (Perloff)Chapter 7 Costs7.1 Measuring Costs1) Economic costs of an input includeA) only implicit costs.B) only explicit costs.C) both implicit and explicit costs.D) whatever management wishes to report to the shareholders.Answer: CTopic: Measuring Costs2) The cost of waiting two months for health care to address a debilitating problem in Canada is most accurately described asA) an explicit cost.B) an accounting cost.C) no real cost.D) an opportunity cost.Answer: DTopic: Measuring Costs3) Sarah earns $40,000 per year working for a large corporation. She is thinking of quitting this job to work full time in her own business. She will invest her savings of $50,000 (which currently has an annual 10% rate of return) into the business. Her annual opportunity cost of this new business isA) $0.B) $40,000.C) $45,000.D) $90,000.Answer: CTopic: Measuring Costs4) The Nifty Gum Co. has purchased a large parcel of land for $1 million. The company recently discovered that the land is contaminated and is worthless to all possible buyers. The opportunity cost of the land isA) $0.B) $1 million.C) some amount greater than $0 but less than $1 million.D) equal to the cost of the factory that was planned to be built there.Answer: ATopic: Measuring Costs5) Johnny has worked as a CPA for five years and wants to open his own public accounting practice. The cost of his college degree in accounting representsA) the opportunity cost of this endeavor.B) a sunk cost.C) an expense.D) a variable cost.Answer: BTopic: Measuring Costs6) Economists proclaim that competitive firms make zero economic profit in the long run. This shows howA) detached economists are from the real world.B) unrealistic economic theory is.C) firms cover all their cost, both monetary and non-monetary.D) firms cover only monetary cost when economic profits are zero.Answer: CTopic: Measuring Costs7) If a firm buys a building so as to have office space for its workers, the monthly opportunity cost of the building is best measured asA) the monthly mortgage payment the firm must pay.B) the price the firm paid divided by twelve.C) zero.D) the rent the firm could earn if it rented the building to another firm.Answer: DTopic: Measuring CostsFor the following, please answer "True" or "False" and explain why.8) When buying a piece of equipment, it is always best for the firm to pay cash instead of borrowing the funds since this renders the equipment less costly.Answer: False. It depends. The opportunity cost of the capital when paying cash is the interest the firm receives on its cash reserves. This is an implicit cost. The opportunity cost of the capital when the funds are borrowed is the interest the firm must pay to the lender. This is an explicit cost. If the rate the firm receives on its cash reserves exceeds the rate at which it borrows, the firm is better off borrowing the funds to buy the equipment.Topic: Measuring Costs9) Four years after graduating from college you must decide if you want to go on as an accountant (your college major) or if you want to make a career change and become a singer. The cost of your education will matter for your decision.Answer: False. At this point the cost of your education represents a sunk cost and therefore should not figure into your decision. You incur it no matter what decision you make.Topic: Measuring Costs10) An accountant may amortize the expense of a durable good by dividing the total amount spent on the good by the number of years the good is expected to last. An economist may amortize the expense of a durable and never fully account for the total expense.Answer: True. The accountant uses a set of predetermined rules to amortize the total expense of the good. The economist amortizes based on the opportunity cost of the good, which may never sum to the total expense of the good.Topic: Measuring Costs11) Your company makes copper pipes. Over the years, you have collected a large inventory of raw copper. The production process involves melting the copper and shaping it into pipes. You also have a large stockpile of pennies. Suppose the price of copper rises so much that the copper in the penny becomes worth more than one cent. Should you melt down your pennies?Answer: This problem appeared as a puzzle in the Journal of Economic Perspectives (Winter, 1988). It is true (in this problem) that the pennies when melted currently have a value greater than one cent. Yet, the price of copper can fluctuate. If the price of copper stays high, it does not matter if you melt pennies or not. However, if the price of copper falls so that the value of the copper in the penny falls below one cent, your unmelted pennies are still worth one cent. Your melted pennies would be worth less than one cent. Thus, as long as you have some other source of copper, you are better off melting that copper and not the pennies.Topic: Measuring Costs12) You have two career options. You can work for someone else for $50,000 a year, or, you can run your own business, with an annual revenue of $100,000, and explicit costs of $40,000 annually. Explain which career option a profit-maximizer would select and why.Answer: In the absence of other implicit costs a profit-maximizer will run their own business. The business owner will receive $100,000 - $40,000 = $60,000. The opportunity cost is only $50,000.Topic: Measuring Costs7.2 Short-Run Costs1) A firm's marginal cost can always be thought of as the change in total cost ifA) the firm produces one more unit of output.B) the firm buys one more unit of capital.C) the firm's average cost increases by $1.D) the firm moves to the next highest isoquant.Answer: ATopic: Short-run Costs2) Fixed costs areA) a production expense that does not vary with output.B) a production expense that changes with the quantity of output produced.C) equal to total cost divided by the units of output produced.D) the amount by which a firm's cost changes if the firm produces one more unit of output.Answer: ATopic: Short-run Costs3) Variable costs areA) a production expense that does not vary with output.B) a production expense that changes with the quantity of output produced.C) equal to total cost divided by the units of output produced.D) the amount by which a firm's cost changes if the firm produces one more unit of output.Answer: BTopic: Short-run Costs4) Which of the following statements is NOT true?A) AC = AFC + AVCB) C = F + VCC) AVC = wage/MP LD) AFC = AC - AVCAnswer: CTopic: Short-run Costs5) Joey's Lawncutting Service rents office space from Joey's dad for $300 per month. Joey's dad is thinking of increasing the rent to $400 per month. As a result Joey's marginal cost of cutting grass willA) increase by $100 divided by the amount of grass cut.B) increase by $100.C) decrease by $100.D) not change.Answer: DTopic: Short-run Costs6) Suppose a firm can only vary the quantity of labor hired in the short run. An increase in the cost of capital willA) increase the firm's marginal cost.B) decrease the firm's marginal cost.C) have no effect on the firm's marginal cost.D) More information is needed to answer the question.Answer: CTopic: Short-run Costs7) Suppose the total cost of producing T-shirts can be represented as TC = 50 + 2q. The marginal cost of the 5th T-shirt isA) 2.B) 10.C) 12.D) 60.Answer: ATopic: Short-run Costs8) Suppose the total cost of producing T-shirts can be represented as TC = 50 + 2q. The average cost of the 5th T-shirt isA) 2.B) 12.C) 52.D) 60.Answer: BTopic: Short-run Costs9) Suppose the total cost of producing T-shirts can be represented as TC = 50 + 2q. Which of the following statements is TRUE at all levels of production?A) MC = AVCB) MC = ACC) MC > AFCD) All of the above.Answer: ATopic: Short-run Costs10) Suppose the short-run production function is q = 10 * L. If the wage rate is $10 per unit of labor, then AVC equalsA) q.B) q/10.C) 10/q.D) 1.Answer: DTopic: Short-run Costs11) Suppose the short-run production function is q = 10 * L. If the wage rate is $10 per unit of labor, then MC equalsA) q.B) q/10.C) 10/q.D) 1.Answer: DTopic: Short-run Costs12) If average cost is decreasingA) Marginal cost equals average cost.B) Marginal cost exceeds average cost.C) Marginal cost is less average cost.D) Not enough informationAnswer: CTopic: Short-run Costs13) If average cost is positiveA) Marginal cost equals average cost.B) Marginal cost exceeds average cost.C) Marginal cost is less average cost.D) Not enough informationAnswer: DTopic: Short-run Costs14) Suppose the short-run production function is q = L0.5. If the marginal cost of producing the tenth unit is $5, what is the wage per unit of labor?A) $1B) $0.5C) $0.25D) It cannot be determined without more information.Answer: CTopic: Short-run Costs15) Suppose the short-run production function is q = 10 * L. If the wage rate is $10 per unit of labor, then AFC equalsA) 0.B) 1.C) 10/q.D) It cannot be determined from the information provided.Answer: DTopic: Short-run Costs16) When a firm produces one unit, the variable cost is $3. When the firm produces two units, the variable cost is $6. What is the marginal cost associated with two units of production?A) $2B) $0.5C) $6D) $3Answer: DTopic: Short-run Costs17) In the short run, the point at which diminishing marginal returns to labor begin is the point at which the marginal cost curveA) peaks.B) bottoms out.C) is upward sloping.D) is downward sloping.Answer: BTopic: Short-run Costs18) If the marginal cost of producing a good is increasing as a firm produces more of the good, then which of the following must be TRUE?A) AFC is rising.B) AVC is rising.C) MC > AVC.D) MPL is falling.Answer: DTopic: Short-run Costs19) If the average cost of producing a good is increasing as a firm produces more of the good, then which of the following must be TRUE?A) AFC is falling.B) AVC is rising.C) MC > AVC.D) All of the above.Answer: DTopic: Short-run Costs20) If a particular production process is subject to diminishing marginal returns to labor at every level of output, then at every level of outputA) AC is upward sloping.B) MC exceeds AVC.C) AFC is constant.D) All of the above.Answer: BTopic: Short-run Costs21) Marginal Cost is equal toA) the increase in total cost from increasing the amount of labor by one unit.B) the increase in average cost from increasing the amount of labor by one unit.C) Both A and B.D) Neither A nor B.Answer: CTopic: Short-run Costs22) Suppose each worker must use only one shovel to dig a trench, and shovels are useless by themselves. In the short run, an increase in the price of shovels will result inA) fewer shovels being purchased.B) more workers being hired.C) a decrease in the firm's output.D) no change in the firm's output.Answer: DTopic: Short-run Costs23) Which of the following will cause the marginal cost curve of making cigarettes to shift?A) A $5 million penalty charged to each cigarette maker.B) A $1 per pack tax on cigarettes.C) A $1 million advertising campaign by the American Cancer Society.D) All of the above.Answer: BTopic: Short-run Costs24) Which of the following will cause the average cost curve of making cigarettes to shift?A) A $5 million penalty charged to each cigarette maker.B) A $1 per pack tax on cigarettes.C) A $1 an hour wage increase paid to all cigarette production workers.D) All of the above.Answer: DTopic: Short-run Costs25) Which of the following will cause the average fixed cost curve of making cigarettes to shift?A) A $5 million penalty charged to each cigarette maker.B) A $1 per pack tax on cigarettes.C) A $3 per hour wage increase.D) An increase in the demand for cigarettes.Answer: ATopic: Short-run Costs26) A specific tax of $1 per unit of output will affect a firm'sA) average total cost, average variable cost, average fixed cost, and marginal cost.B) average total cost, average variable cost, and average fixed cost.C) average total cost, average variable cost, and marginal cost.D) marginal cost only.Answer: CTopic: Short-run CostsFor the following, please answer "True" or "False" and explain why.27) The "Law of Diminishing Marginal Returns" could also be termed the "Law of Increasing Marginal Costs."Answer: True. Since MC = w/MP L in the short run, the fact that MPL eventually declines means that MC must eventually increase.Topic: Short-run Costs28) The marginal cost curve intersects the average fixed cost curve at its minimum.Answer: False. Marginal cost intersects average variable cost (and average cost) at its minimum.Topic: Short-run Costs29) A consumer purchases a book by driving across town to a bookstore, standing in line for five minutes to pay the cashier, and then pays $5. The same book is purchased by another consumer who spends 2 minutes placing the order over the internet for $10. The book necessarily cost the first consumer less.Answer: False. The opportunity cost of driving across town and standing in line may have raised the total cost of the book to the first consumer to more than $10.Topic: Short-run Costs30) A firm's production function for pretzels is shown in the above figure. If the firm's fixed cost equals $100 per time period and the wage rate equals $1 per unit of labor per time period, calculate the firm's MC, AVC, and AC schedules. Do these cost functions follow the general rules concerning the relationships between MC, AVC and AC?Answer:❑✌☞ ✌✞✌ MC > AVC, AVC is rising.MC < AC, AC is falling.Topic: Short-run Costs31) Explain why the marginal cost curve intersects a U-shaped average cost curve at its minimum point. Answer: At low quantities, the average cost curve declines as the quantity increases. The marginal cost is below the average cost. The marginal cost represents the cost of an additional unit of production. Thus, as the marginal cost curve declines, this pulls the average cost down from its previous level. Then, the marginal cost curve will begin to rise. However, the marginal cost is still below the average cost, which will continue to lower the average cost. When the two costs are equal the marginal cost will leave the average cost unchanged. Then, the marginal cost will be above the average cost so it will start to pull up the average cost. Thus, the marginal cost curve will intersect the average cost curve at its minimum point.Topic: Short-run Costs7.3 Long-Run Costs1) In the long run, fixed costs areA) sunk.B) avoidable.C) larger than in the short run.D) not included in production decisions.Answer: BTopic: Long-run Costs2) The slope of the isocost line tells the firm how muchA) capital must be reduced to keep total cost constant when hiring one more unit of labor.B) capital must be increased to keep total cost constant when hiring one more unit of labor.C) more expensive a unit of capital costs relative a unit of labor.D) the isocost curve will shift outward if the firm wishes to produce more.Answer: ATopic: Long-run Costs3) Which of the following does NOT represent a possible shape of the long-run average cost curve?A) downward-slopingB) upward-slopingC) U-shapedD) verticalAnswer: DTopic: Long-run Costs4) The slope of the isoquant tells the firm how muchA) output increases when labor increases by one unit.B) output increases when capital and labor are doubled.C) capital must decrease to keep output constant when labor increases by one unit.D) a unit of capital costs relative to the cost of labor.Answer: CTopic: Long-run Costs5) If an isocost line crosses the isoquant twice, a cost minimizing firm willA) use a different isocost line to select the bundle of inputs.B) use the input bundle associated with the intersection on the higher point of the isoquant.C) use the input bundle associated with the intersection on the lower point of the isoquant.D) Both B and C.Answer: ATopic: Long-run Costs6) When the isocost line is tangent to the isoquant, thenA) MRTS = w/r.B) the firm is producing that level of output at minimum cost.C) the last dollar spent on capital yields as much extra output as the last dollar spent on labor.D) All of the above.Answer: DTopic: Long-run Costs7) A firm can minimize cost byA) picking the bundle of inputs where the lowest isocost line touches the isoquant.B) picking the bundle of inputs where the isoquant is tangent to the isocost line.C) picking the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input.D) All of the above.Answer: DTopic: Long-run Costs8) When the isocost line is tangent to the isoquant, thenA) MPL = MPK.B) the firm is producing that level of output at minimum cost.C) the firm has achieved the right economies of scale.D) All of the above.Answer: BTopic: Long-run Costs9) If the wage in increases the isocost line willA) stay the same.B) shift outward in parallel fashion.C) rotate inward around the point where only capital is employed in production.D) shift inward in parallel fashion.Answer: CTopic: Long-run Costs10) If the isoquants are straight lines or L-shaped, then a cost-minimizing firm willA) not be able to minimize costs.B) find the lowest isocost line touching the relevant isoquant.C) find the highest isocost line touching the relevant isoquant.D) choose not to produce any output.Answer: BTopic: Long-run Costs11) If the marginal rate of technical substitution for a cost minimizing firm is 10, and the wage rate for labor is $5, what is the rental rate for capital in dollars?A) .5B) 1C) 2D) 10Answer: ATopic: Long-run Costs12) Suppose MPL = 0.5 * (q/L) and MPK = 0.5 * (q/K). In the long run, the firm will hire equal amounts of capital and laborA) all of the time.B) only when w = r.C) only when w = 0.5 * r.D) at no point in time.Answer: BTopic: Long-run Costs13) Suppose that each worker must use only one shovel to dig a trench, and shovels are useless by themselves. In the long run, an increase in the price of shovels will result inA) fewer shovels being purchased to produce the same number of trenches.B) more workers being hired to produce the same number of trenches.C) the firm wishing to produce more trenches.D) no change in the firm's input mix.Answer: DTopic: Long-run Costs14) Suppose that each worker must use only one shovel to dig a trench, and shovels are useless by themselves. In the long run, the firm will experienceA) increasing returns to scale.B) constant returns to scale.C) decreasing returns to scale.D) The returns to scale cannot be determined from the information provided.Answer: BTopic: Long-run Costs15) Suppose that each worker must use only one shovel to dig a trench, and shovels are useless by themselves. In the long run, the firm's cost function isA) TC = (w/r) * q.B) TC = (w + r)/q.C) TC = (w + r).D) TC = (w + r) * q.Answer: DTopic: Long-run Costs16) At the XYZ Co., a unit of capital costs 3 times as much as a unit of labor. If the isoquants are convex, and the firm does not change its input mix in the long run, we can conclude thatA) MPK = 3 * MP L.B) the firm will not hire any capital.C) the firm will hire 3 times as much labor as capital.D) the firm will hire 3 times as much capital as labor.Answer: ATopic: Long-run Costs17) The production of cigarettes is highly automated; however, a worker is required to monitor each machine. Machines and workers do not interact with one another. Given this information, there are most likelyA) economies of scale.B) economies of scope.C) constant returns to scale.D) increasing returns to scale.Answer: CTopic: Long-run Costs18) Suppose that capital and labor must be kept in a fixed proportion to produce a particular good. For example, digging a trench requires one worker who has one shovel. What does this imply about returns to scale?A) There are constant returns to scale.B) There are increasing returns to scale.C) There are decreasing returns to scale.D) Nothing.Answer: ATopic: Long-run Costs19) A change in relative factor prices will always result inA) a change in the slope of the isoquants.B) a tangency between the new isocost line and a new isoquant.C) a rotation of the isocost lines.D) All of the above.Answer: CTopic: Long-run Costs20) Assuming that w and r are both positive, if the long-run expansion path is horizontal, thenA) MP K = 0.B) MRTS is a function of capital only.C) w = r.D) All of the above.Answer: BTopic: Long-run Costs21) The above figure shows the long-run expansion path. The long-run average cost curve will beA) horizontal.B) downward sloping.C) upward sloping.D) vertical.Answer: BTopic: Long-run Costs22) The long run average cost curve may initially slope downward due toA) decreasing average fixed costs.B) increasing marginal returns.C) economies of scale.D) All of the above.Answer: CTopic: Long-run Costs23) If a production function is represented as q = LαKβ, the long-run average cost curve will be horizontal as long asA) a + b = 0.B) a + b = 1.C) q > 0.D) L = K.Answer: BTopic: Long-run Costs24) If there are diseconomies of scale within a given range of output, which of following is(are) TRUE?A) The short-run average cost curve must be upward sloping within that range of output.B) The long-run average cost curve must be upward sloping within that range of output.C) Long-run average cost must equal short-run average cost.D) All of the above.Answer: BTopic: Long-run Costs25) The total cost of producing one unit is $50. The total cost of producing two units is $75. At a production level of two units, the cost function exhibitsA) economies of scale.B) rising average costs.C) increasing marginal costs.D) constant returns to scale.Answer: ATopic: Long-run CostsFor the following, please answer "True" or "False" and explain why.26) If increasing returns to scale are present, the long-run average cost increases as more output is produced. Answer: False. Increasing returns to scale imply that with a doubling of inputs, output more than doubles. Since average cost is the ratio of total cost divided by output, this increase in inputs will cause the numerator to be just double the old value while the new denominator is more than double the old value. As a result, long-run average cost falls as more output is produced.Topic: Long-run Costs27) Economies of scale and Increasing Returns to Scale are the same thing looked at from either the production or cost perspective.Answer: False. Increasing returns to scale imply economies of scale but the reverse is not true. A firm can experience economies of scale for other reasons (without increasing returns to scale)Topic: Long-run Costs28) Explain the difference between fixed costs in the short run and fixed costs in the long run.Answer: In the short run fixed costs are sunk; in the long run, fixed costs are avoidable.Topic: Long-run Costs29) What are the functions for MC and AC if TC = 100q + 100q2? Are the returns to scale increasing, decreasing, or constant?Answer: MC = 100 + 200qAC = 100 + 100qSince AC increases with an increase in output, there are decreasing returns to scale.Topic: Long-run Costs30) Explain how a firm can have constant returns to scale in production and economies of scale in cost. Answer: A firm can have constant returns to scale in production at every output level. If the firm doubled all inputs the output would double. However, the firm may have a decreasing average cost. As more inputs areused and output increases, the average cost declines, which is known as economies of scale.Topic: Long-run Costs31) Explain why the long-run total cost curve, not the short-run total cost curve, shows the lowest cost of producing any level of output. Is there an exception?Answer: In the long run, all costs are variable so the firm can select the least-cost mix of all inputs to produce any given quantity. The exception would be at minimum long-run cost where min. LR and min. SR costs are equal.Topic: Long-run Costs32) A local non-profit group prints a weekly newsletter. Professional typists earn $10 per hour and can type 2 pages per hour. Unpaid volunteers can type only 1 page per hour. Measuring hours of professional typist services on the vertical axis and hours of unpaid volunteer typist services on the horizontal axis, draw the relevant isoquant and isocost curves if the newsletter is 10 pages long. What input mix is chosen by the non-profit group if they wish to minimize the cost of the newsletter? If the group will reimburse volunteers for expenses (lunch, driving), how much must the reimbursement be for your answer to change? Answer:See the above figure. The isoquant is a straight line with a slope of 1/2. The group can use either 5 pros, 10 volunteers, or some combination of the two. The isocost curves are horizontal since volunteers are free. As a result, the lowest isocost curve is achieved by hiring all volunteers. If the group reimbursed volunteers for expenses (lunch, driving, etc.) then the group will still hire all volunteers as long as they do not cost more than $5 per hour.Topic: Long-run Costs33) A firm pays $5 for each unit of capital. Labor costs $5 per hour for the first 10 hours and $10 per hour for every hour thereafter. Draw the isocost curves for total costs of $50 and $100.Answer:See the above figure.Topic: Long-run Costs34) To dig a trench, each worker needs a shovel. Workers can use only one shovel at a time. Workers without shovels do nothing, and shovels cannot operate on their own. Graphically determine the number of shovels and workers used by a firm to dig 2 trenches when:(a) w = 10 and r = 10(b) w = 10 and r = 5Answer:See the above figure. Because the production process requires fixed proportions of K and L, the firm cannot change input mix when the relative factor costs change.Topic: Long-run Costs35) Suppose the production function is q = 12 L0.25K0.75. Determine the long-run capital-to-labor ratio (K/L) if the cost a unit of capital (r) is three times the cost of a unit of labor (w).Answer: The firm minimizes costs by setting MRTS = w/r. MRTS = MP L/MP K = K/3L = 1/3 = w/r. This firm will set K/L equal to one.Topic: Long-run Costs36) "If the wage rate paid to one form of labor is twice the cost of another form of labor, the first type of labor must be twice as productive." Comment.Answer: This is true. Firms minimize cost by setting the ratio of marginal productivity per unit cost equally across all inputs. If one form of labor is twice as expensive as another, the firm will want the MP of the first type of labor to be twice that of the second.Topic: Long-run Costs。

