1、Macroec ono mics1、 Cinsider Hr fLonomy fhirt produces ind Ci)nsLinn brd nnd autrnnb lex. The iblxjwing table contains dara for two di fferenl years:Year 2000Year 2010Price uf an autumobiteS4O.00QS50.00DPrice of a loaf uf breadSI.50S250Number cf autoTicblt?s produced100120Slumber uf loaves of bread p

2、roduced5,00(X0004,(K)6,0U0Usin琴 the year 2000 as the bdse yejr, compute the fbl lur ing ta:isties for each year, nunmidl GDP* GDP, tlie implkit prix deELur lor QDPTand a fixeJ- YhCigJil pner index such .tis the CPLSUJOOOO畑柚川GDPJ0 =(亠嚴(yán)* 0陽(yáng)丿-f PJM * QzU= S16,OOMOORea/ GDP訕=厲嚴(yán)* Q2ftStt)+ (際嚴(yán)丿* Q沁嚴(yán)/-SiO

3、MOOOImpticil Price Deflator2nio = Nominal GDP2VIQ / R訕 GDP抑o = /一砧CP； - t p 刃M tzi 2叫p叫LX刑f Fif二 dF2t p :伽* 亍剛,亠f p :剛審一XM ,廠 cao/廠 Arearf尼的 re口曲/-1.522、Suppose that this years money supply is $600 billion nominal GDP is 10 trillion and real GDP is S6 trilliona) What is the price level? what ib the

4、velocity of money?b) If the fed keeps their money constant and the velocity is constant and the output of goods 白n equation Fvl.P-Y.V.M=500bNGDP=10Q00bRGOP=5OQObNGOP = RGDPx P - PY10R000 - 5C00 x PP = 1000/000 = 2V 二 PY/M 二 1Q1000/500 - 20b) AM=0; AV=&; AY=+5%c)(1+fiArt)/(1*AP)二 i1+AY)/(1+AV1 / (1+A

5、P) = 1+5% / 11/ (1+ZiP) = 1.051+AP 二 VI Q5AP = (1-1 05X1 朋=0 05/1 05*-0 0476 4 76%AFJGDP = iPY= (I+ZIPX1* -1 = (t1/1 DSM1.05) -1 = 1-1 = 0Nominal GCP will refnain the same no change) * because growth in RGDP will be ofTset by fall in price I aval.Price level will fall thus delfaior will decrease.d)n

6、=AP=0 : ZlV%=0 : A%=+5%(1+AM) /(1+APJ = (1+AY；/ (1+AVj(1+AIVI)/1 = (1+5*%)/11+AM = 1+5%AM = +5%M = 500 billion +5% = 5WM 05 = 525 billionu=APix)=+io% ； av%=& ； ay=+5%(1+AM)/(1-bAP) = (1+AYJ/(1+iV)(1+AM)/ 1.1 = 1.05 / 11+AM = 1.05x1.1 = 1.155Af% = +15 5%M 二 500 billiofi +15.5% = 500x1.156 = 5Z7.5 bil

7、lionAM=+77.S billion3、SupposE the governrrient reduces taxes by 20 billion that there is no crowding out and that the marginal propensity to consume (MFC) is 3/4(a.) W hrat is the initial effect of the tax reduction on aggregate demand?(b.) What additional effects follow this initial effect? What is

8、 tho total effect of the tax cut on aggregate demand?(c ) How does the total effect of this S20 billion tax cut compare to the total effect of a $20 billion increase in government purehases? Why?(a J The initial effect of the tax reduction of $20 billion on aggregate dem arid is S15 bi|lionr A tax r

9、eduction of 2Qbln is already esrned disposable irrcome uf the households and others Of this additional income, they consurre only 34ths as th& npc is 3/4 And 3/4th of $20 billion is $15 billion.(b.) The additional effects that follow this initial effect is $4S billion. This happens because after lhe

