高宏课件CHAPTER(1)

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高宏课件Chapter 1 Solow Growth Model

Conditions
• These conditions imply each input is essential: F(0, L) = F(K, 0) = 0. • An example of a neoclassical production function is the Cobb-Douglas one: • Y = AKαL1-α, A > 0; 0 < α < 1. • This form implies unit elasticity of substitution between K and L. If factors paid marginal products, factor shares of income are constant at α for K and 1-α
Labor
• L = labor supply (market clears with full employment). Labor supply = population (or proportional to population). No labor leisure choice and labor-force-participation rate is constant. Can extend model to make these endogenous. • Population grows exogenously at rate n ≥ 0: (1/L)· (dL/dt) = n L(t) = L(0)· exp(nt) • Can extend model to make fertility, mortality, immigration endogenous—then n is endogenous.

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.

全套教学课件《高级宏观经济学》

全套教学课件《高级宏观经济学》一、教学内容本节课的教学内容来自于《高级宏观经济学》教材的第五章，主要内容包括：国民收入的测量、国民收入的决定、消费与储蓄、投资与资本形成、货币与利率、通货膨胀与失业等。

本节课将重点讲解国民收入的测量和决定。

二、教学目标1. 让学生了解和掌握国民收入的测量方法，包括GDP和GNP的计算方法。

2. 让学生理解国民收入的决定因素，包括消费、储蓄、投资等。

3. 培养学生运用宏观经济学理论分析和解决实际问题的能力。

三、教学难点与重点重点：国民收入的测量方法，国民收入的决定因素。

难点：GDP和GNP的计算方法，投资与资本形成的区别与联系。

四、教具与学具准备教具：PPT课件、黑板、粉笔。

学具：笔记本、课本、文具。

五、教学过程1. 实践情景引入：通过播放一段关于我国经济增长的新闻报道，引发学生对国民收入的兴趣。

2. 知识讲解：讲解国民收入的测量方法，包括GDP和GNP的计算公式，并通过PPT课件展示实例。

3. 例题讲解：选取一道关于国民收入测量的例题，引导学生运用所学知识进行解答。

4. 随堂练习：布置一道关于国民收入测量的练习题，要求学生在课堂上完成。

5. 知识拓展：讲解国民收入的决定因素，包括消费、储蓄、投资等，并通过PPT课件展示相关数据和图表。

6. 例题讲解：选取一道关于国民收入决定的例题，引导学生运用所学知识进行解答。

7. 随堂练习：布置一道关于国民收入决定的练习题，要求学生在课堂上完成。

9. 板书设计：板书国民收入的测量方法和决定因素。

六、作业设计1. 作业题目：请运用所学知识，计算我国2019年的GDP和GNP。

答案：2019年我国GDP为99.1万亿元，GNP为100.6万亿元。

2. 作业题目：请分析影响我国国民收入决定的主要因素。

答案：影响我国国民收入决定的主要因素包括消费、储蓄、投资等。

七、课后反思及拓展延伸课后反思：本节课通过实践情景引入，激发了学生的学习兴趣，通过知识讲解、例题讲解和随堂练习，使学生掌握了国民收入的测量方法和决定因素。

北大张延高宏课件4599

高级宏观经济学教师：张延北大经济学院硕士、博士生课程2008年12月23日2008-12-23高宏（14）《高宏》讲义，张延著。

2008-12-23高宏（14）《高宏》讲义，张延著。

•期末考试结束交第6次作业。

2008-12-23高宏（14）《高宏》讲义，张延著。

我们将看到，缓慢的名义调整使得既定价格水平下商品总需求的变动会影响厂商生产的数量。

2008-12-23高宏（14）《高宏》讲义，张延著。

此外，许多真实冲击，包括政府购买的变化、投资需求的变化以及技术的变化，在既定价格水平下也影响总需求；因此，缓慢的价格调整在真实经济周期模型的跨期代机制之外又形成了另一种渠道，外来冲击通过这一渠道影响就业和产量。