Principles of Corporate Finance 英文第十版习题解答Chap007

CHAPTER 7Introduction to Risk and ReturnAnswers to Problem Sets1. Expected payoff is $100 and expected return is zero. Variance is 20,000 (%squared) and standard deviation is 141%.2. a. Standard deviation = 19.3%b. Average real return = -2.2%3. Ms. Sauros had a slightly higher average return (14.6% vs. 14.4% for the market).However, the fund also had a higher standard deviation (13.6% vs. 9.4% for themarket).4. a. Falseb. Truec. Falsed. Falsee. Falsef. Trueg. Trueh. False5. d6.7. a. 26% b. zero c. .75d. L ess than 1.0 (the portfolio’s risk is the same as the market, but some ofthis risk is unique risk).8. 1.3 (Diversification does not affect market risk.) 9. A, 1.0; B, 2.0; C, 1.5; D, 0; E, 21.0 10.Recall from Chapter 4 that:(1 + r nominal ) = (1 + r real ) ⨯ (1 + inflation rate)Therefore:r real = [(1 + r nominal )/(1 + inflation rate)] – 1a.The real return on the stock market in each year was: 1929: -14.7% 1930: -23.7% 1931: -38.0% 1932: 0.5% 1933:56.5%b. From the results for Part (a), the average real return was: -3.89%c.The risk premium for each year was: 1929: -19.3% 1930: -30.7% 1931: -45.0% 1932: -10.9% 1933:57.0%d. From the results for Part (c), the average risk premium was: –9.78%e.The standard deviation (σ) of the risk premium is calculated as follows:[22220.0978))0.450(0978))0 0.307(0.0978))0.193(151σ---+---+---⨯⎪⎪⎭⎫ ⎝⎛-=(.((0.1557390.0978))(0.5700.0978))0.109(22=--+---+]((39.46%0.3946370.155739σ===11.a.A long-term United States government bond is always absolutely safe in terms of the dollars received. However, the price of the bond fluctuates as interest rates change and the rate at which coupon payments received can be invested also changes as interest rates change. And, of course, the payments are all in nominal dollars, so inflation risk must also be considered.b.It is true that stocks offer higher long-run rates of return than do bonds, but it is also true that stocks have a higher standard deviation of return. So, which investment is preferable depends on the amount of risk one iswilling to tolerate. This is a complicated issue and depends on numerous factors, one of which is the investment time horizon. If the investor has a short time horizon, then stocks are generally not preferred.c. Unfortunately, 10 years is not generally considered a sufficient amount of time for estimating average rates of return. Thus, using a 10-year average is likely to be misleading.12.The risk to Hippique shareholders depends on the market risk, or beta, of the investment in the black stallion. The information given in the problem suggests that the horse has very high unique risk, but we have no information regarding the horse’s market risk. So, the best estimate is that t his horse has a market risk about equal to that of other racehorses, and thus this investment is not a particularly risky one for Hippique shareholders.13.In the context of a well-diversified portfolio, the only risk characteristic of a single security that matters is the security’s contribution to the overall portfolio risk. This contribution is measured by beta. Lonesome Gulch is the safer investment for a diversified investor because its beta (+0.10) is lower than the beta ofAmalgamated Copper (+0.66). For a diversified investor, the standard deviations are irrelevant. 14.x I = 0.60 σI = 0.10 x J = 0.40 σJ = 0.20a.1ρIJ =)]σσρx 2(x σx σx [σJ I IJ J I 2J 2J 2I 2I 2p ++=b.c. 15.a.Refer to Figure 7.13 in the text. With 100 securities, the box is 100 by 100. The variance terms are the diagonal terms, and thus there are 100variance terms. The rest are the covariance terms. Because the box has (100 times 100) terms altogether, the number of covariance terms is:1002 – 100 = 9,900Half of these terms (i.e., 4,950) are different.b.Once again, it is easiest to think of this in terms of Figure 7.13. With 50 stocks, all with the same standard deviation (0.30), the same weight in the portfolio (0.02), and all pairs having the same correlation coefficient (0.40), the portfolio variance is:σ2 = 50(0.02)2(0.30)2 + [(50)2 – 50](0.02)2(0.40)(0.30)2 =0.03708 σ = 0.193 = 19.3%c.For a fully diversified portfolio, portfolio variance equals the average covariance:σ2 = (0.30)(0.30)(0.40) = 0.036 σ = 0.190 = 19.0%16.a.Refer to Figure 7.13 in the text. For each different portfolio, the relative weight of each share is [one divided by the number of shares (n) in the portfolio], the standard deviation of each share is 0.40, and the correlation between pairs is 0.30. Thus, for each portfolio, the diagonal terms are the same, and the off-diagonal terms are the same. There are n diagonal terms and (n 2 – n) off-diagonal terms. In general, we have:Variance = n(1/n)2(0.4)2 + (n 2 – n)(1/n)2(0.3)(0.4)(0.4)0.0196]0)(0.20)40)(1)(0.12(0.60)(0.(0.20)0.40)((0.10)(0.60)[2222=++=0ρij=0.0148])0.10)(0.2040)(0.50)(2(0.60)(0.(0.20)0.40)((0.10)(0.60)[2222=++=0.50ρIJ =0.0100]0)(0.20)40)(0)(0.12(0.60)(0.(0.20)0.40)((0.10)(0.60)[2222=++=)]σσρx 2(x σx σx [σJ I IJ J I 2J 2J 2I 2I 2p ++=)]σσρx 2(x σx σx [σJ I IJ J I 2J 2J 2I 2I 2p ++=For one share: Variance = 1(1)2(0.4)2 + 0 = 0.160000For two shares:Variance = 2(0.5)2(0.4)2 + 2(0.5)2(0.3)(0.4)(0.4) = 0.104000 The results are summarized in the second and third columns of thetable below.b. (Graphs are on the next page.) The underlying market risk that can not bediversified away is the second term in the formula for variance above:Underlying market risk = (n2 - n)(1/n)2(0.3)(0.4)(0.4)As n increases, [(n2 - n)(1/n)2] = [(n-1)/n] becomes close to 1, so that theunderlying market risk is: [(0.3)(0.4)(0.4)] = 0.048c. This is the same as Part (a), except that all of the off-diagonal terms arenow equal to zero. The results are summarized in the fourth and fifthcolumns of the table below.(Part a) (Part a) (Part c) (Part c)No. of Standard StandardShares Variance Deviation Variance Deviation1 .160000 .400 .160000 .4002 .104000 .322 .080000 .2833 .085333 .292 .053333 .2314 .076000 .276 .040000 .2005 .070400 .265 .032000 .1796 .066667 .258 .026667 .1637 .064000 .253 .022857 .1518 .062000 .249 .020000 .1419 .060444 .246 .017778 .13310 .059200 .243 .016000 .126Graphs for Part (a):Graphs for Part (c):17. The table below uses the format of Figure 7.13 in the text in order to calculate theportfolio variance. The portfolio variance is the sum of all the entries in the matrix. Portfolio variance equals: 0.03664355518.“Safest” means lowest risk; in a portfolio context, thi s means lowest variance of return. Half of the portfolio is invested in Canadian Pacific stock, and half of the portfolio must be invested in one of the other securities listed. Thus, we calculate the portfolio variance for seven different portfolios to see which is the lowest. The safest attainable portfolio is comprised of Canadian Pacific and Nestle.19.⨯ change inchange is +1.25%.b. “Safest” implies lowest risk. Assuming the well-diversified portfolio isinvested in typical securities, the portfolio beta is approximately one. Thelargest reduction in beta is achieved by investing the $20,000 in a stockwith a negative beta. Answer (iii) is correct.20. Expected portfolio return = x A E[R A ] + x B E[R B ] = 12% = 0.12Let x B = (1 – x A )x A (0.10) + (1 – x A) (0.15) = 0.12 ⇒ x A = 0.60 and x B = 1 – x A = 0.40Portfolio variance = x A2σA2 + x B2σB2 +2(x A x B ρAB σA σB )= (0.60 2 ) (20 2 ) + (0.40 2 ) (40 2 ) + 2(0.60)(0.40)(0.50)(20)(40) = 592 Standard deviation = 24.33%592σ==21. a. In general:Portfolio variance = σP2 = x12σ12 + x22σ22 + 2x1x2ρ12σ1σ2Thus:σP2 = (0.52)(30.92)+(0.52)(17.22)+2(0.5)(0.5)(0.31)(30.9)(17.2)σP2 = 395.942Standard deviation = σP = 19.88%b. We can think of this in terms of Figure 7.13 in the text, with threesecurities. One of these securities, T-bills, has zero risk and, hence, zerostandard deviation. Thus:σP2 = (1/3)2(30.92)+(1/3)2(17.22)+2(1/3)(1/3)(0.31)(30.9)(17.2)σP2 = 175.574Standard deviation = σP = 13.25%Another way to think of this portfolio is that it is comprised of one-thirdT-Bills and two-thirds a portfolio which is half Dell and half McDonalds.Because the risk of T-bills is zero, the portfolio standard deviation is two-thirds of the standard deviation computed in Part (a) above:Standard deviation = (2/3)(19.88) = 13.25%c. With 50% margin, the investor invests twice as much money in theportfolio as he had to begin with. Thus, the risk is twice that found in Part(a) when the investor is investing only his own money:Standard deviation = 2 ⨯ 19.88% = 39.76%d. With 100 stocks, the portfolio is well diversified, and hence the portfoliostandard deviation depends almost entirely on the average covariance ofthe securities in the portfolio (measured by beta) and on the standarddeviation of the market portfolio. Thus, for a portfolio made up of 100stocks, each with beta = 1.41, the portfolio standard deviation isapproximately: 1.41 ⨯ 15% = 21.15%For stocks like McDonalds, it is: 0.77 ⨯ 15% = 11.55%22. For a two-security portfolio, the formula for portfolio risk is:Portfolio variance = x12σ12 + x22σ22 + 2x1x2ρρ12σ1σ2If security one is Treasury bills and security two is the market portfolio, then σ1 is zero, σ2 is 20%. Therefore:Portfolio variance = x22σ22 = x22(0.20)2Standard deviation = 0.20x2Portfolio expected return = x1(0.06) + x2(0.06 + 0.85)Portfolio expected return = 0.06x1 + 0.145x2Portfolio X1X2ExpectedReturnStandardDeviation1 1.0 0.0 0.060 0.0002 0.8 0.2 0.077 0.0403 0.6 0.4 0.094 0.0804 0.4 0.6 0.111 0.1205 0.2 0.8 0.128 0.1606 0.0 1.0 0.145 0.20023. The matrix below displays the variance for each of the eight stocks along thediagonal and each of the covariances in the off-diagonal cells:The covariance of BP with the market portfolio (σBP, Market) is the mean of the eight respective covariances between BP and each of the eight stocks in the portfolio. (The covariance of BP with itself is the variance of BP.) Therefore, σBP, Market is equal to the average of the eight covariances in the first row or, equivalently, the average of the eight covariances in the first column. Beta for BP is equal to the covariance divided by the market variance, which we calculated at 0.03664 in problem 17. The covariances and betas are displayed in the table below:。

chap7 矿物的形态

(2) 放射状集合体(radiated aggregate)：
由长柱状、针状、片状或板状的许多单体围绕某一中心成放射状排列而成。如红柱石。
(3) 晶簇(druse)：
指在岩石的空洞或裂隙中、丛生于同一基底、另一端朝向自由空间发育而具完好晶形的簇状单晶体群。如石英晶簇、方解石晶簇、辉锑矿晶簇等。几何淘汰率：晶簇中，晶习具一向延长的单晶体往往最终发育成与基底近于垂直的、大致平行排列的梳状晶簇(comb)。
三向等长型：
粒状或等轴状。如：黄铁矿、石榴子石和橄榄石等。过渡类型：短柱状、板柱状、板条状和厚板状等。
晶体习性
板状／片状两向延展
柱状／棒状／针状
一向延长
三向等长粒状
晶体形态发育的内因
1）化学成分简单，结构对称程度高的晶体，一般呈等轴状。如自然金(Au)和石盐(NaCl)等。 2）实际晶体往往沿其内部结构中化学键强的方向发育。如金红石、辉石和角闪石等链状结构的矿物呈现柱状、针状晶习，而云母、石墨等层状结构的矿物则呈片状、鳞片状习性。 3）晶体上发育的晶面都是对应于晶格中面网密度较大的面网。一般地，面网密度较大的晶面具有较小的比表面能，晶体的晶面发育总是趋向于使总的表面能最小。
纤维状集合体（直闪石石棉）
放射状集合体（红柱石）水晶晶簇
晶簇
晶洞中的石英晶簇
（2）矿物隐晶集合体和胶体的形态
1、隐晶集合体(cryptocrystalline aggregate)：
只有在显微镜的高倍镜下才可分辨矿物单体的集合体称为隐晶集合体。
2、胶态集合体(colloidal aggregate)：
本章思考题
1. 实际晶体和理想晶体在外形上有何不同？ 2. 结晶习性的含义？ 3. 晶面花纹与双晶纹相同吗？晶面条纹在矿物对称性研究中的意义？ 4. 为什么鲕状集合体不能称为粒状集合体? 5. 如何判断集合体中的单体形态? 6. 钟乳石是单体还是集合体?为什么? 7. 几种特殊的胶体/隐晶集合体形态的形成机理？

