宏观经济学期末复习

Part 1CONCEPT

Marketclearing

Exogenous variables EndogenousvariablesInflation GDPdeflatorCPI

Unemploymentrate

Labor-force

participationrateNominal versus realGDPMPKMPL Real rental price ofcapitalConstant returns toscale

Cobb?Douglas productionfunction

PrivatesavingPublicsaving

Marginal propensity

toconsumeMonetarybase High-poweredmoney

Reserve–deposit ratio Currency–depositratio

Menucosts Quantityequation

Real and nominalvariablesFisher equation and

FishereffectMonetary neutrality! Small openeconomy

Moneymultiplier

Purchasing-power parity!Natural rate

ofunemploymentFrictionalunemploymentStructuralunemploymentDiscouragedworkers Golden Rule level ofcapital

Part 2Question

Chapter2

CPI VS GDP DEFLATOR

Q: Consider an economy that produces and con- sumes

breadandautomobiles. In the following table are data for two differentyears.

2000

2010

Price $50,000 $10

Quantity 120 400,000

Price $60,000 $20

Good

Quantity 100 500,000

Automobiles Bread

a) Using 2000 as the base year, compute the following

statisticsforeach year: nominal GDP, real GDP, the implicit price deflatorforGDP, and a fixed-weight price index such as theCPI.

b) How much did prices rise between 2000 and 2010?

Comparetheanswers given by the Laspeyres and Paasche price indexes.Explainthedifference.

c) Suppose you are a senator writing a bill to index Social

Securityandfederal pensions. That is, your bill will adjust these benefits tooffsetchanges in the cost of living.Will you use the GDP deflator ortheCPI?Why?

Chapter31.MPKMPL

income share oflabor/capitalQ:

Consider a Cobb–Douglas production function with three inputs. K

iscapital(the number of machines), L is labor (the number of workers), and H ishumancapital (the number of college degrees among the workers).Theproductionfunctionis

Y ??K1/3L1/3H1/3.

a) Derive an expression for the marginal product of labor. How doesanincrease in the amount of human capital affect the marginal productoflabor?

b) Derive an expression for the marginal product of human

capital.Howdoes an increase in the amount of human capital affect the mar-ginalproduct of humancapital?

c) What is the income share paid to labor? What is the income sharepaidto human capi-tal? In the national income accounts of

thiseconomy,what share of total income do you think workers would appeartoreceive? (Hint: Consider where the return to human capital showsup.)

d) An unskilled worker earns the marginal prod- uct of labor,

whereasaskilled worker earns the marginal product of labor plus the mar-ginalproduct of human capital. Using your answers to parts (a) and (b),findthe ratio of the skilled wage to the unskilled wage. How

doesanincrease in the amount of human capital affect this ratio?Explain.

e) Some people advocate government funding of college

scholarshipsasa way of creatinga more egalitarian society. Others arguethatscholarships help only those who are able to go to college. Doyouranswers to the preced- ing questions shed light on thisdebate?

6、考虑有三种投入的柯布-道格拉斯生产函数。K-资本；L-劳动；H-人力资本。生产函数为Y=K1/3L1/3H1/3

（1）推导出劳动的边际产量的表达式。人力资本量的增加怎样影响劳动的边际产量？ 解：Y=K1/3L1/3H1/3 MPL=1/3K1/3L-2/3H1/3

因此，H增加将使劳动的边际产量MPL增加

（2）推导出人力资本的边际产量表达式。人力资本量的增加怎么影像人力资本的边际产量？ 解：Y=K1/3L1/3H1/3 MPH=1/3K1/3L1/3H-2/3

因此，H增加将使劳动的边际产量MPH下降

（3）支付给劳动的收入份额是多少？支付给人力资本的收入分析是多少？工人得到多大份额的收入？

解：劳动份额=L*MPL/Y=L*1/3K1/3L-2/3H1/3/K1/3L1/3H1/3=1/3 人力资本份额=H*MPH/Y=H*1/3K1/3L1/3H-2/3/K1/3L1/3H1/3=1/3

由于劳动与人力资本份额各占产出的1/3，两者又都归工人所有。因此，工人得到2/3的产出份额。

（4）如果一个无技术工人的报酬=MPL，一个技术工人的报酬=MPL+MPH，找出技术工人与无技术工人工资的比率并分析人力资本如何影响此比例。

解：MPL=1/3K1/3L-2/3H1/3，MPH=1/3K1/3L1/3H-2/3

W技/W无技术=（MPL+MPH）/MPL=（1/3K1/3L-2/3H1/3+1/3K1/3L1/3H-2/3）/1/3K1/3L-2/3H1/3=1+L/H

（5）大学奖学金是创造平等社会环境还是只针对那些能上大学的人？ 解：大学奖学金提高了人力资本H，有利于形成一个更加平等的机会，因为随着人力资本的增加，人力资本的边际产量减少，劳动的边际产量增加，缩小了收教育程度不同的工人之间的差异，使技术工人与非技术工人件的差距缩小，社会更加平等。

2. privatesavingpublicsaving Q:

Consider an economy described by the follow- ingequations:

Y?C?I?G Y ??5,000

G ??1,000

T ??1,000

C ??250 ??0.75(Y?T)

I ??1,000 ??50r

In this economy, compute private saving, pub- lic saving,andnationalsaving.

a) Find the equilibrium interestrate.

b) Now suppose that G rises to 1,250. Compute

privatesaving,public saving, and nationalsaving.

c) Find the new equilibrium interestrate.