2008-12-23高宏（14）《高宏》讲义，张延著。

本章有两个主要目标。

一是考查总需求。

我们将检查既定价格水平下总需求的决定因素以及价格水平变化的影响。

二是考虑有关名义刚性形成的其他一些假设。

我们将考查不同的假设对如下问题的含义：针对总需求的变化，厂商是否愿意改变其产量，真实工资、加成(markups)和通货膨胀的行为。

然后，第6章转而考虑如下问题：名义价格和工资为什么不对扰动作出立即调整？2008-12-23高宏（14）《高宏》讲义，张延著。

高宏讲义02

Lecture V Economics 202A Fall 20031. Sections/Times2. Everyone should be on the class e-mail list. Send your e-mail to Fernando if you have not done so already.Last time I went through the Lucas-Sargent model. At the end I omitted criticisms of it. Instead I took a poll of what you thought of it overall.Results of poll.Today, we will look at Taylor’s model in this class. We will continue with Taylor’s model in the next class.Taylor’s model is a model of rational expectations, but it also has money illusion of a natural sort. The most distinguishing feature of the Lucas-Sargent model is its absence of money illusion. It is that absence that is the most fundamental reason for their results of the neutrality of money and the lack of serial correlation of output.With Taylor’s model we will see three separate points.First, in Taylor’s model there is serial correlation of output and also monetary policy that is effective in stabilizing output.Second, we will see that with RE and with a little bit of money illusion, monetary policy will be effective and there will be serial correlation of output (even in the absence of serially correlated supply shocks).Third, I also said that if the economy was linear, as in Lucas’ and Sargent’s equations, it would be easy to solve.The simple model by Taylor illustrates all three of these points.I shall describe Taylor’s model:His model has unsynchronized price setting.½ of the firms set their prices in even periods.½ of the firms set their prices in odd periods.Measuring time in 6-month periods we might view½ of the firms as setting their price every January1and ½ of the firms as setting their prices every July.Money illusion is introduced in the following way:nominal prices are constant over the two-period interval.A firm setting a price for time t, sets its price both for time t and for time t+1. Its pricing decision is based on information available at t-1.How could a two-period contract be different?The contract made at t could specify prices at t+1 contingent on information available at t+1.For example: labor contracts may be indexed by the cost of living. In that case the wages in the second period of the contract are contingent on information available only after the contract is made.We are assuming that does not happen here. Curiously, most U.S. union contracts are not indexed. They are not indexed at all.Let me continue describing Taylor’s model. I am going to give a more microeconomic basis than the Romer textbook.I am going to give you the equations of the model and their justification.The microeconomic basis for the model assumes that there are just two firms.The demand for the product of each firm depends on its own price, on the price of its competitor’s product, and on aggregate demand.To be simple, assume that these firms have no costs of production—so the firms setting prices will try to maximize expected discounted revenues.USE RHBB TO LIST VARIABLESWRITE SYMBOLS AS YOU GO – WITH SPACESNow let’s adopt a clever notation.Let xt be the price that is set at time t.We will consider one of these firms that is setting its price at time t.The firm setting its price at time t will see that its demand in the current period will dependon the price of its competitor, or xt-1.We have a t-1 subscript because that price was set last period, at t-1.The expected demand for the firm setting its price at t will also depend on expectedaggregate demand, We shall denote this as y$t .$ in Taylor’s notation denotes expectations made on the basis of t-1 information.2The firm’s expected demand at t+1 will also depend on the expected value of the competitor’s price at t+1, which will be the expected price set next period or x$t+1.The firm’s expected demand will also depend on the expected value of aggregate demand next period, which will bey$t+1.Let’s not be worried about the functional form.The firm that sets the nominal price over the two periods to maximize profits will then set: FAR RHBB; divide in ½ by line(1) xt = bxt-1+ d y$t+ ( (b x$t+1+ d y$t+1) + ,twhere ,t is an additional random variable term in the firm’s prices due to the mistakes inits pricing behavior.The notation is in logarithms:x t is the log of the price set at time tx t-1 is the log of the price set by the competitor at t-1y$ t is the log of expected income at tx$ t+1 is the log of the expected price set by the competitor at t+1y$ t+1 is the log of expected income at t+1.This is Taylor’s key equation.FOOTNOTE ON NOTATION: d is a constant coefficient. It does not represent a differential or anything fancy. END NOTEERASE LHBBNow let’s add some standard stuff — keeping things very simple to complete the model. By definition the aggregate price level will be(2) wt = ½ xt+ ½ xt-1That is, the aggregate price level is a weighted average of prices set this period and prices set last period.To be precise: wt is the log of the aggregate price level. So we are taking a geometric meanrather than an arithmetic mean.And suppose further that aggregate demand is determined by a Quantity Theoretic3equation:(3) yt = mt- wt+ vtwhere mt is the log of money balanceswt is the log of the aggregate price levelvtis the random error term.Now let’s introduce a money supply rule.The monetary authority is stabilizing.This means that as the price level wt goes up, Real Balances, which determine aggregatedemand, should go down.As a result the monetary authority has the rule:(4) mt = (1 - $) wt0 < $ < 1.We now have the whole model.There are two salient questions that are motivated by Lucas and Sargent.(1) Is this monetary policy stabilizing, with rational expectations?(2) Is there serial correlation in output and prices so that there is a business cycle?Does this occur even in the absence of serially correlated supply shocks?Since these equations may look a bit unfamiliar to you, it is useful to do a short review so that you can see why they describe the whole economy.Equation (1) is an aggregate supply equation. It gives an admittedly complicated relation between income and price. It tells what level of price firms will charge given expectedincome y$t and y$t+1.Equation (3) is an aggregate demand curve. Given the money supply it tells the relation between price and aggregate goods demanded. Aggregate goods demanded will be aggregate income.So equations (1) and (3) are the Aggregate Demand and Supply curves, given the supply of money.If you know money, you can determine prices and aggregate demand.45Then equation (4) tells you how much money there is.Equation (2) links the definition of prices in (1) to the definition of prices in (3).David Romer has a particularly clever way of solving the model. I will review that in a few minutes. Let me now solve the model as Taylor does.Let’s do a little algebra and see if we can solve the model.To solve such a model we would want to express all the endogenous variables in terms of current and past shocks.If we can get formulas in terms of the random shocks then we know everything there is to know about the model.Before we solve the model let’s think about what we mean by a solution.We know the basic equation of the model:x t = bx t-1 + d y$t + ( (b x $t+1 + d y $t+1) + ,t If we knew y $t , x $t+1 , and y $t+1 we could plug them in, and then we would know the actual value of x t by solving the difference equation that would result.If you think about it for a while you will realize that you can find the values of y $t , x $t+1 , and y $t+1 that are consistent with the structure of the economy. It turns out that people knowing the structure of the economy will have expectations abouty $t , x $t+1 , and y $t+1 .It turns out that these consistent or rational expectations must be solutions to a difference equation, which we will now set up and solve.DIVIDE LHBB IN 2;We know from the quantity theory equation:y t = m t - w t + v tSo y $t = m $ t - w $ t .And we know the monetary rule:m t = (1 - $) w t So m $ t = (1 - $) w $ t So y $t = (1 - $) w $ t - w $ t = - $ w $ tAnd similarly y$t+1 = - $ w$t+1GO TO SIDE BOARD We also knowwt = .5 xt-1+ .5 xtSo w$t= .5 xt-1+ .5 x$tGO TO LHS OF SIDE BOARDSo y$t = - $ (.5 xt-1+ .5 x$t)And y$t+1 = - $ (.5 x$t+ .5 x$t+1)So if we want to discover x$t , y$t, y$t+1and x$t+1all we need to know is the path of the x$t’s.Go over to RHBBSince xt = bxt-1+ d y$t+ ( (b x$t+1+ d y$t+1) + ,tERASE RHBB below this equationand since ,tis not known for all times s > t-1, it follows that for s > t-1x$ s = b x$s-1+ d y$s+ ( (b x$s+1+ d y$s+1).The reason: according to rational expectations the behavior of expectations must conform to the behavior of the system.Formally you obtain this difference equation by taking the E*2t-1 of the LHS and of theRHS of the equation for s>t-1.Substituting the value of y$s in terms of x$sand x$s+1AND y$s+1 in terms of x$s+1and x$s+2POINT TO TWO EQUATIONS ON LHBB; ERASE LHBByields a difference equation in terms of x$s.That difference equation is of the form:c x$s = x$s-1+ (x$s+1where c is a complicated constant, which comes out of the algebra. FOOTNOTE:67END FOOTNOTE.This constant is obtained just by substituting into the equation for x$sthe respective formulae for all the variables on the RHS and then gathering terms.NOW ERASE LHBB leaving only the difference equation.This difference equation yields the expected path of prices consistent with the model.It is a second order difference equation with solution of the form:x$s= a1"1s + a2"2s,whereand"1and "2are the roots of the associated quadratic of the difference equation.We know this from our Difference Equation BOX for the solution to the second order linear difference equation.That associated quadratic WRITE IT UNDER THE EQUATION is:(x2 - cx + 1 = 0The larger of the two roots, which is "2has absolute value greater than one.FOOTNOTE:Proof: "1@"2= 1/( > 1. END FOOTNOTEIn consequence if the economy is well-behaved in the long-run a2must be zero.Why? In the long-run this root will dominate if a2is not zero.If a2 is not zero, the log of income and the log of prices will behave very erratically in thelong run. We impose the additional condition that we want a long-run solution that, qualitatively, makes good economic sense.If we impose the assumption of long-run stability on the system, then a2= 0 andx$ s = a1"1s.And at time t-1 we have the initial conditionx$ t-1 = xt-1.So x$s = "1s-(t-1)xt-1.In particular,x$ t-1 = xt-1x$ t = "1xt-1x$ t+1 = "12 xt-1If we substitute these values, and also the values ofy$ t and y$t+1into the fundamental pricing equation we findthe elegant solutionx t = "1xt-1+ ,t.This is the solution to the model.We can solve this difference equation, as you may remember, and get an equation for xt interms of current and past shocks. The solution comes from our very first difference equation: the first one we put into a BOX.And with a bit of algebra you can compute any other variable in the model once you know the value of the xt’s.8This completes the solution to the model.ERASE LHBB EXCEPT FOR (1)****************************************Having completed, in detail, the solution to the model, let me now go back and review what we did, in a nutshell.And then I also want to discuss at greater length why we chose the smaller root to the difference equation.Let me review what we did—so you can see the broader picture.We started with the basic pricing equation:(1) xt = bxt-1+ d y$t+ ( (b x$t+1+ d y$t+1) + ,tBy finding out how y$t depended on x$t-1and x$tand y$t+1depended on x$tand x$t+1and substituting in this equation, we get a difference equation consistent with the pricing behavior (1). This difference equation determined what consistent price expectations would be.This difference equation had a solution of the form:x$ s = a1"1s + a2"2s.By definition, let’s assume that "2is the larger root and that it is greater than one.Then a2 the coefficient associated with the larger root must be zero. It must be zerobecause otherwise as t grows large the system behaves very erratically.Let me go over that argument in greater detail than I have so far.Why do we throw out the larger root?Let’s go back and look at the system.The system here has a steady state equilibrium if the stochastic terms are 0. We can find this steady state. This steady state will have constant money, income, and prices.We assume that people will have rational expectations and assume that the system will approach this steady state in the absence of exogenous shocks.Why not allow weight on the root that is greater than one?9In that case in the long run the solution is not stable. In fact the variance of income growth becomes larger and larger.F 2 (yt - yt-1) 64 as t 64.For this reason solutions to the difference equation with nonzero weight on "2 should berejected.I will leave the proof as a footnote in the lecture. FOOTNOTE:Proof. yt=mt- wt+ vt= ( 1 - $) wt- wt+ vt= - $ wt+ vt.Similarly yt-1= - $ wt-1+ vt-1.E(yt @ yt-1) = $2E (wt@ wt-1)But wt = .5 (xt+ xt-1)Asymptotically,– .5 ("22 xt-2+"2 ,t-1 + ,t + "2 x t-2 + ,t-1)= "2 .5 ( "2xt-2+ ,t-1+ xt-2) + .5(,t+,t-1)= "2 .5(xt-1+ xt-2) + .5(,t+,t-1).We can therefore view as an approximation, if a2…0wt = "2wt-1+ .5(,t+,t-1)The growth in income is then:y t - yt-1= - $wt+ vt+$wt-1-vt-1= -$(wt- wt-1) + vt- vt-1F2 (yt - yt-1)= $2F2 (wt- wt-1) + 2Fv210wt - wt-1= ("2- 1) wt-1+ .5(,t+,t-1)F2 (wt - wt-1) = ("2- 1)2F2 (wt-1)+ ("2- 1) (.5) cov [(,t+,t-1),wt-1] + .5F,2.F2 (wt-1), however, is ever increasing in time becausewt = G ti=1"2t-i (,i+ ,i-1) + "2t wBy inspection F2 (wt ) will be ever increasing if "2> 0.END FOOTNOTESo the growth in income will have ever increasing variance as t increases. If we reject this instability, then a2must be zero.It is highly peculiar for an economy with no technical change to have long-run growth in income which is either extremely large or extremely small. This will occur ifF2 (yt - yt-1) is unbounded.So let’s return to our review of how we got our solution. The solution is of the form:x$ s = a1"1s.With the initial conditionx$ t-1 = xt-1we find thatx$ s = "1s-(t-1)xt-1for s>t-1.We then knowx$ t-1 = xt-1x$ t = "1xt-1x$ t+1 = "12 xt-1Solving for the implicit values of y$t and y$t+1and substituting for x$t-1and x$t+1into (1) yieldsx t = "1xt-1+ ,t.11This is absolutely wonderful because this equation is an old friend.We know everything about her. She is just our old friend the AR(1) equation.And either because we proved it in class or because we can easily work it out, we know its solutionx t = Ei4=0"1i,t-i.And, second, we know that there will be serial correlation because we have already worked out the autocorrelation function of this AR(1) process.Third, we can write out what yt will be in an explicit formula, and we can compute thecovariance between yt and yt-1.You find that ytis serially correlated.Fourth, you can calculate the variance of yt as a function of the monetary rule described bythe parameter $.You will find that the variance of yt changes with $ and therefore systematic monetarypolicy in this model may be stabilizing.How do you know this? Because the calculated variance yt depends on "1. And in turn "1depends on the parameter $, which describes monetary policy.What is the message of this model? The message of this model is that Rational expectations models with money illusion, (but without serially correlated supply shocks), may have serially correlated output.The further message is that monetary policy may be stabilizing in such an economy.Bob Barro has told us that he does not like this model: because the agents are not maximizing. It is not maximizing for the price to be set the same in nominal terms for two periods.If price setters were maximizing, the price in the second period would be contingent on information that becomes newly available.This is a Keynesian model, in the sense that nominal prices are a bit sticky. This small amount of stickiness in prices makes monetary policy effective in stabilizing output. It also makes output serially correlated.