经济学原理曼昆课后答案chapter7.doc

Problems and Applications1.If an early freeze in California sours the lemon crop, the supply curve for lemons shiftsto the left, as shown in Figure 7-5.The result is a rise in the price of lemons and adecline in consumer surplus from A + B + C to just A. So consumer surplus declines by the amount B + C.Figure 7-5In the market for lemonade, the higher cost of lemons reduces the supply of lemonade,as shown in Figure 7-6.The result is a rise in the price of lemonade and a decline inconsumer surplus from D + E + F to just D, a loss of E + F. Note that an event that affectsconsumer surplus in one market often has effects on consumer surplus in other markets.Figure 7-62. A rise in the demand for French bread leads to an increase in producer surplus in themarket for French bread, as shown in Figure 7-7.The shift of the demand curve leads to an increased price, which increases producer surplus from area A to area A + B + C.Figure 7-7The increased quantity of French bread being sold increases the demand for flour, asshown in Figure 7-8.As a result, the price of flour rises, increasing producer surplusfrom area D to D + E + F. Note that an event that affects producer surplus in onemarket leads to effects on producer surplus in related markets.Figure 7-83. a.Bert’ s demand schedule is:Price Quantity DemandedMore than $7 0$5 to $7 1$3 to $5 2$1 to $3 3$1 or less 4Bert’ s demand curve is shown in Figure 7 -9.Figure 7-9b.When the price of a bottle of water is $4, Bert buys two bottles of water.Hisconsumer surplus is shown as area A in the figure.He values his first bottle ofwater at $7, but pays only $4 for it, so has consumer surplus of $3.He valueshis second bottle of water at $5, but pays only $4 for it, so has consumersurplus of $1.Thus Bert’ s total consumer surplus is $3 + $1 = $4, which isthe area of A in the figure.c.When the price of a bottle of water falls from $4 to $2, Bert buys three bottlesof water, an increase of one. His consumer surplus consists of both areas Aand B in the figure, an increase in the amount of area B. He gets consumersurplus of $5 from the first bottle ($7 value minus $2 price), $3 from thesecond bottle ($5 value minus $2 price), and $1 from the third bottle ($3 valueminus $2 price), for a total consumer surplus of $9. Thus consumer surplusrises by $5 (which is the size of area B) when the price of a bottle of water fallsfrom $4 to $2.4. a. Ernie ’ s supply schedule for water is:Price Quantity SuppliedMore than $7 4$5 to $7 3$3 to $5 2$1 to $3 1Less than $1 0Ernie’ s supply curve is shown in Figure 7 -10.Figure 7-10b.When the price of a bottle of water is $4, Ernie sells two bottles of water.Hisproducer surplus is shown as area A in the figure.He receives $4 for his firstbottle of water, but it costs only $1 to produce, so Ernie has producer surplusof $3.He also receives $4 for his second bottle of water, which costs $3 toproduce, so he has producer surplus of$1. Thus Ernie’ s total producersurplus is $3 + $1 = $4, which is the area of A in the figure.c.When the price of a bottle of water rises from $4 to $6, Ernie sells three bottlesof water, an increase of one.His producer surplus consists of both areas Aand B in the figure, an increase by the amount of area B.He gets producersurplus of $5 from the first bottle ($6 price minus $1 cost), $3 from the secondbottle ($6 price minus $3 cost), and $1 from the third bottle ($6 price minus $5price), for a total producer surplus of $9.Thus producer surplus rises by $5(which is the size of area B) when the price of a bottle of water rises from $4to $6.5. a. From Ernie ’ s supply schedule and Bert ’ s demand schedule, the quantitydemanded and supplied are:Price Quantity Supplied Quantity Demanded$ 2 1 34 2 26 3 1Only a price of $4 brings supply and demand into equilibrium, withan equilibrium quantity of 2.b.At a price of $4, consumer surplus is $4 and producer surplus is $4, as shownin problems 3 and 4.Total surplus is $4 + $4 = $8.c.If Ernie produced one fewer bottle, his producer surplus would decline to $3,as shown in problem 4.If Bert consumed one fewer bottle, his consumersurplus would decline to $3, as shown in problem 3. So total surplus would declineto $3 + $3 = $6.d.If Ernie produced one additional bottle of water, his cost would be $5, but theprice is only $4, so his producer surplus would decline by $1.If Bertconsumed one additional bottle of water, his value would be $3, but the priceis $4, so his consumer surplus would decline by $1.So total surplus declinesby $1 + $1 = $2.6. a.The effect of falling production costs in the market for stereos results in a shiftto the right in the supply curve, as shown in Figure 7-11.As a result, theequilibrium price of stereos declines and the equilibrium quantity increases.b.The decline in the price of stereos increases consumer surplus from area A to A+ B + C + D, an increase in the amount B + C + D.Prior to the shift in supply,producer surplus was areas B + E (the area above the supply curve and belowthe price).After the shift in supply, producer surplus is areas E + F + G.Soproducer surplus changes by the amount F + G - B, which may be positive ornegative.The increase in quantity increases producer surplus, while thedecline in the price reduces producer surplus.Since consumer surplus risesby B + C + D and producer surplus rises by F + G - B, total surplus rises by C+ D+F+G.c.If the supply of stereos is very elastic, then the shift of the supply curvebenefits consumers most.To take the most dramatic case, suppose thesupply curve were horizontal, as shown in Figure 7-12.Then there is noproducer surplus at all.Consumers capture all the benefits of fallingproduction costs, with consumer surplus rising from area A to area A + B.Figure 7-11Figure 7-127. Figure 7-13 shows supply and demand curves for haircuts. Supply equals demand ata quantity of three haircuts and a price between $4 and $5. Firms A, C, and D shouldcut the hair of Sally Jessy, Jerry, and Montel. Oprah ’ s willingness to pay is too low and firm B ’ s costs are too high, so they do not participate. The maximum total surplus isthe area between the demand and supply curves, which totals $11 ($8 value minus$2 cost for the first haircut, plus $7 value minus $3 cost for the second, plus $5 valueminus $4 cost for the third).Figure 7-138. a.The effect of falling production costs in the market for computers results in ashift to the right in the supply curve, as shown in Figure 7-14.As a result, theequilibrium price of computers declines and the equilibrium quantity increases.The decline in the price of computers increases consumer surplus from area Ato A + B + C + D, an increase in the amount B + C + D.Figure 7-14Prior to the shift in supply, producer surplus was areas B + E (the area abovethe supply curve and below the price).After the shift in supply, producersurplus is areas E + F + G.So producer surplus changes by the amount F + G- B, which may be positive or negative.The increase in quantity increasesproducer surplus, while the decline in the price reduces producer surplus. Sinceconsumer surplus rises by B + C + D and producer surplus rises by F + G - B,total surplus rises by C + D + F + G.——Figure 7-15b.Since adding machines are substitutes for computers, the decline in the priceof computers means that people substitute computers for adding machines,shifting the demand for adding machines to the left, as shown in Figure 7-15.The result is a decline in both the equilibrium price and equilibrium quantity ofadding machines.Consumer surplus in the adding-machine market changesfrom area A + B to A + C, a net gain of C - B.Producer surplus changes fromarea C + D + E to area E, a net loss of C + D.Adding machine producers aresad about technological advance in computers because their producersurplus declines.c.Since software and computers are complements, the decline in the price andincrease in the quantity of computers means that people’ s demand forsoftware increases, shifting the demand for software to the right, as shown inFigure 7-16. The result is an increase in both the price and quantity of software.Consumer surplus in the software market changes from B + C to A+B, a net increase of A - C. Producer surplus changes from E to C + D + E, anincrease of C + D, so software producers should be happy about the technologicalprogress in computers.d.Yes, this analysis helps explain why Bill Gates is one the world’ s richest msince his company produces a lot of software that’ s a complement withcomputers and there has been tremendous technological advance incomputers.——Figure 7-169. a. Figure 7-17 illustrates the demand for medical care. If each procedure has aprice of $100, quantity demanded will be Q 1 procedures.Figure 7-17b.If consumers pay only $20 per procedure, the quantity demanded will be Q 2procedures.Since the cost to society is $100, the number of proceduresperformed is too large to maximize total surplus.The quantity thatmaximizes total surplus is Q 1 procedures, which is less than Q2.c.The use of medical care is excessive in the sense that consumers getprocedures whose value is less than the cost of producing them.As a result,——the economy’ s total surplus is reduced.d.To prevent this excessive use, the consumer must bear the marginal cost ofthe procedure.But this would require eliminating insurance.Anotherpossibility would be that the insurance company, which pays most of themarginal cost of the procedure ($80, in this case) could decide whether theprocedure should be performed.But the insurance company doesn’ t get thebenefits of the procedure, so its decisions may not reflect the value to theconsumer.10. a. Figure 7-18 illustrates the effect of the drought. The supply curve shifts tothe left, leading to a rise in the equilibrium price from P 1 to P 2 and a decline inthe equilibrium quantity from Q 1 to Q 2 .Figure 7-18b.If the price of water is not allowed to change, there will be an excess demandfor water, with the shortage shown on the figure as the difference between Q 1and Q 3 .c.The system for allocating water is inefficient because it no longer allocateswater to those who value it most highly.Some people who value water atmore than its cost of production will be unable to obtain it, so societysurplus isn’ t maximized.The allocation system seems unfair as well.Water is allocated simply on pastusage, rewarding past wastefulness.If a family’ s demand for water increases,——say because of an increase in family size, the policy doesn ’ t allow them to obtain more water. Poor families, who probably used water mostly fornecessary uses like drinking, would suffer more than wealthier families whowould have to cut back only on luxury uses of water like operating backyardfountains and pools. However, the policy also keeps the price of water lower,which benefits poor families, since otherwise more of their family budgetwould have to go for water.d. If the city allowed the price of water to rise to its equilibrium price P 2 , theallocation would be more efficient. Quantity supplied would equal quantitydemanded and there would be no shortage. Total surplus would bemaximized.Whether the market allocation would be more or less fair than theproportionate reduction in water under the old policy is difficult to say, but it islikely to be more fair. Notice that the quantity supplied would be higher (Q 2)in this case than under the water restrictions (Q 3 ), so there ’ s less reduction inwater usage. To make the market solution even more fair, the governmentcould provide increased tax relief or welfare payments for poor families whosuffer from paying the higher water prices.。

