上财罗大庆高宏作业2
上财金融学院高宏课件(谭继军) (2)
— Again, we are interested in the properties of s. This time we use implicit function theorem to find
∂st ∂st ∂w1 , ∂w2
rief review of implicit function theorem (see Appendix ) — Define H (st , w1 , w2 , rt ) ≡ −U1 (w1 − st ) + rt U2 (wt + rt st ) = 0, where st is endogenous variable, and w1 , w2 and rt are parameters. If U is additive separable, which ensures c1 and c2 are normal goods, then 1> U11 ∂st 1 = − ∂w = > 0, 2U ∂H ∂w1 U11 + rt 22 ∂s
∂H rU2 ∂s ∂τ = − ∂H = < 0. 2 ∂τ U11 + r (1 − τ )U22 ∂s
From
∂s ∂τ ,
only substitute effect exists, no income effect.
— Because τ only changes gross real interest rate, real income doesn’t change at all (rsi (1 − τ ) + w2 + a and τ rsi = a ⇒ rsi + w2 ). Income is compensated. — Another word: Though people’s real income doesn’t change, they still response to the tax by decreasing saving. Another word: No neutral tax on price (interest rate), even if real income doesn’t change.
上财金融学院高宏课件(谭继军) (3)
Graphically (insert a graph) How can the government solve this problem?
— Using less centralized methods, short of taking over the entire economy as done in the G.R. administration.
— Transfers from young to old, which is called social security.
—
Look at
U1(w1−k) U2(w2+f (k))
.
Such transfers mean
U1(w1−k−τ ) U2(w2+f (k)+σ)
.
— For a given k, these transfers increase c2 and lower c1.
— The C.E. tells us the best that individuals can do for a given budget.
— It may not be the best possible allocation. The key to understanding these models is to distinguish between the decision of individuals and those of the social planner.
A social planner’s problem: maximizing utility of future generations, ignoring the initial old (Golden Rule of Phelps (AER, 1965)).
上财高级计量经济学朱东明作业2
Econometrics I,Fall2012Assignment2The due date for this assignment is Monday Nov.5.1.The…le consumption.txt contains data on real personal disposable income and con-sumption expenditures in Canada,seasonally adjusted in1986dollars,from the…rst quarter of1947until the last quarter of1996.The layout of the data is explained at the end of the…le.(a)The simplest imaginable model of the Canadian consumption function would haveconsumption expenditures as the dependent variable,and a constant and personaldisposable income as explanatory variables.Run this regression for the period1953:1to1996:4.What is your estimate of the marginal propensity to consumeout of disposable income?(b)Plot a graph of the OLS residuals for the consumption function regression againsttime.All modern regression packages will generate these residuals for you onrequest.Does the appearance of the residuals suggest that this model of theconsumption function is well speci…ed?(c)Simulate the consumption function model you have just estimated in(a)for thesame sample period,using the actual data on disposable income.For the para-meters,use the OLS estimates obtained in(a).For the error terms,use drawingsfrom the N(0;s2)distribution,where s2is the estimate of the error variance pro-duced by the regression package.(d)Run a regression using the simulated consumption data as the dependent vari-able and the constant and disposable income as explanatory variables.Are theparameter estimates the same as those obtained using the real data?Why or whynot?(e)Plot the residuals from the regression with simulated data.Does the plot looksubstantially di¤erent from the one obtained using the real data?It should!2.The…le tbrate.txt contains data for1950:1to1996:4for three series:r t,the interestrate on90-day treasury bills, t,the rate of in‡ation,and y t,the logarithm of real GDP.For the period1950:4to1996:4,run the regression4r t= 1+ 2 t 1+ 34y t 1+ 44r t 1+ 5r t 2+u t;(1) where4is the…rst-di¤erence operator,de…ned so that4r t=r t r t 1.(a)Plot the residuals and…tted values against time.Then regress the residuals on the…tted values and on a constant.What do you learn from this second regression?Now regress the…tted values on the residuals and on a constant.What do youlearn from this third regression?(b)For the same sample period,regress4r t on a constant,4y t 1,4r t 1and4r t 2.Save the residuals from this regression,and call them b e t.Then regress t 1on aconstant,4y t 1,4r t 1and4r t 2.Save the residuals from this regression,andcall them b v t .Now regress b e t on b v t .How are the estimated coe¢cient and the residuals from this last regression related to anything that you obtained when you estimated regression (1)?