*************************************12I will return to the Taylor model next time. Let me now take a few minutes to go over David Romer’s version of the same model with its different method of solution, with matching coefficients.David has an alternative version of the Taylor model. I am going to go over that to show you a different method of solution: matching coefficients.First, for simplicity his monetary rule is that money follows a random walk:mt = mt-1+ ,t.From microeconomic assumptions he derives the optimal price charged by the individual firm. This is the price the individual firm would ideally like to charge for its product at time t.p it * = N mt+ (1 - N) pt,where ptis the aggregate price level at t.Note that the equation is normalized so that if mt were constant ptwould be equal to mt.This is equivalent to treating pt and mtas index numbers equal to 100 in the base year.Thus if mt should increase by 5 percent to 105 we would expect ptto increase to 105 as well.This formula makes intuitive sense. There are two factors that determine the price a firm wants to set. One is demand, which is determined by the money supply. The other is the price set by competitors, which is on average, pt.Returning to the pricing equation, we see further that if the money supply should double and the price set by the competition should double, the individual firm would want to double its own price.So the price that the firm sets should be homogeneous of degree one in the money supplyand the average price level. Thus the coefficient on pt should be one minus the coefficienton mt.Let’s continue the analysis.In the Taylor model the firm sets a constant price for two periods. If the firm sets the price as close to the optimum as possible it will set:x t = ½ (pit* + Etpit+1*)As a result (using the fact that pt = ½ (xt-1+ xt)1314x t = ½ [N m t + (1 - N ) ½ (x t-1 + x t )]+ ½ [N E t m t+1 + (1 - N ) ½ E t (x t + x t+1)]= ½ [N m t + (1 - N ) ½ (x t-1 + x t )]+ ½ [N m t + (1 - N ) ½ (x t + E t x t+1)]= N m t + ¼ ( 1 - N ) (x t-1 + 2x t + E t x t+1)Note: in Romer’s model x t is known at t.Solving for x t yieldsx t = A (x t-1 + E t x t+1) + (1 - 2A) m twhereThe algebra is straightforward.Now let’s use the method of matching coefficients to solve this equation.Let’s guess that the solution of the difference equation is of the form.x t = 8x t-1 + <m t .Now let’s try our solution by the method of matching coefficients.We will choose the values of those coefficients that will make our expectations “correct” or “rational” given the behavior of the model.We knowx t = 8 x t-1 + <m tso E t x t+1 = E t ( 8 x t + <m t+1)= E t 8( 8 x t-1 + <m t ) + <m t= 82 x t-1 + (8 + 1) <m tNow rememberx t = A (xt-1+ Etxt+1) + (1 - 2A) mt= A xt-1 + A 82 xt-1+ A(8 + 1) <mt+ (1 - 2A) mtNow remember our best guess:x t = 8 xt-1+ <mt.So the coefficients must match:8 = A + A 82< = A (8 + 1) < + (1 - 2A)And 8 must solve the quadratic equation8 = A + A82.Knowing 8 we can use our second equation [POINT TO IT] to solve for the value of <. [You can also check David’s proposition that if < = 1 - 8, then the equation for < is satisfied. So < = 1 - 8.]This solves the problem of the motion of prices.As in Taylor, we find two solutions: two values of 8. But we throw away the value of 8 greater than one–since that is the unstable root.We get the same type of results that we got before.*****************************Let me review the method and how it works.You have two expressions for xt .One is by assumption that it follows a linear difference equation.The other is that it follows the equation of motion of the system with Et xt+1consistent with the linear difference equation.The two equations must be consistent and this determines the coefficients of the linear difference equation.15Lecture VI Economics 202A Fall 2003Let me now begin with a note on the strategy of reading for the course.1. In this section on Lucas and Sargent and Taylor.I would recommend the following strategy.First listen to the lectures.Then read the articles.I then commend the textbook as the clean-up batter.The reason for this is that I think that the textbook is, in fact, the most difficult of the three. It is also very clear, so you can use it to clear up any questions you may have.2. My advice, however, varies section by section.In subsequent sections on Keynesian Unemployment,Open Economy Macro, andDemand for MoneyI recommend reading the textbook first. It is easier than the readings.Today I will continue going over the Taylor model.Last time I showed you Taylor’s model as originally written.Then I showed you David Romer’s variant of it and his method of solution by matching coefficients, which I will review briefly now.The essence of that method was to do the following three steps.1. Assume a form of the key variable.Such as:x t = 8xt-1+ <mt2. We took the following from David Romer: The price that firms ideally want to charge is:p it * = N mt+ (1 - N) pt,12where p t is the aggregate price level at t.The firm then setting its price at time t, x t , will set:x t = ½ (p it * + E t p it+1*)As a result—using the fact that p t = x t-1 + x t —we can find easily that:x t = A (x t-1 + E t x t+1) + (1 - 2A) m twhereThe algebra is straightforward.As a further step, ifx t = 8x t-1 + <m tandm t is a random walk,with a bit of further algebra that is straightforward, we can get a formula for x t in terms of x t-1 and m t .That formula turns out to be:x t = A x t-1 + A 82 x t-1 + A(8 + 1) < m t + (1 - 2A) m t .3.Then match the coefficients of x t-1 with 8and of m t with <.This means that8 = A + A 82< = A (8 + 1) < + (1 - 2A)So 8 must solve the quadratic equation8 = A + A82.Knowing 8 we can use our second equation [POINT TO IT] to solve for the value of <. [You can also check David’s proposition that if < = 1 - 8, then the equation for < is satisfied. So < = 1 - 8.]This solves the problem of the motion of prices.As in Taylor, we find two solutions: two values of 8. But we throw away the value of 8 greater than one–since that is the unstable root.We get the same type of results that we got before.*****************************Let me review the method and how it works.You have two expressions for xt .One is by assumption that it follows a linear difference equation.The other is that it follows the equation of motion of the system with Et xt+1consistent with the linear difference equation.The two equations must be consistent and this determines the coefficients of thelinear difference equation.iiiiiiiiiiiiiiI am now going to give you yet a third way of solving this same system by “lag operators.”I think that I should give you some motivation for spending time on three methods of solution of the model.There used to be, and still is, a cult that says “we are what we eat.”This view of the world is not true because we are the net of what we engorge minus what we disengorge. (There may also be some re-arrangements inside).3Similarly, there is a view of economics that economics is the resultant of the problems that we can algebraically solve.Let me give you two examples.Keynes’ General Theory developed because he was able to construct a system of equations with three endogenous variables: income, interest and prices. That made him, remarkably, one of the mathematical economists of his day.We got rational expectations when Lucas and Sargent discovered ARMA processes.It is very important for you as individual economists and for the profession as a whole to have the widest possible range of problem-solving techniques.A new technique widens our horizons.For that reason I am going to review David’s two methods for solving the Taylor model. This time I will show you a second method of solution, by lag operators.The lecture today will have 3 parts.1. Lag operators solution to Romer’s version of the Taylor model.2. Review of the Taylor model.3. Comments on the Taylor model.To plug you in, let me re-derive David’s key equation.DIVIDE LHBB IN TWO.From microfoundations he derived:p it * = N mt+ (1 - N) pt,where pit* is the optimal price for the firm to charge for its product at time t.And then assuming that xtis chosen as close as possible to the optimum:x t = ½ (pit* + Etpit+1*)where, of course, xtis the price that is newly set at t. As a result4。