计算机网络自顶向下第七版第七章答案

Computer Networking: A Top-Down Approach,7th Edition计算机网络自顶向下第七版Solutions to Review Questions and ProblemsChapter 7 Review Questions1.In infrastructure mode of operation, each wireless host is connected to the largernetwork via a base station (access point). If not operating in infrastructure mode, a network operates in ad-hoc mode. In ad-hoc mode, wireless hosts have noinfrastructure with which to connect. In the absence of such infrastructure, the hosts themselves must provide for services such as routing, address assignment, DNS-like name translation, and more.2.a) Single hop, infrastructure-basedb) Single hop, infrastructure-lessc) Multi-hop, infrastructure-basedd) Multi-hop, infrastructure-less3.Path loss is due to the attenuation of the electromagnetic signal when it travelsthrough matter. Multipath propagation results in blurring of the received signal at the receiver and occurs when portions of the electromagnetic wave reflect off objects and ground, taking paths of different lengths between a sender and receiver. Interference from other sources occurs when the other source is also transmitting in the samefrequency range as the wireless network.4.a) Increasing the transmission powerb) Reducing the transmission rate5.APs transmit beacon frames. An AP’s beacon frames will be transmitted over one ofthe 11 channels. The beacon frames permit nearby wireless stations to discover and identify the AP.6.False7.APs transmit beacon frames. An AP’s beacon frames will be transmitted over one ofthe 11 channels. The beacon frames permit nearby wireless stations to discover and identify the AP.8.False9.Each wireless station can set an RTS threshold such that the RTS/CTS sequence isused only when the data frame to be transmitted is longer than the threshold. This ensures that RTS/CTS mechanism is used only for large frames.10.No, there wouldn’t be any advantage. Suppose there are two stations that want totransmit at the same time, and they both use RTS/CTS. If the RTS frame is as long asa DATA frames, the channel would be wasted for as long as it would have beenwasted for two colliding DATA frames. Thus, the RTS/CTS exchange is only useful when the RTS/CTS frames are significantly smaller than the DATA frames.11.Initially the switch has an entry in its forwarding table which associates the wirelessstation with the earlier AP. When the wireless station associates with the new AP, the new AP creates a frame with the wireless station’s MAC address and broadcasts the frame. The frame is received by the switch. This forces the switch to update itsforwarding table, so that frames destined to the wireless station are sent via the new AP.12.Any ordinary Bluetooth node can be a master node whereas access points in 802.11networks are special devices (normal wireless devices like laptops cannot be used as access points).13.False14.“Opportunistic Scheduling” refers to matching the physical layer protocol to channelconditions between the sender and the receiver, and choosing the receivers to which packets will be sent based on channel condition. This allows the base station to make best use of the wireless medium.15.UMTS to GSM and CDMA-2000 to IS-95.16.The data plane role of eNodeB is to forward datagram between UE (over the LTEradio access network) and the P-GW. Its control plane role is to handle registration and mobility signaling traffic on behalf of the UE.The mobility management entity (MME) performs connection and mobility management on behalf of the UEs resident in the cell it controls. It receives UE subscription information from the HHS.The Packet Data Network Gateway (P-GW) allocates IP addresses to the UEs and performs QoS enforcement. As a tunnel endpoint it also performs datagram encapsulation/decapsulation when forwarding a datagram to/from a UE.The Serving Gateway (S-GW) is the data-plane mobility anchor point as all UE traffic will pass through the S-GW. The S-GW also performs charging/billing functions and lawful traffic interception.17.In 3G architecture, there are separate network components and paths for voice anddata, i.e., voice goes through public telephone network, whereas data goes through public Internet. 4G architecture is a unified, all-IP network architecture, i.e., both voice and data are carried in IP datagrams to/from the wireless device to severalgateways and then to the rest of the Internet.The 4G network architecture clearly separates data and control plane, which is different from the 3G architecture.The 4G architecture has an enhanced radio access network (E-UTRAN) that is different from 3G’s radio access network UTRAN.18.No. A node can remain connected to the same access point throughout its connectionto the Internet (hence, not be mobile). A mobile node is the one that changes its point of attachment into the network over time. Since the user is always accessing theInternet through the same access point, she is not mobile.19.A permanent address for a mobile node is its IP address when it is at its homenetwork. A care-of-address is the one its gets when it is visiting a foreign network.The COA is assigned by the foreign agent (which can be the edge router in theforeign network or the mobile node itself).20.False21.The home network in GSM maintains a database called the home location register(HLR), which contains the permanent cell phone number and subscriber profileinformation about each of its subscribers. The HLR also contains information about the current locations of these subscribers. The visited network maintains a database known as the visitor location register (VLR) that contains an entry for each mobile user that is currently in the portion of the network served by the VLR. VLR entries thus come and go as mobile users enter and leave the network.The edge router in home network in mobile IP is similar to the HLR in GSM and the edge router in foreign network is similar to the VLR in GSM.22.Anchor MSC is the MSC visited by the mobile when a call first begins; anchor MSCthus remains unchanged during the call. Throughout the call’s duration and regardless of the number of inter-MSC transfers performed by the mobile, the call is routed from the home MSC to the anchor MSC, and then from the anchor MSC to the visitedMSC where the mobile is currently located.23.a) Local recoveryb) TCP sender awareness of wireless linksc) Split-connection approachesChapter 7 ProblemsProblem 1Output corresponding to bit d 1 = [-1,1,-1,1,-1,1,-1,1]Output corresponding to bit d 0 = [1,-1,1,-1,1,-1,1,-1]Problem 2Sender 2 output = [1,-1,1,1,1,-1,1,1]; [ 1,-1,1,1,1,-1,1,1]Problem 3181111)1()1(111111)1()1(1112=⨯+⨯+-⨯-+⨯+⨯+⨯+-⨯-+⨯=d 181111)1()1(111111)1()1(1122=⨯+⨯+-⨯-+⨯+⨯+⨯+-⨯-+⨯=dProblem 4Sender 1: (1, 1, 1, -1, 1, -1, -1, -1)Sender 2: (1, -1, 1, 1, 1, 1, 1, 1)Problem 5a) The two APs will typically have different SSIDs and MAC addresses. A wirelessstation arriving to the café will associate with one of the SSIDs (that is, one of the APs). After association, there is a virtual link between the new station and the AP. Label the APs AP1 and AP2. Suppose the new station associates with AP1. When the new station sends a frame, it will be addressed to AP1. Although AP2 will alsoreceive the frame, it will not process the frame because the frame is not addressed to it. Thus, the two ISPs can work in parallel over the same channel. However, the two ISPs will be sharing the same wireless bandwidth. If wireless stations in different ISPs transmit at the same time, there will be a collision. For 802.11b, the maximum aggregate transmission rate for the two ISPs is 11 Mbps.b) Now if two wireless stations in different ISPs (and hence different channels) transmitat the same time, there will not be a collision. Thus, the maximum aggregatetransmission rate for the two ISPs is 22 Mbps for 802.11b.Problem 6Suppose that wireless station H1 has 1000 long frames to transmit. (H1 may be an AP that is forwarding an MP3 to some other wireless station.) Suppose initially H1 is the onlystation that wants to transmit, but that while half-way through transmitting its first frame, H2 wants to transmit a frame. For simplicity, also suppose every station can hear every other station’s signal (that is, no hidden terminals). Before transmitting, H2 will sense that the channel is busy, and therefore choose a random backoff value.Now suppose that after sending its first frame, H1 returns to step 1; that is, it waits a short period of times (DIFS) and then starts to transmit the second frame. H1’s second frame will then be transmitted while H2 is stuck in backoff, waiting for an idle channel. Thus, H1 should get to transmit all of its 1000 frames before H2 has a chance to access the channel. On the other hand, if H1 goes to step 2 after transmitting a frame, then it too chooses a random backoff value, thereby giving a fair chance to H2. Thus, fairness was the rationale behind this design choice.Problem 7A frame without data is 32 bytes long. Assuming a transmission rate of 11 Mbps, the time to transmit a control frame (such as an RTS frame, a CTS frame, or an ACK frame) is (256 bits)/(11 Mbps) = 23 usec. The time required to transmit the data frame is (8256 bits)/(11 Mbps) = 751DIFS + RTS + SIFS + CTS + SIFS + FRAME + SIFS + ACK= DIFS + 3SIFS + (3*23 + 751) usec = DIFS + 3SIFS + 820 usecProblem 8a) 1 message/ 2 slotsb) 2 messages/slotc) 1 message/slota)i) 1 message/slotii) 2 messages/slotiii) 2 messages/slotb)i) 1 message/4 slotsii) slot 1: Message A→ B, message D→ Cslot 2: Ack B→ Aslot 3: Ack C→ D= 2 messages/ 3 slotsiii)slot 1: Message C→ Dslot 2: Ack D→C, message A→ BRepeatslot 3: Ack B→ A= 2 messages/3 slotsProblem 10a)10 Mbps if it only transmits to node A. This solution is not fair since only A is gettingserved. By “fair” it m eans that each of the four nodes should be allotted equal number of slots.b)For the fairness requirement such that each node receives an equal amount of dataduring each downstream sub-frame, let n1, n2, n3, and n4 respectively represent the number of slots that A, B, C and D get.Now,data transmitted to A in 1 slot = 10t Mbits(assuming the duration of each slot to be t)Hence,Total amount of data transmitted to A (in n1 slots) = 10t n1Similarly total amounts of data transmitted to B, C, and D equal to 5t n2, 2.5t n3, and t n4 respectively.Now, to fulfill the given fairness requirement, we have the following condition:10t n1 = 5t n2 = 2.5t n3 = t n4Hence,n2 = 2 n1n3 = 4 n1n4 = 10 n1Now, the total number of slots is N. Hence,n1+ n2+ n3+ n4 = Ni.e. n1+ 2 n1 + 4 n1 + 10 n1 = Ni.e. n1 = N/17Hence,n2 = 2N/17n3 = 4N/17n4 = 10N/17The average transmission rate is given by:(10t n1+5t n2+ 2.5t n3+t n4)/tN= (10N/17 + 5 * 2N/17 + 2.5 * 4N/17 + 1 * 10N/17)/N= 40/17 = 2.35 Mbpsc)Let node A receives twice as much data as nodes B, C, and D during the sub-frame.Hence,10tn1 = 2 * 5tn2 = 2 * 2.5tn3 = 2 * tn4i.e. n2 = n1n3 = 2n1n4 = 5n1Again,n1 + n2 + n3 + n4 = Ni.e. n 1+ n1 + 2n1 + 5n1 = Ni.e. n1 = N/9Now, average transmission rate is given by:(10t n1+5t n2+ 2.5t n3+t n4)/tN= 25/9 = 2.78 MbpsSimilarly, considering nodes B, C, or D receive twice as much data as any other nodes, different values for the average transmission rate can be calculated.Problem 11a)No. All the routers might not be able to route the datagram immediately. This isbecause the Distance Vector algorithm (as well as the inter-AS routing protocols like BGP) is decentralized and takes some time to terminate. So, during the time when the algorithm is still running as a result of advertisements from the new foreign network, some of the routers may not be able to route datagrams destined to the mobile node.b)Yes. This might happen when one of the nodes has just left a foreign network andjoined a new foreign network. In this situation, the routing entries from the oldforeign network might not have been completely withdrawn when the entries from the new network are being propagated.c)The time it takes for a router to learn a path to the mobile node depends on thenumber of hops between the router and the edge router of the foreign network for the node.Problem 12If the correspondent is mobile, then any datagrams destined to the correspondent would have to pass through the correspondent’s home agent. The foreign agent in the network being visited would also need to be involved, since it is this foreign agent thatnotifies the correspondent’s home agent of the location of the correspondent. Datagrams received by the correspondent’s home agent would need to be encapsulated/tunneled between the correspondent’s home agent and for eign agent, (as in the case of the encapsulated diagram at the top of Figure 6.23.Problem 13Because datagrams must be first forward to the home agent, and from there to the mobile, the delays will generally be longer than via direct routing. Note that it is possible, however, that the direct delay from the correspondent to the mobile (i.e., if the datagram is not routed through the home agent) could actually be smaller than the sum of the delay from thecorrespondent to the home agent and from there to the mobile. It would depend on the delays on these various path segments. Note that indirect routing also adds a home agent processing (e.g., encapsulation) delay.Problem 14First, we note that chaining was discussed at the end of section 6.5. In the case of chaining using indirect routing through a home agent, the following events would happen: •The mobile node arrives at A, A notifies the home agent that the mobile is now visiting A and that datagrams to the mobile should now be forwarded to thespecified care-of-address (COA) in A.•The mobile node moves to B. The foreign agent at B must notify the foreign agent at A that the mobile is no longer resident in A but in fact is resident in Band has the specified COA in B. From then on, the foreign agent in A willforward datagrams it receives that are addressed to the mobile’s COA in A to t he mobile’s COA in B.•The mobile node moves to C. The foreign agent at C must notify the foreign agent at B that the mobile is no longer resident in B but in fact is resident in C and has the specified COA in C. From then on, the foreign agent in B will forwarddatagrams it receives (from the foreign agent in A) that are addressed to themobile’s COA in B to the mobile’s COA in C.Note that when the mobile goes offline (i.e., has no address) or returns to its home network, the datagram-forwarding state maintained by the foreign agents in A, B and C must be removed. This teardown must also be done through signaling messages. Note that the home agent is not aware of the mobile’s mobility beyond A, and that the correspondent is not at all aware of the mobil e’s mobility.In the case that chaining is not used, the following events would happen: •The mobile node arrives at A, A notifies the home agent that the mobile is now visiting A and that datagrams to the mobile should now be forwarded to thespecified care-of-address (COA) in A.•The mobile node moves to B. The foreign agent at B must notify the foreign agent at A and the home agent that the mobile is no longer resident in A but infact is resident in B and has the specified COA in B. The foreign agent in A can remove its state about the mobile, since it is no longer in A. From then on, thehome agent will forward datagrams it receives that are addressed to the mobile’sCOA in B.•The mobile node moves to C. The foreign agent at C must notify the foreign agent at B and the home agent that the mobile is no longer resident in B but in fact is resident in C and has the specified COA in C. The foreign agent in B canremove its state about the mobile, since it is no longer in B. From then on, thehome agent will forward datagrams it receives that are addressed to the mobile’sCOA in C.When the mobile goes offline or returns to its home network, the datagram-forwarding state maintained by the foreign agent in C must be removed. This teardown must also bedone through signaling messages. Note that the home agent is always aware of the mobile’s cu rrent foreign network. However, the correspondent is still blissfully unaware of the mobile’s mobility.Problem 15Two mobiles could certainly have the same care-of-address in the same visited network. Indeed, if the care-of-address is the address of the foreign agent, then this address would be the same. Once the foreign agent decapsulates the tunneled datagram and determines the address of the mobile, then separate addresses would need to be used to send the datagrams separately to their different destinations (mobiles) within the visited network.Problem 16If the MSRN is provided to the HLR, then the value of the MSRN must be updated in the HLR whenever the MSRN changes (e.g., when there is a handoff that requires the MSRN to change). The advantage of having the MSRN in the HLR is that the value can be provided quickly, without querying the VLR. By providing the address of the VLR Rather than the MSRN), there is no need to be refreshing the MSRN in the HLR.。

等级考试chap7_基础题

基础题一．选择题1．以下几组控件中，均可直接添加到表单中的是_____。

A. 命令按钮组、选项按钮、文本框B. 页面、页框、表格C. 命令按钮、选项按钮组、列表框D. 页面、选项按钮组、组合框2．以下几组控件中，均具有ControlSource属性的是__ ____。

A. EditBox,Grid,ComboBox C. ComboBox,Grid,TimerB. ListBox,Label,OptionButton D. CheckBox,EditBox,OptionButton3．对于表单来说，用户可以设置其ShowWindow属性。

该属性的取值可以为___ ___。

A.在屏幕中或在顶层表单中或作为顶层表单B.普通或最大化或最小化C.无模式或模式D.平面或3维4．表单的WindowsType属性值可设为。

A 默认数据工作期和私有数据工作期B 普通、最大化和最小化C 无模式和模式D 无边框、单线边框、固定对话框和可调边框5．在运行表单时，为设置属性值或指定操作的默认值，有时需要将参数传递到表单。

若要将参数传递到表单，则应在表单的_ ____事件代码中包含PARAMETERS语句。

A.LoadB.InitC.DestroyD.Activate6. 运行某个表单，表单LOAD,INIT,ACTIVATE事件的触发顺序为。

A INIT,LOAD,ACTIVATEB LOAD,INIT,ACTIVATEC INIT,ACTIVATE,LOAD D ACTIVATE,INIT,LOAD7. 如果要引用一个控件所在的表单集对象，则可以使用下列关键字。

A THISB THISFORMSETC PARENTD 都可以8.一个表单集中包含一个表单，该表单中包含一个命令按钮，释放表单集时，下列事件中最先发生的事件是。

A 表单集的Destroy事件B 表单的Destroy事件C 命令按钮的Destroy事件D 表单集的Unload事件9. 文本框绑定到一个字段后，对文本框中的内容进行输入或修改时，文本框中的数据将同时保存到。

数据结构-chap7 (4)AOV网与拓扑排序

//若入度减为0，则入栈
}//for }//while if (count<G.vexnum) return ERROR; //该有向图有回路 else return OK; }//TopologicalSort
自测题2 AOV-网的拓扑排序
v2 v1 v3 v4 v5 v6 v1 v2
1
3 0 1 0 3 S.top S.base
5 4
1
2 3
3
2 1 4 0 2
C2
1
0
5 0
1
4
5
C3
C4
C5
C3 0 C4
5 0
C5 0
while(! StackEmpty(S)){ Pop(S, i); printf(i, G. vertices[i].data); ++count; for (p=G.vertices[i].firstarc; p; p=p->nextarc) { k = p->adjvex; if ( !(- -indegree[k]) ) Push(S, k); }//for }//while data firstarc C0 1 3 0 栈S C1 5 0
Status TopologicalSort(ALGraph G) { FindInDegree(G, indegree); //求各顶点入度indegree[0..vexnum-1] InitStack(S); for(i=0; i<G. vexnum; ++i) if (! indegree[i]) Push(S, i); //入度为0顶点的编号进栈 count = 0; //对输出顶点计数 count=6 while(! StackEmpty(S)){ Pop(S, i); //从零入度顶点栈S 栈顶，获得一入度为零的顶点i printf(i, G. vertices[i].data); ++count; //输出i号顶点的数据，并计数 for (p=G. vertices[i]. firstarc; p; p=p->nextarc) { k = p->adjvex; if ( !(- -indegree[k]) ) Push(S, k); //对i号顶点邻接到的每个顶点入度减1

chap7音高追踪

1.(**) 计算ACF：请写一个函数 myFrame2acf，将一个音框转换成 ACF，其用法如下：acf = myFrame2acf(frame);其中 acf 的长度应该是和 frame 一样。

2. (**) 计算AMDF：请写一个函数 myFrame2amdf，将一个音框转换成AMDF，其用法如下：amdf = myFrame2amdf(frame);其中 amdf 的长度应该是和 frame 一样。

3. (**) 计算AMDF/ACF：请写一个函数 myFrame2amdfOverAcf，将一个音框转换成 AMDF/ACF，其用法如下：amdfOverAcf = myFrame2amdfOverAcf(frame);其中 amdfOverAcf 的长度应该是和 frame 一样。

请利用此函数，画出类似此范例（frame2acfOverAmdf01.m）的图，看看此方法是否能够比单独使用 ACF 或是AMDF 更有用。

若此方法不适合用来进行音高追踪，请问有何改进方法？（提示：请直接参考 SAP Toolbox 里面的 frame2acfOverAmdf.m。

）4.(**) 由ACF计算音高：请写一个函数 myAcf2pitch，由一个 ACF 向量来计算音高，其用法如下：pitch = myAcf2pitch(acf, fs, plotOpt);其中 acf 是一个 ACF 向量，fs 则是取样频率，pitch 则是音高（以 Semitone 为单位），plotOpt 则决定是否画图，若其值不等于 0，则必须画出 ACF 及你的程序所选出来的「ACF音高点」。

5.(**) 由AMDF计算音高：请写一个函数 myAmdf2pitch，由一个 AMDF 向量来计算音高，其用法如下：pitch = myAmdf2pitch(amdf, fs, plotOpt);其中 amdf 是一个 AMDF 向量，fs 则是取样频率，pitch 则是音高（以 Semitone 为单位），plotOpt 则决定是否画图，若其值不等于 0，则必须画出 AMDF 及你的程序所选出来的「AMDF音高点」。

策划案例—CHAP7可靠性设计与分析

f (t )
1

(ln t u ) 2
2
2
t 2
e
F (t )

t
f ( t ) dt
0

t
1

(ln t u ) 2
2
2
0
t 2
e
dt
四、威布尔分布(金属材料的疲劳寿命) [正态分布、指数分布
是其特例]
f (t )
t

( t )
r (t t ) r (t )
N
r ( t ) t

16 0 (1000 0 ) 5
0 . 32 %
2.产品失效率曲线(浴盆曲线或寿命特性曲线)
早期失效期
偶然失效期
耗损失效期
(１）早期失效期特点：失效率较高，但随着工作时间的增加，失效率迅速下降。
2.固有可用性Ａｉ
将产品的平均故障间隔时间与平均故障间隔时间及平均修复时间的和之比. 理想状态，即：ＭＤＴ(平均延误时间)＝０
MTBF为平均故障间隔时间; MTTR为平均修复时间;
反映了生产方的设计、制造和管理的综合水平，越大越好。
（5）可信性
可信性是一个非定量的集合性术语，表述可用性及其影响因素：可靠性（Ｒ）、维修性（Ｍ）、保障性（Ｓ）、测试性（Ｔ），简写为Ｒ· Ｓ· Ｍ· Ｔ
原因由于原材料不均匀和制造工艺缺陷等引起的采取措施：
加强原材料检验、改进设计、采用合理的筛选技术和加负荷试验将有缺陷、不可靠的产品尽早暴露出来，使剩下的产品有较低的失效率。
(2）偶然失效期特点：失效率低而稳定，失效率是一常数或近似常数，这是产品最好的工作时间。原因