(c)Calculate the diagonal elements of the hat matrix P X for regression (1)anduse them to calculate a measure of leverage,h t X 0t [X 0X ] 1X t ,where X i =(x t;1;:::;x t;k )0.We say that observations for which h t is large have high leverage or are leverage points.A leverage point is not necessarily in‡uential,but it has the potential to be in‡uential.Plot this measure against time.On the basis of this plot,which observations seem to have unusually high leverage?3.Consider the following linear regression:y =X +"=X 1 1+X 2 2+",where y is n 1,X 1is n k 1,X 2is n k 2,X =[X 1;X 2]is n k (k 1+k 2=k <n ),and 0=[ 01; 02].Suppose that X ,X 1and X 2are of full column rank.The OLS estimator b = b 01;b 020are expressed as b = b 1b 2 =(X 0X ) 1X 0y = X 01X 02 [X 1;X 2] 1 X 01X 02 y = X 01X 1X 01X 2X 02X 1X 02X 2 1 X 01y X 02y:(a)Use the formula of partitioned inverse (see A-74,page824)to show thatb 1=[X 01M 2X 1] 1X 01M 2y =[X 01X 1] 1X 01y b 2=[X 02M 1X 2] 1X 02M 1y =[X 02X 2] 1X 02y whereP i X i (X 0i X i ) 1X 0i ,M i I P i ,i =1;2X 1=M 2X 1;y =M 2y ;X 2=M 1X 2;y =M 1y :(b)Note that a square matrix is an orthogonal projection if and only if it is symmetricand e this result to show that P X P 1is an orthogonal projection matrix.What is the trace of P X P 1?(c)Show that any n 1vector z of the form M 1X 2 ,for an arbitrary k 2 1vec-tor ,is left unchanged when premultiplied by P X P 1;that is,show that(P X P 1)M 1X 2 =M 1X 2 .(d)Why do the above results prove that P X P 1=P M 1X 2,where this last matrix denotes the orthogonal projection on to S (M 1X 2)?(e)Consider the following regressions,all to be estimated by OLS:(a)y =X 2 2+u ;(b)P 1y =X 2 2+u ;(c)P 1y =P 1X 2 2+u ;(d)P X y =X 1 1+X 2 2+u ;(e)P X y =X 2 2+u ;(f)M 1y =X 2 2+u ;(g)M 1y =M 1X 2 2+u ;(h)M 1y =X 1 1+M 1X 2 2+u ;(i)M 1y =M 1X 1 1+M 1X 2 2+u ;(j)P X y =M 1X 2 2+u :For which of these regressions are the estimates of 2the same as for the original regression?Why?For which are the residuals the same?Why?。
上财罗大庆高级宏观作业3
上财罗大庆高级宏观作业3Advanced Macroeconomics IInstructor:Luo DaqingAssignment3Note:You may use either English or Chinese to answer the questions.Question1(5points)Consider the Overlapping Generations framework we discussed in classes.Suppose there are two countries where individuals di?er in their endowment streams.The characteris-tics of the two countries are summarized in the following table: Home Country Foreign CountryN t=60,t≥0N?t=40,t≥0{y1t,y2t+1}={1,1.25},t≥0{y?1t ,y?2t+1}={1,1},t≥0u(c1t,c2t+1)=ln c1t+0.95ln c2t+1,t≥0u(c?1t ,c?2t+1)=ln c?1t+0.95ln c?2t+1,t≥0(1)(4points)Find the sequence of equilibrium interest rate and the consumption allo-cation for this economy,and thenindividual savings in the equilibrium.(The derivation of the consumption and saving functions is not a must for this problem.However,you are de?nitely supposed to know how to derive these functions.)(2)(1points)Verify whether free trade is superior to autarky by comparing the welfare of home and foreign agents in free trade and in autarky.Question2(5points)Consider an Overlapping Generations economy with government.Suppose that in each period,100identical individuals are born(i.e.N t=100for t=0,1,2,...).The utility of an individual born in period t is given byu(c1t,c2t+1)=ln c1t+0.95ln c2t+1.. An individual born in period t has the following endowment stream{y1t,y2t}={1,1.25}∞t=1 In addition,assume the government announces the following policy.In period1,the government borrows5units of the time1good and transfers those units to the old in-dividuals alive in period1.The government will payo?its debt by taxing the members of generation1in their old age and will issue no debt after that.Find the sequence of equilibrium interest rate and the consumption allocation for this economy.(Again,the derivation of the consumption and saving functions is not a must for this problem.)。
上财罗大庆高宏课件 (9)
• Since all periods are identical, the competitive equilibrium prices and consumption allocation are
∞ {r t }∞ t=1 = {0.01}t=1 , ∞ {c 1 t , c 2 t }∞ t=1 = {2.2, 2}t=1 .