高宏课件Chapter 1 Solow Growth Model

高宏课件Chapter 1 Solow Growth Model
# 高宏课件Chapteห้องสมุดไป่ตู้ 1 Solow Growth Model
简介
描述S olow增长模型的意义和应用，解释其重要组成部分。 Introduce the significance and applications of the Solow Growth Model and explain its important components.
总结
S olow模型的优缺点，S olow模型在经济增长研究中的价值，S olow模型的未来应用和发展趋势。 Summary: strengths and weaknesses of the Solow Model, its value in economic growth research, and future applications and development trends.
Solow模型概述
S olow模型的基本假设，生产函数和边际产出，稳态状态和收敛性。 Overview of the Solow Model: assumptions, production function and marginal output, steady state and convergence.
模型应用
S olow模型在各种经济系统中的应用，特定假设下的计算，政策建议的制定。 Applications of the Solow Model: its use in various economic systems, calculations under specific assumptions, formulation of policy recommendations.

高级宏观经济学课件

0.563 0.166 0.295 0.809 0.608 1.000 0.500
0.106 0.267 0.224 0.321
0.515 0.326 0.633 0.848 0.263 0.500 1.000
1.3.5产出水平与物质资本
资本产出比1988，美国为1
1.5
1
0.5
0 0
y = 0.4824x + 0.7104 R2 = 0.3059
correlation A
0.060 0.086 0.032 0.039
0.293 0.267 0.912 1.000 0.553 0.809 0.848
0.891 0.709 0.362 0.349
0.851 0.234 0.275 0.553 1.000 0.608 0.263
0.632 0.454 0.390 0.349
¾ 祖先、地理无法选择，是约束； ¾ 改革、消除发展中的障碍是可以选择
43
2.0、爱拼就会赢？
¾ 二战后，发展中国家的增长是大起大落，不可持续
在全球有数据的125个经济体中，
90%的经济体都经历了10 年内的增长记录比美国最高增长记录都要高；
94%的经济体都经历了10 年内的增长记录比美国最低增长记录都要低。
数据来源: Jones和Olken( 2008)
44
2.0、起落式增长没有赢家
¾ 二战后，全球财富分布几乎不变
数据来源: Acemoglu et al( 2002)
45
2.0、起落式增长源于领导人更替
¾ 二战后，发展中国家领导人的自然/意外死亡伴随着经济增长的起落。
数据来源: Jones和Olken( 2002)

厦门大学高宏二2014年笔记-Chapter1 导论

13
Spring, 2014
Spring, 2014
14
History of Macroeconomics

Evolution of Macroeconomic Thought Development of Macroeconomic Model Recent Development
Spring, 2014
Evolution of Macroeconomic Thought
1920
1930 大萧条 1929 1933
1940
Business cycle Monetary theory
Ramsey(1928) 一般均衡模型
Harrod(1939) Hicks(1937) 1936年凯恩斯《通论》 IS-LM模型
thousands of people
19 70 19 71 19 72 19 73 19 74 19 75 19 76 19 77 19 78 19 79 19 80 19 81 19 82 19 83 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98
Spring, 2014
1
Macroeconomic Performance and the Development of Macroeconomic Theory over the Past 100 years
Macroeconomic Performance The Great Depression:1929-33 Golden Age:1950-70; Growth Diffusion Great inflation: Early of 1970s Business Cycle: 1973-the middle of 1980s Great Moderation: 1990-2007 Income divergency High-tech Bubble: Early of 2000s Globalization: 2000s Financial Crisis: 2007-2009 After the Crisis Development of Macroeconomic Thoughts and Models Keynesian: Macroeconomic Theory Solow:Growth theory Samulson: Fridman Lucas Prescott Transition of macroeconomic model Fresh water and Salt water Market efficincy Indogenous growth theory Keynes Hayek: The Clash that Defined Modern Economics, by Spring, 2014 Nicholas Wapshott