计量经济学卡特版课后第七章答案

CHAPTER 7Exercise Solutions141Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 142EXERCISE 7.1(a) When a GPA is increased by one unit, and other variables are held constant, averagestarting salary will increase by the amount $1643 ( 4.66t =, and the coefficient is significant at α = 0.001). Students who take econometrics will have a starting salary which is $5033 higher, on average, than the starting salary of those who did not take econometrics (11.03t =, and the coefficient is significant at α = 0.001). The intercept suggests the starting salary for someone with a zero GPA and who did not take econometrics is $24,200. However, this figure is likely to be unreliable since there would be no one with a zero GPA . The R 2 = 0.74 implies 74% of the variation of starting salary is explained by GPA and METRICS(b) A suitably modified equation is 1234SAL GPA METRICS FEMALE e =β+β+β+β+ Then, the parameter 4β is an intercept dummy variable that captures the effect of genderon starting salary, all else held constant.()()1231423if = 0if = 1GPA METRICSFEMALE E SAL GPA METRICS FEMALE β+β+β⎧⎪=⎨β+β+β+β⎪⎩(c) To see if the value of econometrics is the same for men and women, we change the modelto 12345SAL GPA METRICS FEMALE METRICS FEMALE e =β+β+β+β+β×+ Then, the parameter 4β is an intercept dummy variable that captures the effect of genderon starting salary, all else held constant. The parameter 5β is a slope dummy variable that captures any change in the slope for females, relative to males.()()()12314235if = 0if = 1GPA METRICSFEMALE E SAL GPA METRICS FEMALE β+β+β⎧⎪=⎨β+β+β+β+β⎪⎩Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 143EXERCISE 7.2(a) Considering each of the coefficients in turn, we have the following interpretations.Intercept : At the beginning of the time period over which observations were taken, on a day which is not Friday, Saturday or a holiday, and a day which has neither a full moon nor a half moon, the estimated average number of emergency room cases was 93.69.T : We estimate that the average number of emergency room cases has been increasing by 0.0338 per day, other factors held constant. This time trend has a t -value of 3.058 and a p -value = 0.0025 < 0.01.HOLIDAY : The average number of emergency room cases is estimated to go up by 13.86on holidays. The “holiday effect” is significant at the 0.05 level of significance. FRI and SAT : The average number of emergency room cases is estimated to go up by 6.9and 10.6 on Fridays and Saturdays, respectively. These estimated coefficients are both significant at the 0.01 level. FULLMOON : The average number of emergency room cases is estimated to go up by2.45 on days when there is a full moon. However, a null hypothesis stating that a full moon has no influence on the number of emergency room cases would not be rejected at any reasonable level of significance. NEWMOON : The average number of emergency room cases is estimated to go up by 6.4on days when there is a new moon. However, a null hypothesis stating that a new moon has no influence on the number of emergency room cases would not be rejected at the usual 10% level, or smaller. Therefore, hospitals should expect more calls on holidays, Fridays and Saturdays, and also should expect a steady increase over time.(b)There are very little changes in the remaining coefficients, or their standard errors, when FULLMOON and NEWMOON are omitted. The equation goodness-of-fit statistic decreases slightly, as expected when variables are omitted. Based on these casual observations the consequences of omitting FULLMOON and NEWMOON are negligible. (c) The null and alternative hypotheses are067:0H β=β= 167: or is nonzero.H ββThe test statistic is()2(2297)R U U SSE SSE F SSE −=−whereR SSE = 27424.19 is the sum of squared errors from the estimated equation with FULLMOON and NEWMOON omitted and U SSE = 27108.82 is the sum of squared errors from the estimated equation with these variables included. The calculated value of the F statistic is 1.29. The .05 critical value is (0.95,2,222) 3.307F =, and corresponding p -value is0.277. Thus, we do not reject the null hypothesis that new and full moons have no impact on the number of emergency room cases.Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 144EXERCISE 7.3(a) The estimated coefficient of the price of alcohol suggests that, if the price of pure alcohol goes up by $1 per liter, the average number of days (out of 31) that alcohol is consumed will fall by 0.045.(b) The price elasticity at the means is given by24.780.0450.3203.49q pp q∂=−×=−∂(c) To compute this elasticity, we need q for married black males in the 21-30 age range. It is given by4.0990.04524.780.00005712425 1.6370.8070.0350.5803.97713q =−×+×+−+−=Thus, the price elasticity is24.780.0450.2803.97713q p p q ∂=−×=−∂ (d)The coefficient of income suggests that a $1 increase in income will increase the averagenumber of days on which alcohol is consumed by 0.000057. If income was measured in terms of thousand-dollar units, which would be a sensible thing to do, the estimated coefficient would change to 0.057.(e) The effect of GENDER suggests that, on average, males consume alcohol on 1.637 moredays than women. On average, married people consume alcohol on 0.807 less days than single people. Those in the 12-20 age range consume alcohol on 1.531 less days than those who are over 30. Those in the 21-30 age range consume alcohol on 0.035 more days than those who are over 30. This last estimate is not significantly different from zero, however. Thus, two age ranges instead of three (12-20 and an omitted category of more than 20), are likely to be adequate. Black and Hispanic individuals consume alcohol on 0.580 and 0.564 less days, respectively, than individuals from other races. Keeping in mind that the critical t -value is 1.960, all coefficients are significantly different from zero, except that for the dummy variable for the 21-30 age range.Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 145EXERCISE 7.4(a) The estimated coefficient for SQFT suggests that an additional square foot of floor spacewill increase the price of the house by $72.79. The positive sign is as expected, and the estimated coefficient is significantly different from zero. The estimated coefficient for AGE implies the house price is $179 less for each year the house is older. The negative sign implies older houses cost less, other things being equal. The coefficient is significantly different from zero.(b) The estimated coefficients for the dummy variables are all negative and they becomeincreasingly negative as we move from D92 to D96. Thus, house prices have been steadily declining in Stockton over the period 1991-96, holding constant both the size and age of the house.(c) Including a dummy variable for 1991 would have introduced exact collinearity unless theintercept was omitted. Exact collinearity would cause least squares estimation to fail. The collinearity arises between the dummy variables and the constant term because the sum of the dummy variables equals 1; the value of the constant term.Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 146EXERCISE 7.5(a)The estimated marginal response of yield to nitrogen is()()8.0112 1.9440.5677.444 3.888when 16.877 3.888when 26.310 3.888when 3E YIELD NITRO PHOS NITRO NITRO PHOS NITRO PHOS NITROPHOS ∂=−××−×∂=−==−==−=The effect of additional nitrogen on yield depends on both the level of nitrogen and the level of phosphorus. For a given level of phosphorus, marginal yield is positive for small values of NITRO but becomes negative if too much nitrogen is applied. The level of NITRO that achieves maximum yield for a given level of PHOS is obtained by setting the first derivative equal to zero. For example, when PHOS = 1 the maximum yield occurs when NITRO = 7.444/3.888 = 1.915. The larger the amount of phosphorus used, the smaller the amount of nitrogen required to attain the maximum yield. (b)The estimated marginal response of yield to phosphorous is()()4.80020.7780.5674.233 1.556when 13.666 1.556when 23.099 1.556when 3E YIELD PHOS NITRO PHOS PHOS NITRO PHOS NITRO PHOSNITRO ∂=−××−×∂=−==−==−= Comments similar to those made for part (a) are also relevant here.(c)(i) We want to test 0246:20H β+β+β= against the alternative 1246:20.H β+β+β≠The value of the test statistic is ()24624627.367se 2b b b t b b b ++===++At a 5% significance level, the critical t -value is c t ± where (0.975,21) 2.080c t t ==. Since t > 2.080 we reject the null hypothesis and conclude that the marginal product ofyield to nitrogen is not zero when NITRO = 1 and PHOS = 1.(ii) We want to test 0246:40H β+β+β= against the alternative 1246:40H β+β+β≠.The value of the test statistic is()2462464 1.660se 4b b b t b b b ++===−++Since |t| < 2.080 (0.975,21)t =, we do not reject the null hypothesis. A zero marginal yieldwith respect to nitrogen is compatible with the data when NITRO = 1 and PHOS = 2.Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 147Exercise 7.5(c) (continued)(c)(iii) We want to test 0246:60H β+β+β= against the alternative 1246:60H β+β+β≠.The value of the test statistic is()24624668.742se 6b b b t b b b ++===−++Since |t| > 2.080 (0.975,21)t =, we reject the null hypothesis and conclude that themarginal product of yield to nitrogen is not zero when NITRO = 3 and PHOS = 1.(d) The maximizing levels NITRO ∗ and PHOS ∗ are those values for NITRO and PHOS suchthat the first-order partial derivatives are equal to zero.()()35620E YIELD PHOS NITRO PHOS ∗∗∂=β+β+β=∂()()24620E YIELD NITRO PHOS NITRO ∗∗∂=β+β+β=∂The solutions and their estimates are 253622645228.011(0.778) 4.800(0.567)1.7014(0.567)4( 1.944)(0.778)NITRO ∗ββ−ββ××−−×−===β−ββ−−×−−34262264522 4.800( 1.944)8.011(0.567)2.4654(0.567)4( 1.944)(0.778)PHOS ∗ββ−ββ××−−×−===β−ββ−−×−−The yield maximizing levels of fertilizer are not necessarily the optimal levels. Theoptimal levels are those where the marginal cost of the inputs is equal to the marginal value product of those inputs. Thus, the optimal levels are those for which()()PHOS PEANUTS E YIELD PRICE PHOS PRICE ∂=∂ and ()()NITROPEANUTSE YIELD PRICE NITRO PRICE ∂=∂Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 148EXERCISE 7.6(a) The model to estimate is()()112323ln +PRICE UTOWN SQFT SQFT UTOWN AGE POOL FPLACE e=β+δ+β+γ×β+δ+δ+The estimated equation, with standard errors in parentheses, isn ()()()()()()ln 4.46380.33340.035960.003428(se)0.02640.03590.001040.001414PRICE UTOWN SQFT SQFT UTOWN =++−×()()()20.0009040.018990.0065560.86190.0002180.005100.004140AGE POOL FPLACER −++=(b) In the log-linear functional form 12ln(),y x e =β+β+ we have21dy dx y=β or 2dydx y =β Thus, a 1 unit change in x leads to a percentage change in y equal to 2100×β.In this case2311PRICE UTOWNSQFT PRICE PRICE AGE PRICE∂=β+γ∂∂=β∂Using this result for the coefficients of SQFT and AGE , we find that an additional 100 square feet of floor space increases price by 3.6% for a house not in University town; a house which is a year older leads to a reduction in price of 0.0904%. Both estimated coefficients are significantly different from zero. (c) Using the results in Section 7.5.1a,()2ln()ln()100100%poolnopool PRICEPRICE PRICE −×=δ×≈Δan approximation of the percentage change in price due to the presence of a pool is 1.90%. Using the results in Section7.5.1b,()21001100pool nopool nopool PRICE PRICE e PRICE δ⎛⎞−×=−×⎜⎟⎜⎟⎝⎠the exact percentage change in price due to the presence of a pool is 1.92%.Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 149Exercise 7.6 (continued)(d) From Section 7.5.1a,()3ln()ln()100100%fireplacenofireplace PRICEPRICE PRICE −×=δ×≈Δan approximation of the percentage change in price due to the presence of a fireplace is 0.66%.From Section 7.5.1b,()31001100fireplace nofireplace nofireplace PRICE PRICE e PRICE δ⎛⎞−×=−×⎜⎟⎜⎟⎝⎠the exact percentage change in price due to the presence of a fireplace is also 0.66%. (e)In this case the difference in log-prices is given by()n ()n ()2525ln ln 0.33340.003428250.33340.003428250.2477utown noutown SQFT SQFT PRICE PRICE UTOWN UTOWN ==−=−××=−×= and the percentage change in price attributable to being near the university, for a 2500square-feet home, is()0.2477110028.11%e−×=Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 150EXERCISE 7.7(a) The estimated equation isn ()()()()()()()2ln 8.9848 3.7463 1.1495 1.2880.4237 (se)0.64640.57650.44860.60530.1052 1.4313 0.84280.1562SAL1APR1APR2APR3DISP DISPAD R =−++++=(b) The estimates of2β, 3β and 4β are all significant and have the expected signs. The sign of 2β is negative, while the signs of the other two coefficients are positive. These signs imply that Brands 2 and 3 are substitutes for Brand 1. If the price of Brand 1 rises, then sales of Brand 1 will fall, but a price rise for Brand 2 or 3 will increase sales of Brand 1. Furthermore, with the log-linear function, the coefficients are interpreted as proportionalchanges in quantity from a 1-unit change in price. For example, a one-unit increase in the price of Brand 1 will lead to a 375% decline in sales; a one-unit increase in the price of Brand 2 will lead to a 115% increase in sales. These percentages are large because prices are measured in dollar units. If we wish toconsider a 1 cent change in price – a change more realistic than a 1-dollar change – then the percentages 375 and 115 become 3.75% and 1.15%, respectively. (c) There are three situations that are of interest. (i) No display and no advertisement{}11234exp SAL1APR1APR2APR3Q =β+β+β+β=(ii) A display but no advertisement{}{}2123455exp exp SAL1APR1APR2APR3Q =β+β+β+β+β=β(iii) A display and an advertisement{}{}3123466exp exp SAL1APR1APR2APR3Q =β+β+β+β+β=βThe estimated percentage increase in sales from a display but no advertisement isn n n 210.423751exp{}100100(1)10052.8%Q b Q SAL1SAL1e Q SAL1−−×=×=−×=Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 151Exercise 7.7(c) (continued)(c) The estimated percentage increase in sales from a display and an advertisement isn n n 311.431361exp{}100100(1)100318%Q b Q SAL1SAL1e Q SAL1−−×=×=−×=The signs and relative magnitudes of 5b and 6b lead to results consistent with economiclogic. A display increases sales; a display and an advertisement increase sales by an even larger amount.(d) The results of these tests appear in the table below.Part 0H Test Value Degrees of Freedom 5% Critical ValueDecision(i) β5 = 0 t = 4.03 46 2.01 Reject H 0 (ii) β6 = 0 t = 9.17 46 2.01 Reject H 0 (iii) β5 = β6 = 0 F = 42.0 (2,46) 3.20 Reject H 0 (iv)β6 ≤ β5t = 6.8646 1.68 Reject H 0(e) The test results suggest that both a store display and a newspaper advertisement will increase sales, and that both forms of advertising will increase sales by more than a store display by itself.Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 152EXERCISE 7.8(a) The estimated equation, with standard errors in parentheses, isn 215.45970.2698 2.35820.4391(se) (0.2537)(0.0868)(0.2629)PRICEAGE NET R =+−=All estimated coefficients are significantly different from zero. The intercept suggests thatthe average price of CDs that have a 1999 copyright and are not sold on the internet is $15.46. For every year the copyright date is earlier than 1999, the price increases by 27 cents. For CDs sold through the internet, the price is $2.36 cheaper. The positive coefficient of AGE supports Mixon and Ressler’s hypothesis. (b) The estimated equation, with standard errors in parentheses, isn 215.52880.7885 2.35690.4380(se) (0.2424)(0.2567) (0.2632)PRICEOLD NET R =+−=Again, all estimated coefficients are significantly different from zero. They suggest thatthe average price of new releases, not sold on the internet, is $15.53. If the CD is not a new release, the price is 79 cents higher. If it is purchased over the internet, the price is $2.36 less. The positive coefficient of OLD supports Mixon and Ressler’s hypothesis.Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 153EXERCISE 7.9The estimated coefficients and their standard errors (in parenthesis) for the various parts ofthis question are given in the following table.Variable (a) (b) (c) (f) (g) Constant (β1) 128.98* 342.88* 161.47 109.72 98.48(34.59) (72.34) (120.7) (135.6) (179.1)2()AGE β −7.5756* −2.9774 −2.0383 −1.7200 (2.317) (3.352) (3.542) (4.842) 3()INC β 1.4577* 2.3822* 9.0739* 18.325 22.104(0.5974) (0.6036) (3.670) (11.49) (40.26)4()AGE INC ×β −0.1602 −0.6115 −0.9087 (0.0867) (0.5381) (3.079)25()AGE INC ×β 0.0055 0.0131 (0.0064) (0.0784)36()AGE INC ×β −0.000065 (0.000663) SSE 819286 635637 580609 568869 568708 N K − 38 37 36 35 34* indicates a t -value greater than 2.(a) See table.(b) The signs of the estimated coefficients suggest that pizza consumption responds positivelyto income and negatively to age, as we would expect. All estimated coefficients are greater than twice their standard errors, indicating they are significantly different from zero using one or two-tailed tests. We note that scaling the income variable (dividing by 1000) has increased the coefficient 1000 times. (c) To comment on the signs we need to consider the marginal effects()()24E PIZZA INC AGE ∂=β+β∂()34E PIZZA AGE INC∂=β+β∂We expect β3 > 0 and β4 < 0 implying that the response of pizza consumption to incomewill be positive, but that it will decline with age. The estimates agree with these expectations. Negative signs for b 2 and b 4 imply that, as someone ages, his or her pizza consumption will decline, and the decline will be greater the higher the level of income.Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 154Exercise 7.9(c) (continued)(c) The t value for the age-income interaction variable is t = −0.1602/0.0867 = −1.847.Critical values for a 5% significance level and one and two-tailed tests are, respectively, (0.05,36) 1.688t =− and (0.025,36) 2.028t =−. Thus, if we use the prior information β4 < 0, thenwe find the interaction coefficient is significant. However, if a two-tailed test is employed, the estimated coefficient is not significant. The coefficients of INC and (INC × AGE ) have increased 1000 times due to the effects of scaling.(d) The hypotheses areH 0: β2 = β4 = 0andH 1: β2 ≠ 0 and/or β4 ≠ 0The value of the F statistic under the assumption that H 0 is true is()()()81928658060927.4058060936R U U SSE SSE J F SSE T -K −−===The 5% critical value for (2, 36) degrees of freedom is F c = 3.26 and the p -value of the testis 0.002. Thus, we reject H 0 and conclude that age does affect pizza expenditure. (e) The marginal propensity to spend on pizza is given by()34E PIZZA AGE INC∂=β+β∂Point estimates, standard errors and 95% interval estimates for this quantity, for different ages, are given in the following table.Point Standard Confidence Interval AgeEstimate Error Lower Upper20 5.870 1.977 1.861 9.878 30 4.268 1.176 1.882 6.653 40 2.665 0.605 1.439 3.892 50 1.063 0.923 −0.8092.935The interval estimates were calculated using (0.975,36) 2.0281c t t ==. As an example of how the standard errors were calculated, consider age 30. We have()n ()n ()n ()n ()23434344var 30var 30var 230cov ,13.4669000.0075228600.31421 1.38392se 30 1.1763b b b b b b b b +=++×=+×−×=+==The corresponding interval estimate is4.268 ± 2.028 × 1.176 = (1.882, 6.653)Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 155Exercise 7.9(e) (continued)(e)The point estimates for the marginal propensity to spend on pizza decline as age increases, as we would expect. However, the confidence intervals are relatively wide indicating that our information on the marginal propensities is not very reliable. Indeed, all the confidence intervals do overlap. (f) This model is given by212345+PIZZA INC AGE AGE INC AGE INC e =ββ+β+β×+β×+The marginal effect of income is now given by()2245+E PIZZA AGE AGE INC∂=β+ββ∂If this marginal effect is to increase with age, up to a point, and then decline, then β5 < 0. The sign of the estimated coefficient b 5 = 0.0055 did not agree with this anticipation. However, with a t value of t = 0.0055/0.0064 = 0.86, it is not significantly different from zero.(g)Two ways to check for collinearity are (i) to examine the simple correlations between each pair of variables in the regression, and (ii) to examine the R 2 values from auxiliary regressions where each explanatory variable is regressed on all other explanatory variables in the equation. In the tables below there are 3 simple correlations greater than 0.94 in part (f) and 5 in part (g). The number of auxiliary regressions with R 2s greater than 0.99 is 3 for part (f) and 4 for part (g). Thus, collinearity is potentially a problem. Examining the estimates and their standard errors confirms this fact. In both cases there are no t -values which are greater than 2 and hence no coefficients are significantly different from zero. None of the coefficients are reliably estimated. In general, including squared and cubed variables can lead to collinearity if there is inadequate variation in a variable.Simple CorrelationsAGE AGE INC ×2AGE INC × 3AGE INC ×INC 0.4685 0.9812 0.9436 0.8975 AGE0.5862 0.6504 0.6887 AGE INC × 0.9893 0.9636 2AGE INC ×0.9921R 2 Values from Auxiliary RegressionsLHS variableR 2 in part (f) R 2 in part (g)INC0.99796 0.99983 AGE0.68400 0.82598 AGE INC × 0.99956 0.99999 2AGE INC × 0.99859 0.999993AGE INC × 0.99994Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 156EXERCISE 7.10(a) The estimated equation with gender (FEMALE ) included, and with standard errors written in parentheses, isn ()()()()461.86408.18280.0024190.2581 (se)51.3441 1.55010.000427.7681PIZZA AGE INCOME FEMALE =−+−The t -value for gender is 190.258127.7681 6.8517t =−=− indicating that it is a relevantexplanatory variable. Including it in the model has led to substantial changes in the coefficients of the remaining variables.(b) When level of educational attainment is included the estimated model, with the standarderrors in parentheses, becomesn ()()()()317.38988.30140.002990.7944 (se)83.3909 2.32630.000757.8402PIZZAAGE INCOME HS =−++()()1.680273.204762.662192.0859COLLEGE GRAD−−None of the dummy variable coefficients are significant, casting doubt on the relevance of education as an explanatory variable. Also, including the education dummies has had little impact on the remaining coefficient estimates. To confirm the lack of evidence supporting the inclusion of education, we need to use an F test to jointly test whether the coefficients of HS, COLLEGE and GRAD are all zero. The value of this statistic is()()()63563753944632.020*********R U U SSE SSE J F SSE N K −−===−The 5% critical value for (3, 34) degrees of freedom is F c = 3.05; the p -value is 0.13. Wecannot conclude that level of educational attainment influences pizza consumption. (c) To test this hypothesis we estimate a model where the dummy variable gender (FEMALE ) interacts with every other variable in the equation. The estimated equation, with standard errors in parentheses, isn ()()()()451.36059.36320.0036208.3393 (se)63.9450 1.91550.000796.5078PIZZA AGE INCOME FEMALE =−+−()()2.83370.00183.08710.0008AGE×FEMALE INCOME×FEMALE−Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 157Exercise 7.10(c) (continued)(c)To test the hypothesis that the regression equations for males and females are identical, we test jointly whether the coefficients of FEMALE , AGE ×FEMALE , INCOME ×FEMALE are all zero. Note that individual t tests on each of these coefficients do not suggest gender is relevant. However, when we take all variables together, the F value for jointly testing their coefficients is()()()635636.7244466.5318.1344244466.534R U U SSE SSE J F SSE N K −−===−This value is greater than F c = 2.866 which is the 5% critical value for (3, 36) degrees offreedom. The p -value is 0.0000. Thus, we reject the null hypothesis that males and females have identical pizza expenditure equations. This result implies different equations should be used to model pizza expenditure for males, and that for females. It does not say how the equations differ. For example, all their coefficients could be different, or simply modelling different intercepts might be adequate.Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 158EXERCISE 7.11(a) The estimated result, with standard errors in parentheses, isn ()()()()161.4654 2.97740.009070.00016(se)120.6634 3.35210.003670.0000867PIZZA AGE INCOME INCOME×AGE =−+−This is identical to the result reported in 7.4.(b) From the sample we obtain average age = 33.475 and average income = 42,925. Thus, the required marginal effect of income isn ()0.009070.0001633.4750.00371E PIZZA INCOME∂=−×=∂Using computer software, we find the standard error of this estimate to be 0.000927, and the t value for testing whether the marginal effect is significantly different from zero is t =0.003710.000927 4.00=. The corresponding p -value is 0.0003 leading us to conclude that the marginal income effect is statistically significant at a 1% level of significance.(c) A 95% interval estimate for the marginal income effect is given by0.00371 ± 2.0281 × 0.000927 = (0.00183, 0.00559)(d) The marginal effect of age for an individual of average income is given byn ()()E PIZZA AGE ∂∂= −2.9774 − 0.00016INCOME = −2.9774 − 0.00016 × 42,925 = −9.854 Using computer software, we find the standard error of this estimate to be 2.5616, and thet value for testing whether the marginal effect is significantly different from zero is 9.8542.5616 3.85t =−=−The p -value of the test is 0.0005, implying that the marginal age effect is significantlydifferent from zero at a 1% level of significance. (e) A 95% interval estimate for the marginal age effect is given by −9.854 ± 2.0281 × 2.5616 = (−15.05, −4.66)Chapter 7, Exercise Solutions, Principles of Econometrics, 3e 159Exercise 7.11 (continued)(f)Important pieces of information for Gutbusters are the responses of pizza consumption to age and income. It is helpful to know the demand for pizzas in young and old communities and in high and low income areas. A good starting point in an investigation of this kind is to evaluate the responses at average age and average income. Such an evaluation will indicate whether there are noticeable responses, and, if so, give some idea of their magnitudes. The two responses are estimated asn ()E PIZZA INCOME ∂∂ = 0.0037n ()()E PIZZA AGE ∂∂ = −9.85Both these estimates are significantly different from zero at a 1% level of significance. They suggest that increasing income will increase pizza consumption, but, as a community ages, its demand for pizza declines. Interval estimates give an indication of the reliability of the estimated responses. In this context, we estimate that the income response lies between 0.0018 and 0.0056, while the age response lies between −15.05 and −4.66.。