• Optimization problem solved by an individual born in period t is to maximize u(c1t , c2t+1 ) subject to the Present Value budget constraint. • Logarithmic utility example: – Maximize u(c1t , c2t+1 ) = ln c1t + β ln c2t+1 subject to c 1t + c2t+1 y2t+1 = y 1t + . 1 + rt 1 + rt
(II) Heterogeneity within Cohorts
• Heterogeneity creates incentives for trade. • Assume there are two types of agents born in each period. • Type 1 (group 1) – Nt individuals of type 1 are born in period t – they have utility function u(c1t , c2t+1 ) – and an endowment stream {y1t , y2t+1 }. • Type 2 (group 2) – Nt∗ individuals of type 2 are born in period t
高宏(08)2014年11月17日§2.1§2.2(纯白)
•第三次作业:第117页:•2.8 —2.11•11月24日交第3次作业2014-11-17 高宏(8)《高宏》讲义,张延著。
版权所有2•四、家庭的最大化问题•1、家庭最大化问题的一阶条件•家庭的问题是,在预算约束条件下选择c(t)的路径以最大化一生效用。
尽管这涉及选择每一时点上的c(而非像标准的最大化问题那样,仅选择有限的一组变量),传统的最大化方法仍可使用。
2014-11-17 高宏(8)《高宏》讲义,张延著。
版权所有3•由于消费的边际效用总为正,所以家庭满足其预算约束的等号形式。
因此,我们可用目标函数(2.14)和预算约束(2.7)来构造拉格朗日函数:•目标函数:∞[ e -βt c(t)1-θ/(1-θ) ] dt (2.14)•U ≡ B∫t=02014-11-17 高宏(8)《高宏》讲义,张延著。
版权所有4•约束条件:•∫t=0∞e -R(t) c(t) e(n+g)t dt•≤ k(0) + ∫t=0∞e -R(t) w(t) e(n+g)t dt (2.7)•L= B∫t=0∞[e -βt c(t) 1-θ/(1-θ)]dt +λ[ k(0) +•∫t=0∞e -R(t) e(n+g)t w(t)dt -∫t=0∞e -R(t) e(n+g)t c(t)dt ]•(2.15)2014-11-17 高宏(8)《高宏》讲义,张延著。
版权所有5•c(t):选择变量,政策可控制。
如何选择,以最大化一生的效用。
•k(t):状态变量。
•t :时间变量。
2014-11-17 高宏(8)《高宏》讲义,张延著。
版权所有6•即以某一时期t为例,写出某一时期t的拉格朗日函数:•L = B e -βt c(t)1-θ/(1-θ) +•λ [ k(0) +e -R(t)e(n+g)t w(t) -e -R(t)e(n+g)t c(t) ]•存在极值的一阶条件为:•∂L /∂c=B e-βt c(t)-θ-λe -R(t)e(n + g)t= 0 2014-11-17 高宏(8)《高宏》讲义,张延著。
管理方法与艺术第二次作业参考答案.doc
管理方法与艺术第二次作业参考答案--单选--0(本题2分) 领导方格理论是由( )提出的布莱克和穆顿费德勒坦南鲍姆施密特1(本题2分) ( )是组织文化最直观的部分潜层次的精神层表层的制度系统显现层的组织文化载体组织价值观2(本题2分) 下列不能作为管理人员考评的目的是()确定薪酬的依据人事调整提供依据为管理人员培训提供依据进行惩罚的标准3(本题2分) 组织规模一定的条件下,管理幅度较大、管理层次较少的组织形态为()。
扁平结构直线型结构矩阵结构锥形结构4(本题2分) ()是一种传统的、普遍的组织形式。
矩阵组织产品部门化职能部门化区域部门化5(本题2分) 一些大公司喜欢采取内部提升的选拔制度。
你认为以下哪些是它的弊病()可能造成“近亲繁殖” 的现象有利于保证选聘工作的正确性。
有利于吸引人才。
有利于鼓舞士气6(本题2分) 下行沟通是指( )组织中的上层领导按指挥系统从上而下的情报沟通下级的意见、信息向上级反映下级之间的意见交流通过上级组织明文规定的渠道进行信息传递7(本题2分) 对于组织的看法,你认为哪种正确()正式组织中不存在非正式组织。
正式组织中也存在非正式组织非正式组织中通常会传递小道消息,因此应尽量消除非正式组织。
非正式组织是由企业管理者用非正式的方式建立的。
8(本题2分) 一般说来,管理层次所拥有的能够确定集权或分权程度的是( )。
审批权计划权组织权决策权9(本题2分) 组织结构设计中,划分管理层次的主要原因是( ) 组织高层领导的偏好法律的规定组织规模管理幅度10(本题2分) 不利于分权的因素主要有()。
组织规模的扩大组织活动的分散较多受过良好训练的管理人员政策的统一性11(本题2分) 距阵式组织的主要缺点是()。
分权不充分多头领导对项目经理要求高组织稳定性差12(本题2分) 下列不是组织分权的标志()决策的频度决策的幅度决策的重要性组织的规模13(本题2分) 下列不属于委员会制的优点的是()责任明确集体决策可以产生更多的方案集思广益14(本题2分) 关于沟通,下列说法正确的是()。
上海财经大学附属中学2012届高三10月月考数学试卷
上海财经大学附属中学2012届高三10月月考数学试卷2011.10.9(满分100分,时间90分钟) 成绩___________________一、填空题(每题4分,满分56分)1、已知{}{}R x x y y B R x x y y A ∈==∈==,,,22,则=B A I _________。
[0,)+∞2、函数y =___________。
(]0,93、已知幂函数()y f x =的图象过点12⎛ ⎝⎭,则2log (2)f = 。
12 4、下面给出四个命题:①直线l 与平面a 内两直线都垂直,则l a ⊥; ②棱柱的侧棱都相等,侧面都是平行四边形;③圆锥的侧面展开图为扇形,这个扇形的半径等于圆锥底面的半径;④函数2()2log xf x x =-的零点有1个;⑤函数2()1,(0)f x x x =+≤的反函数是1()1)f x x -=≥。
其中正确的命题序号是 。
②⑤5、有五位同学报名参加两个课外活动小组,每位同学限报其中的一个小组,则不同的报名方法共有___________种。