10、 initial increase in aggr&gale demand and therefore in aggregate income by $15 billion, in ths next eurd there 低 furth&r addrtion to aggr&gate demand by 3/4 of S15 till ion ar 510.25. billion. In the same way the next successive rounds the increases in aggregate demand are 3/ith cf 10 25. 3/4：h of 3

11、/4 erf 10.25, and so on. Ttie tolal effect of the tax cut on aggregate denand is :he reduction in the tax amount multiplied by the tax multiplier -(-$20 billion f(-3/4)/(1-3/4) = S (20*3M 1/4 = 60 billion.(c.) The total effect of a S2Q billion increase in lovernnwnt purchases would t)e higher becaus

12、e the initial effect is higher. A 520 billion govt purchase is a straight addition to aggregate demand and initial round income exfansion unlike in the case of 520 billion tax cul, the taxpayers increased their co ns um option demand fcy only 315 billion . mpc b&img 3/4.The to：al effect of goxt purc

13、hases is given by the incresse in gc/t. purchase of t20 billiorr multiplied by the spending multiplier. The spend ng mult plier is given by 1i 1 - moc) = 1/ (1-3/4) = 1/(1.4) = 4. So the total effect of the gcivt purchase addition cf 320 billion is $(20 *4 billion = S&O billion. Thus, the total effe

14、ct af this $20fatten tax cut is 320 billin lower than the the total effect of 3 S20 billion ncrease in govermnent purchases.4、Abby consumes only apples. In year 1, red apples cost 1 dollar each, green apples cost 2 dollar each, and Abby buys 10 red apples. In year 2, red apples cost 2 dollar, gree n

15、 apples cost 1 dollar, and Abby buys 10 gree n apples.a. Compute a consumer price index for apples for each year. Assume that year 1is the base year in which the con sumer basket is fixed. How does your in dex cha nge from year 1 to year 2?b. Compute Abby s nominal spending on apples in each year. H

16、ow doeit change from year 1 to year 2?c. Using year 1 as the base year, compute Abby Beal spending on apples in each year. How does it cha nge from year 1 to year 2?d. Defining the implicit price deflator as nominal spending divided by real spending, compute the deflator for each year. How does the

17、deflator cha nge from year 1 to year 2?Suppose that Abby is equally happy eati ng red or gree n apples. How much has the true cost of livi ng in creased for Abby? Compare this an swer to your an swers to parts (a) and (d). What does this example tell you about Laspeyres and Paasche price in dexes?、（

18、氏d w爲(wèi)）十仔;嗣旳爲(wèi)？($2x 10)+ ($1xO)=2.a.CPI吧電/十哼J爲(wèi)k($1 x 10)+ (S2xO)According to the CPI(消費(fèi)物價(jià)指數(shù))，prices have doubled.b. N-spe nding is the total value of output produced in each year. I n Y1 and Y2, Abby buys 10 apples for $1 each, so her N-spe nding rema ins con sta nt at $10.Nomina) Spending. = (Ph x Q初

19、)十(Pn % Q 曲“)=(S2 x + (SI x 10)= $10.c. R-spe nding is the total value of output produced in each year valued at the prices prevail ing in Y1.ln Y1,the base year,her R-spe nding equals her N-spe nding of $10 .In year 2, she con sumes 10 gree n apples that are each valued at their Y1 price of $2, so

20、her real spe nding is $20.Real Spending;.二(P爲(wèi))= ($1 x 0) + ($2x 10)= $20.Hence, Abby s real spendinges from $10 to $20.Implicit Price Donator = Nominal Spending,d.Real Spending；$20Thus, the implicit price deflator suggests that prices have fallen by half.e. If Abby thinks of red apples and gree n ap

21、ples as perfect substitutes, the n the cost of liv ing in this economy has not cha nged.According to the CPI, however, the cost of living has doubled. In contrast to the CPI, the implicit price deflator estimates the cost of living has halved.Thus, the CPI, a Laspeyres in dex, overstates the in crea

22、se in the cost of liv ing and the deflator, a Paasche in dex, un derstates it.This chapter of the text discusses the differe nce betwee n Laspeyres and Paasche in dices in more detail.5、3. Corsider sn tcontrn/ay the fol dwirg equations：Y = C-l-GV = 5.0DI)C - 1,0007 = 1.QDUC = 25ft + 0 7F5(y - f)/ -