Chapter4

M B c/rd/r

Q:

An economy has a monetary base of 1,000 $1 bills.

Calculatethemoney supply in scenarios (a)–(d) and then answer part(e).

a) All money is held ascurrency.

b) All money is held as demand deposits. Banks hold 100 percentofdeposits asreserves.

c) All money is held as demand deposits. Banks hold 20 percentofdeposits asreserves.

d) People hold equal amounts of currency and demand deposits.Bankshold 20 percent of deposits asreserves.

e) The central bank decides to increase the money supply by 10

percent.Ineach of the above four scenarios, how much should it increase themonetarybase?

Chapter5

MV=PY

dM/M+dV/V=dP/P+dY/YQ:

Suppose a country has a money demand function (M/P)d??kY,where kis a constant parameter .The money supply grows by

12percentper year, and real income grows by 4 percent peryear.

a) What is the average inflationrate?

b) How would inflation be different if real income growth werehigher?Explain.

c) How do you interpret the parameter k? What is its relationship tothevelocity ofmoney?

d.) Suppose, instead of a constant money demand function, the

velocityofmoney in this econ- omy was growing steadily because of financialinnovation.How would that affect the infla- tion rate?Explain.

Q: Suppose that the money demand function takes the form(M/P)d

??L(i,Y) ??Y/(5i)

a) If output grows at rate g, at what rate will the demand for realbalancesgrow (assuming constant nominal interestrates)?

b) What is the velocity of money in thiseconomy?

c.)If inflation and nominal interest rates are constant, at what rate, if any,willvelocitygrow?

d.) How will a permanent (once-and-for-all) increase in the level

ofinterestrates affect the level of velocity? How will it affect the subsequent growthrateofvelocity?

Chapter6

2. Consider an economy described by the follow- ingequations:

Y?C?I?G?NX,

Y ??5,000,

G ??1,000, T ??1,000,C??250 ??0.75(Y ??T),I ??1,000 ??50r, NX ??500 ??500, r??r????5.

a.) In this economy, solve for national saving, investment, the tradebalance,and the equilibrium exchangerate.

b)Suppose now that G rises to 1,250. Solve for national saving,

investment,thetrade balance, and the equilibrium exchange rate. Explain what youfind.

c.)Now suppose that the world interest raterises from 5 to 10 percent. (Gisagain 1,000.) Solve for national saving, investment, the trade balance, andtheequilibrium exchange rate. Explain what youfind.

3. The country of Leverett is a small open economy. Suddenly, a changeinworld fashions makes the exports of Leverettunpopular.

a. What happens in Leverett to saving, invest- ment, net exports, theinterestrate, and the exchangerate?

b. The citizens of Leverett like to travel abroad. How will this change intheexchange rate affectthem?

c. The fiscal policymakers of Leverett want to adjust taxes to

maintaintheexchange rate at its previous level. What should they do? If they do this,whatare the overall effects on saving, investment, net exports, and the interestrate?

6.ACaseStudyinthischapterconcludesthatifpoornationsofferedbetter

production efficiency and legal protections, the tradebalance in rich nations such as the United States would move towardsurplus.Let’s consider why this might be thecase.

a) If the world’s poor nations offer better production efficiency andlegalprotection, what would happen to the investment demand function inthosecountries?

b) How would the change you describe in part (a) affect the demandforloanable funds in world financialmarkets?

c) How would the change you describe in part (b) affect the worldinterestrate?

d) How would the change you describe in part (c) affect the tradebalancein richnations?

Chapter7

5. Consider an economy with the following Cobb–Douglasproductionfunction:

Y =K1/3L2/3.

The economy has 1,000 units of capital andalabor force of 1,000workers.

a) Derive the equation describing labor demand in this economy as

afunctionof the real wage and the capital stock. (Hint: Review Chapter3.)

b) If the real wage can adjust to equilibrate labor supply and

labordemand,what is the real wage? In this equilibrium, what are employ- ment, output,andthe total amount earned byworkers?

c) Now suppose that Congress, concerned about the welfare of theworkingclass, passes a law requiring firms to pay workers a real wageof one unitofoutput. How does this wage compare to the equilibriumwage?

d) Congress cannot dictate how many workers firms hire at the

mandatedwage.Giventhis fact, what are the effects of this law? Specifically, what happenstoemployment, output, and the total amount earned byworkers?

e) Will Congress succeed in its goal of helping the workingclass?Explain.

f) Do you think that this analysis provides a good way of thinkingabouta minimum- wage law? Why or whynot?

6. Suppose that a country experiences a reduction in productivity—that is,anadverse shock to the productionfunction.

a. What happens to the labor demandcurve?

b. How would this change in productivity affect the labor market—

thatis,employment, unemployment, and real wages—if the labor market is alwaysinequilibrium?

c. How would this change in productivity affect the labor market ifunionsprevent real wages fromfalling?

Chapter 89 1. consider k 1) s.s

2) goldenrole

3) starting with too much capital

starting with too littlecapital

2. populationgrowth 1)s.s

2) goldenrule

3 technologicalprogress1)s.s

2) goldenrule

3. growth ofoutput

growth of percapital

Q :chapter1-5

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