326、如果函数23(0)()(0)x x y f x x ->⎧=⎨<⎩是奇函数,则()f x =____________。
23x +7、在北纬45o圈上有甲、乙两地,它们分别在东经50o与东经140o圈上,地球半径为R ,则甲、乙两地的球面距离是___________。
13R π8、在一个水平放置的底面半径为3的圆柱形量杯中装有适量的水,现放入一个半径为R 的实心铁球,球完全浸没于水中且无水溢出,若水面高度恰好上升R ,则R = 。
329、已知0,1a a >≠有两个命题:①函数log a y x =是减函数;②关于x 的不等式210ax +>的解集为R ,如果这两个命题中有且只有一个是真命题,则实数a 的取值范围是 。
()1,+∞10、一个盒子中装有4张卡片,上面分别写着四个函数:31()f x x =,42()f x x =,||3()2x f x =,41()f x x x=+,现从盒子中任取2张卡片,将卡片上的函数相乘得到一个新函数,所得函数为奇函数的概率是_________。
上财罗大庆高宏作业1
Advanced Macroeconomics IInstructor:Luo DaqingAssignment1Note:You may use either English or Chinese to answer the questions.Question1(3points,1point for each part)This question seeks to clarify the concept of expectations,conditional and unconditional.(a)Consider a two-period model where consumption in period t is a random variable denoted C t,for t=0,1.For simplicity,assume that C t can take on two values,c t and c t, for t=0,1.Show that when C t is identically and independently distributed over timeE0(C1)=E[C1].(b)Consider a two-period model where consumption in period t is a random variable denoted C t,for t=0,1.For simplicity,assume that C t can take on two values,c t and c t,for t=0,1.Show thatE[E0(C1)]=E[C1].(c)Consider a three-period model where a consumer seeks to maximize her lifetime expected utilityE02t=0βt u(C t)=u(c0)+β[u(c1)·P r(C1=c1|c0)+u(c1)·P r(C1=c1|c0)] +β2[u(c2)·P r(C2=c2|c0)+u(c2)·P r(C2=c2|c0)]where C1and C2are random variables that can take on only two values,c t and c t,for t=1,2.How would you calculate the conditional probabilities P r(C2=c2|c0)and P r(C2=c2|c0)?Question2(3.5points)Consider an extension of the two-period endowment economy studied in class where agents live for four periods.A representative agent has lifetime expected utilityE1U=ln(c1)+0.96E1ln(c2)+0.962E1ln(c3)+0.963E1ln(c4)where c t denotes consumption in period t.Each agent receives an endowment y t in period t.denote the price of a one-period bond purchased in period t and (a)(0.5pts)Let q Sbtpaying one unit of consumption in period t+1.State(no deviations nor explanations required)an expression relating the price q Sto y1and y2.b1(b)(0.5pts)Let q Mdenote the price of a two-period bond purchased in period t and btpaying one unit of consumption in period t+2.State(no deviations nor explanationsto y1and y3.required)an expression relating the price q Mb1(c)(0.5pts)Let q Ldenote the price of a three-period bond purchased in period t and btpaying one unit of consumption in period t+3.State(no deviations nor explanations required)an expression relating the price q Lto y1and y4.b1(d)(1pts)Consider the following contract.In period1,buyer and seller agree on the following:(1)in period3,the buyer has to pay f units of consumption to the seller;(2)in period4,the seller has to pay1unit of consumption to the buyer.Explain what are the utility costs and benefits to the buyer of signing the above described contract. What is the equation relating