chapter_01

Introduction
Companion slides for The Art of Multiprocessor Programming by Maurice Herlihy & Nir Shavit
Art of Multiprocessor Programming
Moore’s Law
Transistor count still rising
Art of Multiprocessor Programming
19
Parallel Primality Testing
• Challenge
– Print primes from 1 to 1010
• Given
– Ten-processor multiprocessor – One thread per processor
Art of Multiprocessor Programming
17
Road Map
• We are going to focus on principles first, then practice
– – – – Start with idealized models Look at simplistic problems Emphasize correctness over pragmatism “Correctness may be theoretical, but incorrectness has practical impact”
• Need dynamic load balancing
Art of Multiprocessor Programming
24
Shared Counter
19

高宏课件3 lecture

证券投资组合
1
证券投资组合理论
学习如何构建和管理有效的证券投资组合。
2
投资组合管理的实证研究
研究投资组合管理的最新实证研究成果。
3
投资组合管理的实践
介绍投资组合管理的实际操作和策略。
投资银行
投资银行概述
深入了解投资银行的角色和职责。
投资银行业务与利润模式
探讨投资银行的主要业务和盈利模式。
投资银行未来发展趋势
研究方法
1
实证研究方法
学习如何进行实证研究，提供方法和工具。

系统模型的建立与求解
深入了解系统模型的建立和求解过程。
3
财务分析方法
介绍财务分析方法和技巧。
投资决策
投资决策的基本理论
学习投资决策的基本理论和原则。
实证研究
了解投资决策在实践中的应用。
指标体系的建立
掌握建立有效指标体系的方法。
公司财务
1
公司财务概述
深入了解公司财务的相关概念和原则。
财务报表与财务分析
2
学习如何分析财务报表以评估公司的
财务状况。
3
财务风险
了解财务风险的概念和应对策略。
股票分析
股票市场概述
深入了解股票市场的基本概念和运作。
金融市场与股票市场的关系
探讨金融市场与股票市场之间的联系和相互影响。
股票种类及特点
了解不同类型股票的特点和投资策略。
高宏课件3 lecture
这是高宏课件3的第一讲，我们将深入探讨现代金融领域的研究方法、投资决策、公司财务、股票分析、证券投资组合、投资银行等重要主题。
总体介绍
课程背景
深入了解现代金融领域的知识和技能。

chapter1-3PPT课件

When You Do Your Best, Failure Is Great, So Don'T Give Up, Stick To The End
演讲人：XXXXXX 时间：XX年XX月XX日
重要的物理概念—— “模式”，如何理解模式？首先考虑电磁场在无边界的自由空间中的传播情况：
在均匀各向同性介质中，电磁场的波动方程即为：
若介质对场的损耗为0，则得到：沿某一方向传播的单色平面波是它的一个特解，表示为
电磁场在腔内的传播
考虑一个具有理想导电壁的矩形腔，如图所示
y
x
腔内电场满足波动方程
在光频波段 <<L 空腔中模式数很大，这是光谐振腔面临的巨大挑战。
频率越高，即波长越短，模密度越高，激光越难实现。
写在最后
成功的基础在于好的学习习惯
The foundation of success lies in good habits
14
结束语
当你尽了自己的最大努力时，失败也是伟大的，所以不要放弃，坚持就是正确的。
1 4
k
2
•d
k
8
考虑到对每个 k 有两个可能的模，则在给定范围内总模式为
2
1 4
8
2 2 2
c c
d
8 2
c3
Vd
2a 2b l
单位体积在频率附近单位频率间隔的模式数
模密度为：
8 2
n c3
n
8
c3
2
3GHz 即 10cm 微波时模密度非常低
封闭空腔中可以做到只有一个模式，构成Maser
计算腔内单位体积内，在 ~ d 频率范围内可能存在的模式数
两个相邻的模间隔为

高宏教学大纲

《高级宏观经济学讲座》教学大纲左大培课程名称：高级宏观经济学讲座授课对象：经济学部硕士、博士研究生授课教师及职称：左大培，教授授课方式：讲授学时：45小时（每周讲授3小时，讲授15周）学分：由研究生院确定课程内容概要：主要讲授以高等数学为分析手段的宏观经济理论模型，其中包括一、宏观经济政策、宏观经济学的主要问题及两大流派的回答（一）宏观经济政策的主要目标及宏观经济学的主要问题1.宏观经济学与宏观经济政策的四大目标2.新古典经济学回答上述问题的基本精神3.失业的分类与自然失业率4.物价总水平的度量与决定5.储蓄等于投资：产品市场均衡的条件——排除纯结构因素（二）宏观经济学中的古典经济学（Classical Economics）的主要观点：主流微观经济学的宏观推论1.其出发点2.劳动市场3.古典经济学的宏观产品市场和资本市场：充分有效的储蓄和投资的利息率弹性4.古典经济学在物价总水平决定上的辅助支柱：货币数量论5.价格机制稳定性的最后保障、货币数量论的补充：庇古效应6.古典经济学对经济增长和经济波动的解释。

实际经济周期理论（三）凯恩斯主义者对古典经济学的批判1.劳动市场不会自动达到充分就业2.储蓄等于投资不能保证达到充分就业均衡3.产品市场本身也常常由于本身的价格机制失灵而处于不均衡状态4.多重均衡下可能陷于就业不足均衡5.各市场之间：一个市场的不均衡对另一个市场的有效供给与有效需求的影响（一般非均衡分析）二、当代的经济增长理论模型（一）索洛增长模型（二）更完善的新古典经济增长模型1.无限期界模型2.世代交叠模型（三）新增长理论1.将知识的积累内生化2.将人力资本的积累内生化三、解释宏观经济波动的当代理论模型（一）实际经济周期理论（二）传统凯恩斯主义的经济波动理论（三）名义量不完全调整的微观经济基础1.卢卡斯不完美信息模型2.错开价格调整3.新凯恩斯主义经济学教学要求：掌握以模型和数量化方式表述的宏观经济理论，学会以高等数学手段论证和探讨经济增长和宏观经济问题考核方式：开卷笔试，课程结束后交开卷考试作业一份基本教材：David Romer: Advanced Macroeconomics. The Mcgraw-Hill Companies, Inc. 1996 中译本《高级宏观经济学》，（美）戴维·罗默著，商务印书馆，1999年参考书：Blanchard, Olivier Jean; Fischer, Stanley: Lectures on Macroeconomics. 中译本《宏观经济学（高级教程）》，（美）奥利维尔·琼·布兰查德、斯坦利·费希尔著，经济科学出版社授课教师个人简历左大培，男，1952年8月生于辽宁省大连市。