经济学原理曼昆课后答案chapter7

Problems and Applications1. If an early freeze in California sours the lemon crop, the supply curve for lemons shiftsto the left, as shown in Figure 7-5. The result is a rise in the price of lemons and adecline in consumer surplus from A + B + C to just A. So consumer surplus declines by the amount B + C.Figure 7-5In the market for lemonade, the higher cost of lemons reduces the supply of lemonade, as shown in Figure 7-6. The result is a rise in the price of lemonade and a decline in consumer surplus from D + E + F to just D, a loss of E + F. Note that an event that affects consumer surplus in one market often has effects on consumer surplus in other markets.Figure 7-62. A rise in the demand for French bread leads to an increase in producer surplus in themarket for French bread, as shown in Figure 7-7. The shift of the demand curve leads to an increased price, which increases producer surplus from area A to area A + B + C.Figure 7-7The increased quantity of French bread being sold increases the demand for flour, as shown in Figure 7-8. As a result, the price of flour rises, increasing producer surplus from area D to D + E + F. Note that an event that affects producer surplus in onemarket leads to effects on producer surplus in related markets.Figure 7-83. a. Bert’s demand schedule is:Price Quantity DemandedMore than $7 0$5 to $7 1$3 to $5 2$1 to $3 3$1 or less 4Bert’s demand curve is shown in Figure 7-9.Figure 7-9b. When the price of a bottle of water is $4, Bert buys two bottles of water. Hisconsumer surplus is shown as area A in the figure. He values his first bottle ofwater at $7, but pays only $4 for it, so has consumer surplus of $3. He valueshis second bottle of water at $5, but pays only $4 for it, so has consumersurplus of $1. Thus Bert’s total consumer surplus is $3 + $1 = $4, which isthe area of A in the figure.c. When the price of a bottle of water falls from $4 to $2, Bert buys three bottlesof water, an increase of one. His consumer surplus consists of both areas Aand B in the figure, an increase in the amount of area B. He gets consumersurplus of $5 from the first bottle ($7 value minus $2 price), $3 from thesecond bottle ($5 value minus $2 price), and $1 from the third bottle ($3 valueminus $2 price), for a total consumer surplus of $9. Thus consumer surplusrises by $5 (which is the size of area B) when the price of a bottle of water fallsfrom $4 to $2.4. a. Ernie’s supply schedule for water is:Price Quantity SuppliedMore than $7 4$5 to $7 3$3 to $5 2$1 to $3 1Less than $1 0Ernie’s supply curve is shown in Figure 7-10.Figure 7-10b. When the price of a bottle of water is $4, Ernie sells two bottles of water. Hisproducer surplus is shown as area A in the figure. He receives $4 for his firstbottle of water, but it costs only $1 to produce, so Ernie has producer surplusof $3. He also receives $4 for his second bottle of water, which costs $3 toproduce, so he has producer surplus of $1. Thus Ernie’s total producersurplus is $3 + $1 = $4, which is the area of A in the figure.c. When the price of a bottle of water rises from $4 to $6, Ernie sells three bottlesof water, an increase of one. His producer surplus consists of both areas Aand B in the figure, an increase by the amount of area B. He gets producersurplus of $5 from the first bottle ($6 price minus $1 cost), $3 from the secondbottle ($6 price minus $3 cost), and $1 from the third bottle ($6 price minus $5price), for a total producer surplus of $9. Thus producer surplus rises by $5(which is the size of area B) when the price of a bottle of water rises from $4 to$6.5. a. From Ernie’s supply schedule and Bert’s demand schedule, the quantitydemanded and supplied are:Only a price of $4 brings supply and demand into equilibrium, with anequilibrium quantity of 2.b. At a price of $4, consumer surplus is $4 and producer surplus is $4, as shownin problems 3 and 4. Total surplus is $4 + $4 = $8.c. If Ernie produced one fewer bottle, his producer surplus would decline to $3,as shown in problem 4. If Bert consumed one fewer bottle, his consumersurplus would decline to $3, as shown in problem 3. So total surplus woulddecline to $3 + $3 = $6.d. If Ernie produced one additional bottle of water, his cost would be $5, but theprice is only $4, so his producer surplus would decline by $1. If Bertconsumed one additional bottle of water, his value would be $3, but the priceis $4, so his consumer surplus would decline by $1. So total surplus declinesby $1 + $1 = $2.精品文档6. a. The effect of falling production costs in the market for stereos results in a shiftto the right in the supply curve, as shown in Figure 7-11. As a result, theequilibrium price of stereos declines and the equilibrium quantity increases.b. The decline in the price of stereos increases consumer surplus from area A to A+ B + C + D, an increase in the amount B + C + D. Prior to the shift in supply,producer surplus was areas B + E (the area above the supply curve and belowthe price). After the shift in supply, producer surplus is areas E + F + G. Soproducer surplus changes by the amount F + G - B, which may be positive ornegative. The increase in quantity increases producer surplus, while thedecline in the price reduces producer surplus. Since consumer surplus risesby B + C + D and producer surplus rises by F + G - B, total surplus rises by C +D + F + G.c. If the supply of stereos is very elastic, then the shift of the supply curvebenefits consumers most. To take the most dramatic case, suppose thesupply curve were horizontal, as shown in Figure 7-12. Then there is noproducer surplus at all. Consumers capture all the benefits of fallingproduction costs, with consumer surplus rising from area A to area A + B.Figure 7-11精品文档Figure 7-127. Figure 7-13 shows supply and demand curves for haircuts. Supply equals demand ata quantity of three haircuts and a price between $4 and $5. Firms A, C, and D shouldcut the hair of Sally Jessy, Jerry, and Montel. Oprah’s willingness to pay is too low and firm B’s costs are too high, so they do not participate. The maximum total surplus is the area between the demand and supply curves, which totals $11 ($8 value minus $2 cost for the first haircut, plus $7 value minus $3 cost for the second, plus $5 valueminus $4 cost for the third).Figure 7-13精品文档8. a. The effect of falling production costs in the market for computers results in ashift to the right in the supply curve, as shown in Figure 7-14. As a result, theequilibrium price of computers declines and the equilibrium quantity increases.The decline in the price of computers increases consumer surplus from area Ato A + B + C + D, an increase in the amount B + C + D.Figure 7-14Prior to the shift in supply, producer surplus was areas B + E (the area abovethe supply curve and below the price). After the shift in supply, producersurplus is areas E + F + G. So producer surplus changes by the amount F + G- B, which may be positive or negative. The increase in quantity increasesproducer surplus, while the decline in the price reduces producer surplus.Since consumer surplus rises by B + C + D and producer surplus rises by F + G- B, total surplus rises by C + D + F + G.Figure 7-15b. Since adding machines are substitutes for computers, the decline in the priceof computers means that people substitute computers for adding machines,shifting the demand for adding machines to the left, as shown in Figure 7-15.The result is a decline in both the equilibrium price and equilibrium quantity of adding machines. Consumer surplus in the adding-machine market changes from area A + B to A + C, a net gain of C - B. Producer surplus changes from area C + D + E to area E, a net loss of C + D. Adding machine producers are sad about technological advance in computers because their producer surplus declines.c. Since software and computers are complements, the decline in the price andincrease in the quantity of computers means that people’s demand forsoftware increases, shifting the demand for software to the right, as shown in Figure 7-16. The result is an increase in both the price and quantity ofsoftware. Consumer surplus in the software market changes from B + C to A + B, a net increase of A - C. Producer surplus changes from E to C + D + E, an increase of C + D, so software producers should be happy about thetechnological progress in computers.d. Yes, this analysis helps explain why Bill Gates is one the world’s richest men,since his company produces a lot of software that’s a complement withcomputers and there has been tremendous technological advance incomputers.Figure 7-169. a. Figure 7-17 illustrates the demand for medical care. If each procedure has aprice of $100, quantity demanded will be Q1 procedures.Figure 7-17b. If consumers pay only $20 per procedure, the quantity demanded will be Q2procedures. Since the cost to society is $100, the number of proceduresperformed is too large to maximize total surplus. The quantity thatmaximizes total surplus is Q1 procedures, which is less than Q2.c. The use of medical care is excessive in the sense that consumers getprocedures whose value is less than the cost of producing them. As a result,the economy’s total surplus is reduced.d. To prevent this excessive use, the consumer must bear the marginal cost ofthe procedure. But this would require eliminating insurance. Anotherpossibility would be that the insurance company, which pays most of themarginal cost of the procedure ($80, in this case) could decide whether theprocedure should be performed. But the insurance company doesn’t get thebenefits of the procedure, so its decisions may not reflect the value to theconsumer.10. a. Figure 7-18 illustrates the effect of the drought. The supply curve shifts tothe left, leading to a rise in the equilibrium price from P1 to P2 and a decline inthe equilibrium quantity from Q1 to Q2.Figure 7-18b. If the price of water is not allowed to change, there will be an excess demandfor water, with the shortage shown on the figure as the difference between Q1and Q3.c. The system for allocating water is inefficient because it no longer allocateswater to those who value it most highly. Some people who value water atmore than its cost of production will be unable to obtain it, so society’s totalsurplus isn’t maximized.The allocation system seems unfair as well. Water is allocated simply on pastusage, rewarding past wastefulness. If a family’s demand for water increases,say because of an increase in family size, the policy doesn’t allow them toobtain more water. Poor families, who probably used water mostly fornecessary uses like drinking, would suffer more than wealthier families whowould have to cut back only on luxury uses of water like operating backyardfountains and pools. However, the policy also keeps the price of water lower, which benefits poor families, since otherwise more of their family budgetwould have to go for water.d. If the city allowed the price of water to rise to its equilibrium price P2, theallocation would be more efficient. Quantity supplied would equal quantitydemanded and there would be no shortage. Total surplus would bemaximized.Whether the market allocation would be more or less fair than theproportionate reduction in water under the old policy is difficult to say, but it is likely to be more fair. Notice that the quantity supplied would be higher (Q2) in this case than under the water restrictions (Q3), so there’s less reduction in water usage. To make the market solution even more fair, the governmentcould provide increased tax relief or welfare payments for poor families whosuffer from paying the higher water prices.。