the price f to endowments?and (e)(1pts)Using your answer from part(d),derive an expression relating f,q Lb1q Mand briefly explain why this equation has to hold in equilibrium.b1Question3(3.5points)Consider a three-period economy with a large number of identical consumers,firms and banks.Assume the number offirms coincides with the number of consumers and that eachfirm is entirely owned by a consumer with the following utility functionU=ln(c1)+0.95E1ln(c2)+0.952E1ln(c3).A representativefirm considers investing into a new machine.The machine would be bought at price P and installed in period1and would be productive in periods2and3 only.The payoffs generated by the machine in periods2and3are denoted py2and py3, respectively.Assume that consumption is contingent on the state of the economy.More specifically, consumption is equal to1.2when the economy is in a good state and to0.4when the economy is in a bad state.Assume that the economy is in a good state in period1(i.e. c1=1.2).The payoffs generated by the machine are also state contingent.The payoffis0.2in the good state and0.1in the bad state.Finally,the state of the economy evolves independently over time and both states have probability0.5.(a)(0.5pts)Suppose thefirm has the resources necessary to completely cover the purchasing price of the machine in period1.State the Euler equation linking the price of the machine,its payoffs and current and future consumption.Clearly explain your answer in terms of costs and benefits related to such an investment.(b)(0.5pts)Using your answer to part(a),show that the equilibrium price thefirm is willing to pay for the machine is0.4631.From now on,we assume that the market price of the machine is P=0.4631and that thefirm has to borrow to be able to acquire the machine.(c)(0.5pts)Suppose the bank requires thefirm to make a down payment D in period 1and payments of equal amount m in periods2and3.Write the Euler equation linking D,m,the machine’s payoffs and current and future consumption.Clearly explain your answer in terms of costs and benefits related to such an investment.(d)(0.5pts)Using your answer to part(c)and assuming D=0.23,solve for the equilibrium amount m thefirm is willing to pay in periods2and3.(e)(0.5pts)Suppose the bank charges a periodic real interest rate r=0.03and uses the following present-value formulaP=D+m1+r+m(1+r)2to determine m.Again,assuming D=0.23,solve for the amount m the bank will charge afirm borrowing to buy a machine.(f)(1pts)In light of your results,are the market for machines and loans in equilibrium? If not,discuss the adjustments that will take place in the economy to bring the markets to equilibrium.。
上财罗大庆高宏课件 (2)
+
p2 p1
y2
.
Therefore,
p1 p2
=
y2 βy1
.
Connecting the equilibrium relative price in the consumption functions yields
the equilibrium consumption allocations:
c1 = y1,
function:
c2
=
1
β +
β
p1y1 p2
+
y2
.
– Market Clearing: c1 = y1, and c2 = y2.