高级宏观经济学课件(厦门大学,龚敏) chap 1

Lecture 1 The Solow Growth Model Romer(2001), Advanced Macroeconomics, Chapter 1 Blanchard, Olivier J., 2nd edition, Macroeconomics, Prentice Hall曼昆，《宏观经济学》，人民大学，2000年巴罗，萨拉伊马丁，《经济增长》，中国社会科学出版社，2000年Some Basic Facts about Economic Growth Assumptions of One-Sector Growth Models The Dynamics of the ModelThe Impact of a Change in the Saving Rate The Speed of ConvergenceThe Solow Model and the Central Questions of Growth TheoryEmpirical Applications一、Some Basic Facts about EconomicGrowth: the stylized facts of growth1. Economic growth through deep time(F2)2. The stylized facts✓ 0,>>y L Y （F3）✓ o k L K >> ,(F4)✓ t cons Y K Y K tan ,== (F5)✓ t cons YP Y W t cons YP t cons K P tan 1,tan ,tan =-====ρ3. international differences in the standard of living (F6)4. The Solow growth modelThe ultimate objective of research on economic growth is to determine whether there are possibilities for raising overall growth or bringing standards of living in poor countries closer to those in the worldleaders.The Solow model is the starting point for almost all analyses of growth.The principal conclusion of the Solow model is that the accumulation ofphysical capital cannot account for either the vast growth over time in output per person or the cast geographic differences in output per person. The model treats other potential sources of differences in real incomes as either exogenous and thus not explained by the model.( in the case of technological progress) or absent altogether(in the case of positive externalities from capital).二、 Basic assumptions of one-sectorgrowth models1． Input and Output),(t t t t L A K F Y1) Labor-augmenting orHarrod-neutral),(t t t t L K A F Y = capitalaugmenting),(t t t t L K F A Y = Hicks-ueutral2) The ratio of capital to output, K/Y, eventually settles down3) Constant returns to scale(first-degree homogeneity)✓ The economy is big enough that the gains from specializationhave been exhausted.✓ Inputs other than capital, labor, and knowledge are relativelyunimportant.4) intensive form :✓ The amount of output per unit of effective labor depends only on the quantity of capital perunit of effective labor, and not on the overall size of theeconomy.✓ output per worker)(k Af ALY A L Y == 5) Assumptions0)0(=f0,0<''>'f f0)(lim )(lim 0='∞='∞→→k f k f k k ( Inada conditions)✓ The path of the economy does not diverge✓ Cobb-Douglas functionαα==k ALK k f )()( 2． the evolution of the input into production1) Labor and knowledge grow at constant rates:nt L L nL L eL L t t tnt t +=⇔=⇔=00ln )ln( gt L A gA A eA A t tt gt t +=⇔=⇔=00ln )ln(2) Investment and capital formation t t t t t sY S I dtdK dt dK I S GI T S =====+=+ t t t K sY K δ-=三、 The simple dynamics of growth model1． The Harrod-Domar model1) The fixed-coefficients productionfunction⎥⎦⎤⎢⎣⎡αυ=t t t L K Y ,min2) Saving, investment, and the warranted rate of growthυ==s I Y 3) Labor force growth:g n Y +=4) The Harrod-Domar condition:υ=+s g n2． The Solow model1) Cobb-Douglas function(F7)kk y ALK AL YK Y k k MPk k MPk k ALY y AL K Y )(10)1()(0)(211===υ<-αα=∂∂>α====-α-ααα-α2) The dynamics of kg y LY k f LeK f Le Y E Y y E K F Y e L E gt gt t t t tg n t +=======+ )()()(),()(0O ne way: actual and break-even investmentk g n k sf k dtdk t t )()(δ++-== 0)()(>⇒δ++>k k g n k sf t, k is rising 0)()(>⇒δ++<kk g n k sf t , k is falling 0)()(>⇒δ++=kk g n k sf t , k is constant *)(*)(k g n k sf δ++=T he second way: speedk g n k sf k dtdk t t )()(δ++-== )()()ln(δ++-=g n kk sf dt k d t t )(**)(δ++=g n k k sf )()ln(1δ++-=-αg n sk dtk d t t )]([)ln()()ln(1δ++-⨯α=α==-ααg n sk dtk d dt k dlin dt y d t t t t3) the balanced growth path*************)(*k A L K y A L Y y k Y K k L A K Y L A Y k f y t t t t tt t t t t t t t t ======**)(k sg n k f ++δ=)]()([)()()),((t t t t t tt t t t t t t k f k k f A k f L K k f A dL L A K F d w '-='-== )()),((t t t t t k f dKL A K F d r '== t t t t t Y K r L w =+The Solow model implies that,regardless of its starting point, theeconomy converges to a balancedgrowth path --- a situation where eachvariable of the model is growing at aconstant rate. On the balancedgrowth path, the growth rate ofoutput per worker is determinedsolely by the rate of technologicalprogress.四、The impact of a change in the savingrateThe division of the government’spurchanses between consumption andinvestment goods, the division of itsrevenues between taxed and borrowing,and its tax treatments of saving andinvestment are all likely to affect the fraction of output that is invested.1. the impact on output(F24,F25)A change in the saving rate has a level effect but not a growth effec t: it changes the economy’s balanced growt h path, and thus the level of output per worker at any point in time, but it does not affect the growth rate of output per worker in the balanced growth path.In the Solow model only changes in the rate of technological progress have growth effects; all other changes have only level effects .2. saving and consumption (welfare) )()()()1(t t t t k sf k f k f s c -=-=*)(*)(*)(*)(*)()1(*);(**k g n k f k sf k f k f s c s k k δ++-=-=-== sg n s k g n g n s k f s c ∂δ∂δ++-δ'=∂∂),,,(*)](),,,(*([*if )(),,,(*(δ++>δ'g n g n s k f ,0*>∂∂s c if )(),,,(*(δ++<δ'g n g n s k f ,0*<∂∂s c if )(),,,(*(δ++=δ'g n g n s k f , 0*=∂∂sc the golden-rule level of the capital stock: Consumption is at its maximum possible level among balanced growth paths . δ++=δ'=g n g n s k f MPK )),,,(*(Quantitative Implications1． The effect of s on output in the long run sg n s k k f s y ∂δ∂'=∂∂),,,(**)(*),,,(*)()),,,(*(δδ++=δg n s k g n g n s k sf 0*)()(*)(*>'-δ++=∂∂k f s g n k f s k?*)](/*)(*[1*)(/*)(***k f k f k k f k f k s y y s '-'=∂∂⋅*)(/*)(*k f k f k 'is the elasticity of output with respect to capital at *k k =. Denoting this by *)(k K α*)(1*)(**k k s y y s K K α-α=∂∂⋅If markets are competitive and there are no externalities, *)(/*)(*k f k f k ' is the share of total income that goes to capital on the balanced growth path.31*)(≈αk K 21**=∂∂⋅⇒s y y s A 10% increase in the saving rate (from20% of output to 22%) raises output per worker in the long run by about 5% relative to the path it would have followed.Significant changes in saving have only moderate effects on the level of output on the balanced growth path.2． The speed of convergence1) One way)()(δ++-==γg n kk sf k k k k k f )(资本的平均产品。