曼昆微观经济学课后练习英文答案(第七章)

WHAT’S NEW IN THE SIXTH EDITION:There are no major changes to this chapter.LEARNING OBJECTIVES:By the end of this chapter, students should understand:➢ the link between buyers’ willingness to pay for a good and the demand curve.➢ how to define and measure consumer surplus.➢ the link between sellers’ costs of producing a good and the supply curve.➢ how to define and measure producer surplus.➢ that the equilibrium of supply and demand maximizes total surplus in a market.CONTEXT AND PURPOSE:Chapter 7 is the first chapter in a three-chapter sequence on welfare economics and market efficiency. Chapter 7 employs the supply and demand model to develop consumer surplus and producer surplus as a measure of welfare and market efficiency. These concepts are then utilized in Chapters 8 and 9 to determine the winners and losers from taxation and restrictions on international trade.The purpose of Chapter 7 is to develop welfare economics —the study of how the allocation ofresources affects economic well-being. Chapters 4 through 6 employed supply and demand in a positive framework, which focused on the question, “What is the equilibrium price and quantity in a market?” This chapter now addresses the normative question, “Is the equ ilibrium price and quantity in a market the best possible solution to the resource allocation problem, or is it simply the price and quantity thatbalance supply and demand?” Students will discover that under most circumstances the equilibrium price and quantity is also the one that maximizes welfare.7CONSUMERS, PRODUCERS, AND THE EFFICIENCY OF MARKETSKEY POINTS:• Consumer surplus equals buyers’ willingness to pay for a good minus the amount they actually pay for it, and it measures the benefit buyers get from participating in a market. Consumer surplus can be computed by finding the area below the demand curve and above the price.• Producer surplus equals the amount sellers receive for their goods minus their costs of production, and it measures the benefit sellers get from participating in a market. Producer surplus can be computed by finding the area below the price and above the supply curve.•An allocation of resources that maximizes the sum of consumer and producer surplus is said to be efficient. Policymakers are often concerned with the efficiency, as well as the equality, of economic outcomes.• The equilibrium of supply and demand maximizes the sum of consumer and producer surplus. That is,the invisible hand of the marketplace leads buyers and sellers to allocate resources efficiently.• Markets do not allocate resources efficiently in the presence of market failures such as market poweror externalities.CHAPTER OUTLINE:I. Definition of welfare economics: the study of how the allocation of resources affectseconomic well-being.II. Consumer SurplusA. Willingness to Pay1. Definition of willingness to pay: the maximum amount that a buyer will pay for agood.2. Example: You are auctioning a mint-condition recording of Elvis Presley’s first album. Fourbuyers show up. Their willingness to pay is as follows:If the bidding goes to slightly higher than $80, all buyers drop out except forJohn. Because John is willing to pay more than he has to for the album, hederives some benefit from participating in the market.3. Definition of consumer surplus: the amount a buyer is willing to pay for a goodminus the amount the buyer actually pays for it.4. Note that if you had more than one copy of the album, the price in the auction would end upbeing lower (a little over $70 in the case of two albums) and both John and Paul would gain consumer surplus.B. Using the Demand Curve to Measure Consumer Surplus1. We can use the information on willingness to pay to derive a demand curve for the rare ElvisPresley album.PriceBuyersQuantity DemandedMore than $100 None 0 $80 to $100 John1 $70 to $80 John, Paul2 $50 to $70 John, Paul, George3 $50 or lessJohn, Paul, George, Ringo42. At any given quantity, the price given by the demand curve reflects the willingness to pay ofthe marginal buyer . Because the demand curve shows the buyers’ willingness to pay, we can use the demand curve to measure consumer surplus.Figure 1 “This represents the demand curve for the time machine. Consumer surplus is the difference between what consumers are willing to pay and the amount they actually have to pay. The market price will deter mine who uses the time machine and how much surplus they keep.”“If the price of a time machine ride was $500, three rides would be sold—one to Scott, one to Carol, and one to Steve. Jeanne is not willing to pay $500, so she wouldn’t time travel.”“We c an calculate the consumer surplus of three time trips. Scott would pay $3,000 but only pays $500, leaving $2,500 of net benefits.” (Put these numbers on the board.) “Carol has net benefits of $2,000. Steve has $300 in net benefits. Adding up these net savings gives $4,800 in consumer surplus.”Points for DiscussionThe consumer surplus depends on a good’s selling price and the number of consumers who are willing to purchase the good at that price. The lower the price, the greater the consumer surplus.3. Consumer surplus can be measured as the area below the demand curve and above the price. C. How a Lower Price Raises Consumer Surplus1. As price falls, consumer surplus increases for two reasons.a. Those already buying the product will receive additional consumer surplus because theyare paying less for the product than before (area A on the graph).b. Because the price is now lower, some new buyers will enter the market and receiveconsumer surplus on these additional units of output purchased (area B on the graph).D. What Does Consumer Surplus Measure?1. Remember that consumer surplus is the difference between the amount that buyers arewilling to pay for a good and the price that they actually pay.2. Thus, it measures the benefit that consumers receive from the good as the buyersthemselves perceive it.Figure 2Figure 3It is important to stress that consumer surplus is measured in monetary terms. Consumer surplus gives us a way to place a monetary cost on inefficient market outcomes (due to government involvement or market failure).III. Producer SurplusA. Cost and the Willingness to Sell1. Definition of cost: the value of everything a seller must give up to produce a good .2. Example: You want to hire someone to paint your house. You accept bids for the work fromfour sellers. Each painter is willing to work if the price you will pay exceeds her opportunity cost. (Note that this opportunity cost thus represents willingness to sell.) The costs are:3. Bidding will stop when the price gets to be slightly below $600. All sellers will drop out exceptfor Grandma. Because Grandma receives more than she would require to paint the house, she derives some benefit from producing in the market.4. Definition of producer surplus: the amount a seller is paid for a good minus theseller’s cost of providing it.5. Note that if you had more than one house to paint, the price in the auction would end upbeing higher (a little under $800 in the case of two houses) and both Grandma and Georgia would gain producer surplus.ALTERNATIVE CLASSROOM EXAMPLE:Review the material on price ceilings from Chapter 6. Redraw the market for two-bedroom apartments in your town. Draw in a price ceiling below the equilibrium price.Then go through:▪ consumer surplus before the price ceiling is put into place. ▪ consumer surplus after the price ceiling is put into place.B. Using the Supply Curve to Measure Producer Surplus1. We can use the information on cost (willingness to sell) to derive a supply curve for housepainting services.Price Sellers Quantity Supplied$900 or more Mary, Frida, Georgia, Grandma 4$800 to $900 Frida, Georgia, Grandma 3$600 to $800 Georgia, Grandma 2$500 to $600 Grandma 1less than $500 None 02. At any given quantity, the price given by the supply curve represents the cost of the marginalseller. Because the supply curve shows the sellers’ cost (willingness to sell), we can use the supply curve to measure producer surplus.3. Producer surplus can be measured as the area above the supply curve and below the price. Figure 4Figure 5C. How a Higher Price Raises Producer Surplus1. As price rises, producer surplus increases for two reasons.a. Those already selling the product will receive additional producer surplus because theyare receiving more for the product than before (area C on the graph).b. Because the price is now higher, some new sellers will enter the market and receiveproducer surplus on these additional units of output sold (area D on the graph).D. Producer surplus is used to measure the economic well-being of producers, much like consumersurplus is used to measure the economic well-being of consumers.Figure 6ALTERNATIVE CLASSROOM EXAMPLE:Review the material on price floors from Chapter 6. Redraw the market for an agriculturalproduct such as corn. Draw in a price support above the equilibrium price.Then go through:▪ producer surplus before the price support is put in place.▪ producer surplus after the price support is put in place.Make sure that you discuss the cost of the price support to taxpayers.Pretty Woman, Chapter 6. Vivien (Julia Roberts) and Edward (Richard Gere)negotiate a price. Afterward, Vivien reveals she would have accepted a lower price,while Edward admits he would have paid more. If you have done a good job ofintroducing consumer and producer surplus, you will see the light bulbs go off aboveyour students’ heads as they watch this clip.IV. Market EfficiencyA. The Benevolent Social Planner1. The economic well-being of everyone in society can be measured by total surplus, which isthe sum of consumer surplus and producer surplus:Total Surplus = Consumer Surplus + Producer SurplusTotal Surplus = (Value to Buyers – Amount Paid by Buyers) + (Amount Received by Sellers – Cost to Sellers)Because the Amount Paid by Buyers = Amount Received by Sellers:2. Definition ofefficiency: the property of a resource allocation of maximizing thetotal surplus received by all members of society .3. Definition of equality: the property of distributing economic prosperity uniformlythe members of society .B. Evaluating the Market EquilibriumTotal Surplus = Value to Buyers Cost to Sellers Figure 7Now might be a good time to point out that many government policies involve atrade-off between efficiency and equity. When you evaluate government policies, like price ceilings or floors, you can explain them in terms of equity and efficiency.1. At the market equilibrium price:a. Buyers who value the product more than the equilibrium price will purchase the product;those who do not, will not purchase the product. In other words, the free marketallocates the supply of a good to the buyers who value it most highly, as measured bytheir willingness to pay.b. Sellers whose costs are lower than the equilibrium price will produce the product; thosewhose costs are higher, will not produce the product. In other words, the free marketallocates the demand for goods to the sellers who can produce it at the lowest cost.2. Total surplus is maximized at the market equilibrium.Figure 8a. At any quantity of output smaller than the equilibrium quantity, the value of the productto the marginal buyer is greater than the cost to the marginal seller so total surpluswould rise if output increases.b. At any quantity of output greater than the equilibrium quantity, the value of the productto the marginal buyer is less than the cost to the marginal seller so total surplus wouldrise if output decreases.3. Note that this is one of the reasons that economists believe Principle #6: Markets are usuallya good way to organize economic activity.It would be a good idea to remind students that there are circumstances when themarket process does not lead to the most efficient outcome. Examples includesituations such as when a firm (or buyer) has market power over price or when thereare externalities present. These situations will be discussed in later chapters.C. In the News: Ticket Scalping1. Ticket scalping is an example of how markets work to achieve an efficient outcome.2. This article from The Boston Globe descri bes economist Chip Case’s experience with ticketscalping.D. Case Study: Should There Be a Market in Organs?1. As a matter of public policy, people are not allowed to sell their organs.a. In essence, this means that there is a price ceiling on organs of $0.b. This has led to a shortage of organs.2. The creation of a market for organs would lead to a more efficient allocation of resources,but critics worry about the equity of a market system for organs.V. Market Efficiency and Market FailureA. To conclude that markets are efficient, we made several assumptions about how markets worked.1. Perfectly competitive markets.2. No externalities.B. When these assumptions do not hold, the market equilibrium may not be efficient.C. When markets fail, public policy can potentially remedy the situation.SOLUTIONS TO TEXT PROBLEMS:Quick Quizzes1. Figure 1 shows the demand curve for turkey. The price of turkey is P1 and the consumersurplus that results from that price is denoted CS. Consumer surplus is the amount a buyer iswilling to pay for a good minus the amount the buyer actually pays for it. It measures thebenefit to buyers of participating in a market.Figure 1 Figure 22. Figure 2 shows the supply curve for turkey. The price of turkey is P1 and the producersurplus that results from that price is denoted PS. Producer surplus is the amount sellers arepaid for a good minus the sellers’ cost of providing it (measured by the supply curve). Itmeasures the benefit to sellers of participating in a market.Figure 33. Figure 3 shows the supply and demand for turkey. The price of turkey is P1, consumersurplus is CS, and producer surplus is PS. Producing more turkeys than the equilibriumquantity would lower total surplus because the value to the marginal buyer would be lowerthan the cost to the marginal seller on those additional units.Questions for Review1. The price a buyer is willing to pay, consumer surplus, and the demand curve are all closelyrelated. The height of the demand curve represents the willingness to pay of the buyers.Consumer surplus is the area below the demand curve and above the price, which equals theprice that each buyer is willing to pay minus the price actually paid.2. Sellers' costs, producer surplus, and the supply curve are all closely related. The height of thesupply curve represents the costs of the sellers. Producer surplus is the area below the priceand above the supply curve, which equals the price received minus each seller's costs ofproducing the good.Figure 43. Figure 4 shows producer and consumer surplus in a supply-and-demand diagram.4. An allocation of resources is efficient if it maximizes total surplus, the sum of consumersurplus and producer surplus. But efficiency may not be the only goal of economicpolicymakers; they may also be concerned about equity the fairness of the distribution ofwell-being.5. The invisible hand of the marketplace guides the self-interest of buyers and sellers intopromoting general economic well-being. Despite decentralized decision making and self-interested decision makers, free markets often lead to an efficient outcome.6. Two types of market failure are market power and externalities. Market power may causemarket outcomes to be inefficient because firms may cause price and quantity to differ fromthe levels they would be under perfect competition, which keeps total surplus from beingmaximized. Externalities are side effects that are not taken into account by buyers and sellers.As a result, the free market does not maximize total surplus.Problems and Applications1. a. Consumer surplus is equal to willingness to pay minus the price paid. Therefore,Melissa’s willingness to pay must be $200 ($120 + $80).b. Her consumer surplus at a price of $90 would be $200 − $90 = $110.c. If the price of an iPod was $250, Melissa would not have purchased one because theprice is greater than her willingness to pay. Therefore, she would receive no consumersurplus.2. If an early freeze in California sours the lemon crop, the supply curve for lemons shifts to theleft, as shown in Figure 5. The result is a rise in the price of lemons and a decline inconsumer surplus from A + B + C to just A. So consumer surplus declines by the amount B +C.Figure 5 Figure 6In the market for lemonade, the higher cost of lemons reduces the supply of lemonade, asshown in Figure 6. The result is a rise in the price of lemonade and a decline in consumersurplus from D + E + F to just D, a loss of E + F. Note that an event that affects consumersurplus in one market often has effects on consumer surplus in other markets.3. A rise in the demand for French bread leads to an increase in producer surplus in the marketfor French bread, as shown in Figure 7. The shift of the demand curve leads to an increased price, which increases producer surplus from area A to area A + B + C.Figure 7The increased quantity of French bread being sold increases the demand for flour, as shown in Figure 8. As a result, the price of flour rises, increasing producer surplus from area D to D + E + F. Note that an event that affects producer surplus in one market leads to effects on producer surplus in related markets.Figure 84. a. Bert’s demand schedule is:Price Quantity DemandedMore than $7 0$5 to $7 1$3 to $5 2$1 to $3 3$1 or less 4Bert’s demand curve is shown in Figure 9.Figure 9b. When the price of a bottle of water is $4, Bert buys two bottles of water. His consumersurplus is shown as area A in the figure. He values his first bottle of water at $7, butpays only $4 for it, so has consumer surplus of $3. He values his second bottle of water at $5, but pays only $4 for it, so has consumer surplus of $1. Thus Bert’s total consumer surplus is $3 + $1 = $4, which is the area of A in the figure.c. When the price of a bottle of water falls from $4 to $2, Bert buys three bottles of water,an increase of one. His consumer surplus consists of both areas A and B in the figure, an increase in the amount of area B. He gets consumer surplus of $5 from the first bottle($7 value minus $2 price), $3 from the second bottle ($5 value minus $2 price), and $1 from the third bottle ($3 value minus $2 price), for a total consumer surplus of $9. Thus consumer surplus rises by $5 (which is the size of area B) when the price of a bottle ofwater falls from $4 to $2.5. a. Ernie’s supply schedule for water is:Price Quantity SuppliedMore than $7 4$5 to $7 3$3 to $5 2$1 to $3 1Less than $1 0Ernie’s supply curve is shown in Figure 10.Figure 10b. When the price of a bottle of water is $4, Ernie sells two bottles of water. His producersurplus is shown as area A in the figure. He receives $4 for his first bottle of water, but itcosts only $1 to produce, so Ernie has producer surplus of $3. He also receives $4 for his second bottle of water, which costs $3 to produce, so he has producer surplus of $1.Thus Ernie’s total producer surplus is $3 + $1 = $4, which is the area of A in the figure.c. When the price of a bottle of water rises from $4 to $6, Ernie sells three bottles of water,an increase of one. His producer surplus consists of both areas A and B in the figure, anincrease by the amount of area B. He gets producer surplus of $5 from the first bottle($6 price minus $1 cost), $3 from the second bottle ($6 price minus $3 cost), and $1from the third bottle ($6 price minus $5 price), for a total producer surplus of $9. Thusproducer surplus rises by $5 (which is the size of area B) when the price of a bottle ofwater rises from $4 to $6.6. a. From Ernie’s supply schedule and Bert’s demand schedule, the quantity demanded andsupplied are:Price Quantity Supplied Quantity Demanded$2 1 3$4 2 2$6 3 1Only a price of $4 brings supply and demand into equilibrium, with an equilibriumquantity of two.b. At a price of $4, consumer surplus is $4 and producer surplus is $4, as shown inProblems 3 and 4 above. Total surplus is $4 + $4 = $8.c. If Ernie produced one less bottle, his producer surplus would decline to $3, as shown inProblem 4 above. If Bert consumed one less bottle, his consumer surplus would declineto $3, as shown in Problem 3 above. So total surplus would decline to $3 + $3 = $6.d. If Ernie produced one additional bottle of water, his cost would be $5, but the price isonly $4, so his producer surplus would decline by $1. If Bert consumed one additionalbottle of water, his value would be $3, but the price is $4, so his consumer surplus would decline by $1. So total surplus declines by $1 + $1 = $2.7. a. The effect of falling production costs in the market for stereos results in a shift to theright in the supply curve, as shown in Figure 11. As a result, the equilibrium price ofstereos declines and the equilibrium quantity increases.Figure 11b. The decline in the price of stereos increases consumer surplus from area A to A + B + C+ D, an increase in the amount B + C + D. Prior to the shift in supply, producer surpluswas areas B + E (the area above the supply curve and below the price). After the shift in supply, producer surplus is areas E + F + G. So producer surplus changes by the amountF +G – B, which may be positive or negative. The increase in quantity increasesproducer surplus, while the decline in the price reduces producer surplus. Becauseconsumer surplus rises by B + C + D and producer surplus rises by F + G – B, totalsurplus rises by C + D + F + G.c. If the supply of stereos is very elastic, then the shift of the supply curve benefitsconsumers most. To take the most dramatic case, suppose the supply curve werehorizontal, as shown in Figure 12. Then there is no producer surplus at all. Consumerscapture all the benefits of falling production costs, with consumer surplus rising fromarea A to area A + B.Figure 128. Figure 13 shows supply and demand curves for haircuts. Supply equals demand at a quantityof three haircuts and a price between $4 and $5. Firms A, C, and D should cut the hair of Ellen, Jerry, and Phil. Oprah’s willingness to pay is too low and firm B’s costs are too high, so they do not participate. The maximum total surplus is the area between the demand and supply curves, which totals $11 ($8 value minus $2 cost for the first haircut, plus $7 value minus $3 cost for the second, plus $5 value minus $4 cost for the third).Figure 139. a. The effect of falling production costs in the market for computers results in a shift to theright in the supply curve, as shown in Figure 14. As a result, the equilibrium price ofcomputers declines and the equilibrium quantity increases. The decline in the price ofcomputers increases consumer surplus from area A to A + B + C + D, an increase in the amount B + C + D.Figure 14 Figure 15Prior to the shift in supply, producer surplus was areas B + E (the area above the supply curve and below the price). After the shift in supply, producer surplus is areas E + F + G.So producer surplus changes by the amount F + G – B, which may be positive ornegative. The increase in quantity increases producer surplus, while the decline in theprice reduces producer surplus. Because consumer surplus rises by B + C + D andproducer surplus rises by F + G – B, total surplus rises by C + D + F + G.b. Because typewriters are substitutes for computers, the decline in the price of computersmeans that people substitute computers for typewriters, shifting the demand fortypewriters to the left, as shown in Figure 15. The result is a decline in both theequilibrium price and equilibrium quantity of typewriters. Consumer surplus in thetypewriter market changes from area A + B to A + C, a net change of C – B. Producersurplus changes from area C + D + E to area E, a net loss of C + D. Typewriterproducers are sad about technological advances in computers because their producersurplus declines.c. Because software and computers are complements, the decline in the price and increasein the quantity of computers means that the demand for software increases, shifting the demand for software to the right, as shown in Figure 16. The result is an increase in both the price and quantity of software. Consumer surplus in the software market changesfrom B + C to A + B, a net change of A – C. Producer surplus changes from E to C + D + E, an increase of C + D, so software producers should be happy about the technological progress in computers.Figure 16d. Yes, this analysis helps explain why Bill Gates is one the world’s richest people, becausehis company produces a lot of software that is a complement with computers and therehas been tremendous technological advance in computers.10. a. With Provider A, the cost of an extra minute is $0. With Provider B, the cost of an extraminute is $1.b. With Provider A, my friend will purchase 150 minutes [= 150 – (50)(0)]. With Provider B,my friend would purchase 100 minutes [= 150 – (50)(1)].c. With Provider A, he would pay $120. The cost would be $100 with Provider B.Figure 17d. Figure 17 shows the friend’s demand. With Provider A, he buys 150 minu tes and hisconsumer surplus is equal to (1/2)(3)(150) – 120 = 105. With Provider B, his consumersurplus is equal to (1/2)(2)(100) = 100.e. I would recommend Provider A because he receives greater consumer surplus.11. a. Figure 18 illustrates the demand for medical care. If each procedure has a price of $100,quantity demanded will be Q1 procedures.Figure 18b. If consumers pay only $20 per procedure, the quantity demanded will be Q2 procedures.Because the cost to society is $100, the number of procedures performed is too large to maximize total surplus. The quantity that maximizes total surplus is Q1 procedures, which is less than Q2.c. The use of medical care is excessive in the sense that consumers get procedures whosevalue is less than t he cost of producing them. As a result, the economy’s total surplus is reduced.d. To prevent this excessive use, the consumer must bear the marginal cost of theprocedure. But this would require eliminating insurance. Another possibility would be that the insurance company, which pays most of the marginal cost of the procedure ($80, in this case) could decide whether the procedure should be performed. But the insurance company does not get the benefits of the procedure, so its decisions may not reflect the value to the consumer.。