Clearing of the goods market in period 1 requires c1 = y1. This implies:
y1
=
1
1 +
β
y1
k=x c1 + x = y1
c2 = y2 + (1 − δ)k + f (k)
– Representative consumer’s optimization problem:
max
c1,c2,x
u(c1, c2) = log c1 + β log c2
s.t. p1c1 + p2c2 = p1(y1 − x) + p2y2 + qx + P R
sumption function:
c2
=
β
·
p1 p2
·
c1
p1y1
+
p2y2
−
p1c1
上海财经大学高数习题集答案 第六章 定积分的应用
得 a b 2 ,它与 x 轴所围图形的面积为 S a (ax 2 b)dx
0
b
b3 (2 a)3 。 2 6a 6a 2
0
1 4a 2 a 1 4a e d (e 1) 。 a
q* 0
(7)由题 q* 3 ,带入 p D(q) 得 p* 11 ,消费剩余 CS D(q)dq p*q*
1
0
y p 1 ( ) 2 dy [ 2 ln(1 2 )] 。 p 2
(5)由题当 D(q) S (q) 时, q * 4 ,得 P * 20 ,
所以生产者剩余为 PS p *q* S (q)dq 4 20 (4 q 2 )dq
0 0
1 (2 a) 2 (4 a) 2 所 以 S , 所 以 当 a 4 时 , S 0 , 这 时 6 a3 S (4) 8 4a 3 |a 4 0 。即当 a 4 时, S 最小。所以所求抛物线为 32 a4
CS (32 4q q )dq 3 11 69 33 36 。
2a
a
a 。 x dx 2a 2 ) x
0
(2)由①可设抛物线为 y ax 2 bx c ,其中 a 0 ,过 (0,0) 点得 c 0 ,过 (1,2) 点
(6)弧长 L
0
r 2 r '2 d
2 a
e 2 a 4a 2e 2 a d
a b
所以当 x0 1 时,S 0 ,S (1)
e x0 2 所以当 x0 1 时, ( x0 2 x0 1) e 1 0 , 2
《高级宏观经济学》考研罗默版2021考研真题与习题
《高级宏观经济学》考研罗默版2021考研真题与习题1.10 假定与习题1.9类似,资本和劳动按照边际产出支付报酬。
此外,假设所有资本收入用于储蓄,而所有劳动收入均用于消费。
因此。
(a)证明该经济收敛于平衡增长路径。
(b)在平衡增长路径上,k大于、小于还是等于k的黄金律水平?这一结论的直观含义是什么?解:(a)证明:由k=K/AL,对其两边关于时间求导,可得:(1)将,和代入方程(1),可得:(2)将代入方程(2),可得:(3)当时,每单位有效劳动保持不变。
即[f'(k)-(n+g+δ)]=0,因此平衡增长路径上的每单位有效劳动的资本可以由[f'(k)-(n+g+δ)]=0潜在地决定。
k=K/AL,由于在平衡增长路径上k保持不变,因此,K必须与AL保持同样的增长速度。
AL的增长速度为n+g,所以K的增长速度为n+g。
由于生产函数是规模报酬不变的,因此,在平衡增长路径上每单位有效劳动的产出增长速度也必须是n +g。
综上所述,可以发现所有变量增长速度均不变。
下面证明经济收敛于平衡增长路径。
在k=k*时,f'(k)-(n+g+δ)=0,此时经济处于平衡增长路径上。
如果k >k*,由于f"(k)<0,所以,则经济向下偏离平衡增长路径;反之,如果k<k*,则,经济向上偏离平衡增长路径。
所以,不管初始的k如何,经济都将收敛于平衡增长路径,此时,所有的经济变量都以不变的速率增长。
(b)满足黄金规则的资本水平是指使每单位有效劳动的消费最大时的资本水平,即f'(k GR)=(n+g+δ)。
此刻满足生产函数的斜率等于持平投资线的斜率。
而这正是经济收敛到均衡增长路径时k的水平,这时所有的资本收入被储蓄,所有的劳动收入被消费。
在本模型中,将资本的贡献(资本的边际产品乘以资本的数量)储蓄起来。
如果资本的贡献超过持平投资,即kf'(k)>(n+g+δ)k,则k上升;反之,如果kf'(k)<(n+g+δ)k,则k下降。
因此,经济收敛于kf'(k)=(n+g+δ)k,或者f'(k)=(n+g+δ)这一点上,此刻经济收敛于平衡增长路径。
上海财经大学乐理欣赏的作业范文大全
上海财经大学乐理欣赏的作业范文大全第一篇:上海财经大学乐理欣赏的作业1,与音乐有关 2,自己的感悟3,你要写出自己的感悟,要有自己的悟性 4,A4纸小四子音乐欣赏感悟音乐也许是人类表达思想与情感最具有普遍性和感染力的艺术形式之一。
音乐以其独特的,美妙的魅力伴随着人类的发展,它表现形式的多样性,复杂性,和美妙性。
音乐有一种无形的力量可以把杂乱无章的烦恼整理得有条不紊。
当烦恼缠绕着自己的时候,听那些抒情的轻音乐总可以让自己心旷神怡,如临仙境般的享受着某一种魔力,那一种能够可以带来快乐与慰藉的力量。
巴赫的音乐巴赫的音色有着岁月的痕迹与睿智,它是需要一种沉淀下来的态度来面对。
最好的音乐,不过是在对的时间听到适合自己这个阶段乐曲。
除了阅历,也是需要一种孤独的状态。