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8.6 不确定性
8.7 金融市场的不完全性
h
11
f)
pK
(t)
其中: f为公司所得税减税比率
h
(8.5)
5
4.模型的不足之处
(1)假定资本存量调整是完全有弹性的，无成本的，无限制的，实际上投资受限于产出规模，因此投资和资本不可能无限连续(infinite)变动；
(2)未考虑预期因素: 当预期需求上升或资本成本下降时，K↑；
(3)对模型的修正: 引入资本存量的调整成本
1）内部调整成本：如安装新机器设备的成本，训练工人操纵新机器设备的成本，利率变动的成本等。
2）外部成本：资本h品价格的变化。
6
8.2 Q Theory Model of Investment
with Adjustment Cost
1.假定：
一产业有N个同质厂商
(1)一个典型厂商的实际利润与其资本存量(k(t))成正比（若规模报酬不变、产品市场完全竞争、
K(t) I(t) 2. 厂商的利润函数(8.6) 即利润=收益－I－调整成本若用离散时间，则(8.7)
h
8
预算约束 : kt1 kt It
最优化 : (8.8) t : 资本的边际收益
令 q t (1 r ) t , 变成 (8 .9 )
L : (8.10) I
为总收益, Xs:产品价格和要素成本等假定:K 0,KK0
2.合意的资本存量的确定
K P K (K ,X 1 ,X h2 ,X 3 , ,X n ) r K 0 3
K()rK (8.1)
厂商合意的资本存量 Kf(rK,X's)
对 (8.1)式对 rk求导 :
KK(K,X1,X2, ,Xn)K(rK,X1 ,rX K2, ,Xn)1 (8.2)
8.3-8.5:托宾的q理论：对预期利润率提供了一个间接测度指标；
8.6-8.7:考察不确定性和金融市场的不完全性对
投资的影响。
h
2
8.1 Investment and the Cost of Capital
1.厂商的利润函数
P(K,X1,X2,X3, ,Xn)rKK
其中:K为厂商租用0 (8.3)
rK KK
结论:rKK
合意的资本存量与资本的租用成本反向变化
h
4
3.资本的使用成本
rK(t)r(t)pK(t)pK(t)pK(t) [r(t)ppK K((tt))]pK(t) (8.4)
三要素: 利率,折旧,资本价格升降若考虑税率,则:
rK
(t)
[r(t)
pK pK
(t)](1 (t)
1 C ( It ) qt
(8 .1 1)
(8.11)含义 :
左边 : 获得 1单位资本的成本 =购价 (假定为 1)
+边际调整成本
右边 : q t (1 r ) t 为资本价值
若是连续时间 , 则 (8 .2h2 ) 式
9
8.3 Tobin’s q
CHAPTER 8 INVESTMENT
h
1
I的重要性:(1)长期增长效应:I →K →Y
(2)短期波动效应:Ｉ→ＡＤ→Ｙ
以前的投资理论：I=f(MEC或EPR, r)＝I0-σ·r 投资乘数论→投资周期论
本章思路：
8.1-8.2:投资决定的基础模型：拓宽利率的概念, 将利率拓宽成资本的使用成本;
q
1单位资本的市场价值 1单位资本的重置成本
q :包含所有影响利润的因素和信息, 所以
它是衡量预期利润率的一个间接指标
q对K的影响:
当q I K
如图8.1
h
10
8.4 略
8.5 Implications
(影响投资的其他因素)
1.产出的规模(加速原理); 2.利率波动效应(P384第二段); 3.税收效应。
其他生产要素供给完全有弹性）；
(2)当整个产业的资本存量(K(t))增加时，该厂商的利润递减（若该产业产品的需求曲线向下倾
斜）；
若以π表示收益率，π=π(K(t))，则π' (·)<0
厂商收率为π·k (t)
h
7
(3)调整成本是厂商资本存量变化(k)的凸 (Convex)函数, C f (k)
特别假定:C(0) 0, C(0) 0, C() 0 又特别假定资本品的购买价格为常数, 等于1,故只有内部调整成本(不考虑外部成本), 折旧率为0,

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