Chapter 7 课后答案

Chapter 7 答案Discourse Analysis1.Define the following terms briefly.(1)discourse: a general term for examples of language use, i.e. language producedas the result of an act of communication. It refers to the larger units oflanguage such as paragraphs, conversations and interviews.(2)discourse analysis: the study of how sentences in written and spoken languageform larger meaning units such as paragraphs, conversations and interviews.(3)given information: the information that the addresser believes is known to the addressee.(4)new information: the information that the addresser believes is not knownto the addressee.(5)topic: the main center of attention in a sentence.(6)cohesion: the grammatical and/or lexical relationships between the differentelements of a text. This may be the relationship between different sentencesor different parts of a sentence.(7)coherence: the relationship that links the meanings of utterances ina discourseor of the sentences in a text.(8)discourse marker: the technical term for all the items that are used to helpconstruct discourse, such as signifying the beginning or ending of a paragraphor a turn in conversation. They are commonly used in the initial positionof an utterance and are syntactically detachable from a sentence, such aswell, I mean, now, then, first, second, finally.(9)adjacency pair: a set of two consecutive, ordered turns that “go together” in aconversation, such as sequences of question/answer, greeting/greeting, invitation/acceptance, criticism/denial.(10) preference structure: in the conversations there can be several second partsrelated to one first part, but they are not of equal status. The structural likelihoodis called preference, and this likely structure is the preference structurethat divides second parts into preferred and dispreferred. The former is thestructurally expected and the latter unexpected. In answering the question“Have you got a light?”, the reply “Here you are” is preferred and “Sorry, no, I don’t smoke” is dispr eferred.(11 presequence: the opening sequences that are used to set up some special potentialactions, such as greetings before formal conversations. “What are youdoing tonight?” can be used as a presequence if it is followed by “If nothingspecial, come over and have dinner with us please.”(12) critical discourse analysis: the analysis of language use directed at, and committedto, discovering the concealed ideological bias, injustice, inequality in the power relations among speakers and hearers.2.In the study of discourse, cohesion refers to the grammatical and/or lexical relationshipsbetween the different parts of a text. This may be the relationship betweendifferent sentences or different parts of a sentence. It concerns the questionof how sentences are explicitly linked together in a discourse by different kinds ofovert devices. Such cohesive devices include reference, substitution, ellipses, conjunction and lexical cohesion.3.one→the look-out4.them (line 4)→plant and animal species (line 3)that (line 7)→“Every ecosystem everywhere can’t be preserved intact.”it (line 7)→“Every ecosystem everywhere can’t be preserved intact.”it (1st one, line 8)→how can it be made consistent with the earlier objective?it (2nd one, line 8)→to deprive some people in some parts of the world of a pieceof their ecosystem but not others.5.It is not a coherent discourse. Although it has connection words such as a Ford–– a car and black –– Black, which look like cohesive devices, they refer to entirelydifferent things. There is a total lack of internal relation among the sentences. Atext can’t be only based on superficial connections between the words to pursuecoherence; there must be some relationship that links the meanings of the sentencesin a text, too. This text is not in line with our real experience of the way theworld is. Thus, we can’t make sense of it directly unless we are laborious to createmeaningful connections which are not actually expressed by the words and sentences.So it’s not a coheren t discourse.6.Coherence is the relationship that links the meanings of utterances ina discourse or of the sentences in a text. This extract is coherent. All the sentences (questions in fact) are organized around the topic “interview”, and they are arrang ed from the general to the more specific in a logical order so that the text is easy to follow.。

商业银行管理 ROSE 7e 课后答案chapter_07

CHAPTER 7ASSET—LIABILITY MANAGEMENT： DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTEREST-SENSITIVE AND DURATIONGAPSGoals of This Chapter： The purpose of this chapter is to explore the options bankers have today for dealing with risk – especially the risk of loss due to changing interest rates – and to see how a bank’s management can coordinate the management of its assets with the management of its liabilities in order to achieve the institution’s goals。

Key Topic In This Chapter•Asset， Liability, and Funds Management•Market Rates and Interest Rate Risk•The Goals of Interest Rate Hedging•Interest Sensitive Gap Management•Duration Gap Management•Limitations of Hedging TechniquesChapter OutlineI. Introduction: The Necessity for Coordinating Bank Asset and Liability ManagementDecisionsII。

Asset/Liability Management StrategiesA. Asset Management StrategyB。

课后习题参考答案Chap1-7

《计算机硬件》习题参考答案（仅供参考，任何问题请发邮件至yejian@）第一章一、1、D（若是无符号数，答案应为D；若是有符号数，这里未说明用的是哪种码制，且各选项位数不同） 2、A 3、A（‐128的补码是10000000，教材p11页有错） 4、A 5、C 6、D 7、C 8、C二、9、硬件系统软件系统 10、每秒钟执行百万条指令数 11、BIOS芯片 CMOS RAM芯片 12、芯片组南桥芯片北桥芯片 13、高速缓冲存储器（Cache） 14、与或非 15、地址总线AB 数据总线DB 控制总线CB 16、金手指 17、尺寸和点距分辨率刷新频率三、18、教材p2 1.1.1，控制器、运算器、存储器和输入输出设备四个部分。

19、分两种情况讨论，若堆栈的编址方式是向下增长型，压栈后SP自动减量，SP=2000H，压入8个字节，SP=2000H‐8H=1FF8H，弹出4个字节，SP=1FF8H+4H=1FFCH；若堆栈的编址方式是向上增长型，SP=2000H，压入8个字节，SP=2000H+8H=2008H，弹出4个字节，SP=2008H‐4H=2004H。

20、教材p7，先进后出FILO（First In Last Out）的原则。

21、教材p22，每条指令的执行时间没有缩短，只是让几条指令的不同操作步骤在时间上重叠，总体上加快了指令流速度，缩短了程序执行的时间。

22、教材p5，20位地址总线，主存寻址范围220=1MB。

23、教材p6‐7，略。

24、略。

第二章一、1、D 2、D（各条指令的长度不等） 3、B 4、C 5、C 6、A 7、C 8、B 9、C（8、9题不要求）二、10、232字节 11、数据 12、虚拟8086 实地址 13、并行三、14、教材p6，略。

15、教材p30，4个阶段。

16、没有，同第一章21题。

17、不一定正确，比如流水线技术的引入，程序执行的时间会小于各条指令执行的时间总和。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

第七章习题答案
7.1 ARM处理器有几种运行模式，处理器如何区别各种不同的运行模式？
ARM处理器有7中运行模式：
●用户模式（user）：ARM处理器正常的程序执行状态
●快速中断模式（fiq）：处理高速中断，用于高速数据传输或通道处理
●外部中断模式（irq）：用于普通的中断处理
●管理模式（supervisor）：操作系统使用的保护模式，系统复位后的默认模式
●中止模式（abort）：数据或指令预取中止时进入该模式
●未定义模式（undefined）：处理未定义指令，用于支持硬件协处理器的软件仿真
●系统模式（system）：运行特权级的操作系统任务
处理器使用CPSR寄存器中的M4~M0位来指示不同的运行模式。

7.2 通用寄存器中PC、CPSR和SPSR的作用各是什么？
PC：程序计数器，用于保存处理器要取的下一条指令的地址。

CPSR：当前程序状态寄存器，CPSR保存条件标志位、中断禁止位、当前处理器模式标志，以及其他一些相关的控制和状态位。

SPSR：备份程序状态寄存器，当异常发生时，SPSR用于保存CPSR的当前值，当从异常退出时，可用SPSR来恢复CPSR。

7.3 从编程的角度讲，ARM处理器的工作状态有哪两种？这两种状态之间如何转换？
从编程角度讲，ARM处理器的两种工作状态为：
●ARM状态（复位状态）：处理器执行32位的字对齐的ARM指令
●Thumb状态：处理器执行16位的半字对齐的Thumb指令
ARM指令集和Thumb指令集均有切换处理器状态的指令，并可在两种工作状态之间切换：
●进入Thumb状态：当操作数寄存器的状态位（最低位）为1时，执行BX指令就
可以进入Thumb状态。

如果处理器在Thumb状态时发生异常（异常处理要在ARM状态下执行），则当异常处理返回时自动切换到Thumb状态
●进入ARM状态：当操作数寄存器的状态位（最低位）位0时，执行BX指令就可
以进入ARM状态。

处理器进行异常处理时，把PC的值放入异常模式链接寄存器中，从异常向量地址开始执行程序，系统自动进入ARM状态
7.4 作业情况：同学们答的为：ARM支持Thumb和ARM双指令集，内核小，流水线结构；而RISC用寄存器窗口处理异常，延迟转移，单指令周期执行
7.5 哪些特征是ARM和其他RISC体系结构所共有的？
ARM和其他RISC体系结构共有的三个相同特征：
●Load/Store体系结构：也称为寄存器/寄存器体系结构或RR系统结构。

在这类机
器中，操作数和运算结果不能直接从主寄存器中存取，而是必须借用大量的标量或矢量寄存器来进行中转。

采用这一结构的处理器必然要使用更多的通用寄存器存储操作数和运算结果，由于寄存器与运算器之间的数据传输速度远高于主存与运算器之间的数据传输速度，采用这一结构有助于提高计算机整体的运行速度
●采用固定长度精简指令集：这样使得机器译码变得容易，可以通过硬件直接译码
的方式完成对指令的解析。

虽然由于与复杂指令集相比，采用精简指令集需要更多指令来完成相同的任务，但采用硬件直接译码的速度却高于采用微码方式译码。

通过采用高速缓存等提高寄存器存储速度的技术，采用固定长度精简指令集的机器可以获得更高性能
●三地址指令格式：除了除法指令外，ARM的大部分数据处理指令采用三地址指
令。

即在指令中包含了目的操作数、源操作数和第二源操作数。