古典音乐以其独特、美妙的艺术魅力伴随人类历史的发展,伴随我们每一天的生活。
演奏家精湛的表演,令我跃跃欲试,这也许是因为音乐是美的艺术。
了解作品产生的年代作曲家所处的时代背景和作曲家当时的处境,对理解音乐也许有一定的帮助。
但是,也仅仅是“适当的帮助”而已。
因为我即使知道作曲家当时所处的时代环境、生活环境,我也不可能完全了解作曲家当时的心境,虽然巴赫的作品都是阳光的积极向上的。
对于音乐而言,最重要的,还是能不能引起你共鸣。
伯牙与子期的“高山流水”的故事是大家耳熟能详的。
钟子期以一介樵夫,应该也没有什么高深的乐理知识,但是,却能感受伯牙琴声中高山流水的意境。
所以,我觉得,乐理知识对于欣赏(仅仅是欣赏)音乐而言,不是起到的是关键作用。
欣赏音乐,重要的是感悟,而不是知识追求美是人类的天性,高层次的审美追求会使人的精神得到升华,情操受到陶冶,生活也将变得更加丰富而充实。
猫一些优美的西方音乐一直萦绕在我耳边,最让我印象深刻的是歌剧《猫》。
以前一直听人说这部剧很好听,可从来没听过,想想自己是个中国人老外的艺术欣赏不来。
直到老师把它搬上了课堂,我才意识到原来国外的歌剧可以这样震撼,这样美妙。
Advanced Macroeconomics II高宏II习题2
α1 − β Aα1 = (α2 − β Aα2 + β Aα2b1)a1
a1
=
(α 2
−
α1 − β Aα1 β Aα2 + β Aα2b1)
5.2 假定二次效用函数和线性生产技术(the linear quadratic model),即假定效用函数为
u(ct )
= α1ct
− α2 2
ct2 ,生产函数为
f
(kt )
=
Akt
,且假定折旧率 δ
= 1 。猜值函数的形式为
v(k) = φ1 + φ2k + φ3k 2 ;政策函数或策略函数可能为 c = a1 + b1k 以及 k ' = −a1 + b2k 。,利用
待定系数法验证。
首先由于效用函数为二次的形式, u(ct
)
=
α1ct
−
α2 2
ct2
,值函数可能具有类似的形式:
v(k) = φ1 + φ2k + φ3k 2 。构建 Bellman 方程:
v(k)
=
mc,akx' {α1ct
−
α2 2
ct2
+
β v(k
')}
s.t. k '+ c=Ak
带入“猜”的关于策略函数的解,可得:
v(k) = max{u(c) + β v(k ')} c,k '
(5.2.23)
s.t. k '+ c=Ak
构建 Lagrangian 函数:
L
=
α1c
−
α2 2
c2
2021届上海财经大学附属中学高三语文二模试题及答案
2021届上海财经大学附属中学高三语文二模试题及答案一、现代文阅读(36分)(一)现代文阅读I(9分)阅读下面的文字,完成下面小题、大漠里的旗帜刘建超她来看他,是为了离开他,他不知道,兴奋紧张搓着一双皲裂粗壮的手,这么远,天啊,你怎么来了?她看着他,看着相恋10年、那个曾经帅气、充满诗意的小哥,如今粗犷得像工地上的装卸工。
她还是没有忍住泪水,晶莹的泪珠在白嫩的脸颊冰冷地滑落。
她下了火车乘汽车,走了三天三夜,又搭乘过往的大货车颠簸了一天,才在一望无际的荒漠中看到了他居住的那个小屋,西部边陲的一个养路站,只有一个人的养路站,养护着近百公里的国道。
她和他在大学相识,他们都是学校野草诗社的。
他俩相恋了,就因为都喜欢泰戈尔的诗,生如夏花,死如秋叶,还在乎拥有什么?在校园的雁鸣湖边,他轻轻地牵着她,说过不了几年,我将成为中国诗坛的一面旗帜。
浪漫似乎只在校园里才蓬勃疯狂地蔓延。
当毕业走上社会,才知道校园的美好都被现实的无情的铁锤砸得粉碎。
为了寻找工作,他和她早把诗意冲进了马桶。
他的父亲是养路工,在西北,父亲生病期间,他去了父亲生活的城市照顾父亲,父亲去世后,他竟然接过了父亲手中的工具成为了一名养路工。
大漠荒烟,千里戈壁,他给她写信,描绘着他眼前的风景,天空虽不曾留下痕迹,但我已飞过。
我真的感受到泰戈尔这句话的含义了。
她感受不到那些诗意,没有他在身边的日子寂寞无聊。
家里人给她介绍男朋友,她都拒绝了。
可是,她也不确定自己究竟能等到个什么样的结果。
一年一年的春花秋月,把他们推向了大龄的边缘。
经不住妈妈的哭闹哀求,她妥协了,去见了妈妈公司领导的儿子,小伙子很精干,谈吐也很睿智。
她就模棱两可地处着,心中还是牵挂着远方的他。
她要了断同他的情缘,这样下去对谁都不公平。
她给他带了大包的物品。
他笑着说,我这啥都不缺,啥都不缺。
她环顾四周,煤气炉,木板床,米面油,咸菜。
他笑了,似乎恢复了校园里的神气,笑着说,孟子曰:天将降大任于斯人也,必先苦其心志,劳其筋骨,饿其体肤,空乏其身,这些我都具备了,就等着天降大任了。
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Advanced Macroeconomics I
Instructor:Luo Daqing
Assignment2
Note:You may use either English or Chinese to answer the questions.
Question1(5points)
Suppose there is a large number of identical agents with preferences represented by
E0
∞
t=0
βt ln c t
where c t is consumption in period t.Agents can trade one-period real bonds.The gross return on a bond purchased in period t,denoted R t,is known at the time of purchase (i.e.the bonds are risk-free).Therefore,the price of a bond is R−1t.
The constraints faced by a representative agent are
c t+L t R−1
t
=A t,A t+1=L t,A0given
where A t is wealth at the beginning of period t and L t is the holding of one-period bonds.Assume that R t is identically and independently distributed and is such that E R t<1/β.
(a)(1pts)Using L t as the control variable,write down Bellman equation corresponding to the representative agent’s optimization problem.
(b)(2pts)Use dynamic programming to derive the Euler equation corresponding to the representative agent’s problem.Interpret this Euler equation.
(c)(2pts)Use the guess L t=γR t A t to solve for the policy function for bond holdings L t(and consumption).
Question2(5points)
Consider a simple“real business cycles”model where a planner maximizes utility
E0
∞
t=1
βt[ln c t+γln(1−n t)],0<β<1,γ>0
where c t denotes consumption and n t hours worked.The maximization is subject to the resource constraint
c t+x t=z t kα
t n1−α
t
,0<α<1
and the transition equation for capital
k t+1=(1−δ)k t+x t0≤δ<1.
k t denotes the capital stock installed at the beginning of period t and z t is a stochas-tic disturbance interpreted as a productivity shock.δis the capital depreciation rate. Assume that
ln z t∼iid(0,σ2
z
).
(a)(1pts)What are the state variables and the control variables for this problem? What is Bellman equation corresponding to this problem?
(b)(2pts)Using dynamic programming,derive the Euler equation for capital and the first-order condition for hours worked(substitute out any Lagrange multiplier).Interpret these equations.
(c)(1.5pts)Now assume thatδ=ing the guess and verify method,show that the policy function for hours worked is time-invariant and that the policy function for
investment is linear in output.(Hint:Guess k t+1=ηz t kα
t n1−α
t
=ηy t.)
(d)(0.5pts)In light of the results found in part(b),discuss the ability of this model to generate realisticfluctuations in hours worked.。