23、1,000 - 50ra. In tnis economv compute private saving, public saving, aid national saving (2 points)DiSpoSabb Incone= 5,000-1,003=4,COCortsunnption=250+0J54 CX)O)-325OPrivate Saving-4f0X-325O-750Pub ic Savings0NoTionai Saving=75Ob. F nu the equil brium interest r=te (2. pBnt)S=I750tt000-50rr=5c. Mow

24、suppose that G rises to LT2S0. Campute private 歸win缶 public saving, and riHricinal v ng (2 pnints)Ccnsumptior d&ef nat change. So does private sav ngPublic $av i ng1000-12 5O=- 250Natioral saving=750-250= 503ck Find the re% equilibriurn interE，t rate. 1 point)5=1500=1000-50r0.3r=10.6、Suppose that an

25、 economy s product ion function is CobbDouglas with parametera. What fractions of in come do capital and labor receive?b. Suppose that immigrati on in creases the labor force by 10 perce nt. What happe n to total output? The ren tal price of capital? The real wage?c. Suppose that a gift of capita fo

26、rm abroad raises the capital stock by 10 perce nt. What happe ns to total output(i n perce nt). The ren tal price of capital? The real wage?d. Suppose that a tech no logical adva nee raises the value of the parameter A by 10 perce nt. What happe ns to total output? The ren tal price of capital? The

27、real wage?a. A CobbDouglas producrion function has the form Y = AKLThe text showed that themarginal products fior rhe 匚obb-Douglas production funcrion are：MPL - (1 aAKL-1 - (l -a) LMPK = ciAKa，:Llut when the labor fbrf亡 intr亡齡亡 by 10 percent, considerdie formula tor (he Cobts-Douglas production func

28、tion:Y = AKttL X.Lei Y equal the initial value of otnpui and 2 r L increases by 10 nerceiil：Yi = AK.a iL U TYa-AK*L1L)MScte that we iTiultiplied L by- I, I to reflect 10 percent mcreaiie tn the Jabor force.To calculate die percentage change in ourpiiL divide Y?by YuAJC1.1L)071.069Thar i, miipLii inc

29、reases bj 6 9 perceni.To dctcniiine how increase in the labor force afTiccis the re nml price of capital, consider rhe ionnulfl tor the real rental price ot capital R P*R 卩-MPK -oAKL1*1We knov th且t ci= 0.3-e also kiiovi- that labor ( increases by 10 percent. Let t亡口ual theinitial value? of rhe renta

30、l price of capital.fc and (Jl/P工 equl the final rental price of c apital after the labor Cbrce increases by IO percent; To find (/f/P)=, multiply L by I. I to reflect the J 0-percenc imcreaw in the labofbrrECIL P), - 0.3AK Y1*7(R P-OAKI.ILy1 TI he rercal price inertises by ch ratio:CR/P3； 0 3Ar*07(l

31、.lL)07(R/Pt K_o7toT=(1計(jì)二 1-069.So, the rental price incrcascs by 6*9 pcrcccn.To determrne how increase in the labor force affects ihe re ntal price of eapriaL conoid er rhe formula far the real rental price of capital ft PzR P = VPK = OAICL We know liar ci= CLL We also know iliai labor (A) increases

32、 by 10 percent. Lee /? equal (he niiti a alue of the rnta.1 price of capital, a_nd ( R.P equal the final retital price o-f capital ifter the labor force icreases by 10 pcrctnt. To findmultiply L by I. I to reflect the 10-percentincrease in the labor force:(R.P! =03Ak7LUT(IbP = 0 3AK? J I .IL07The re

33、mal price inertby he rauc:(R/P2il嚴(yán)t(彷J7 二 亍=(Li)07=1-069.So, the rental price increases by 6.9 nereetn.To derennine Jiow the increase in ihe labor force affecTS the real wage, consider the fonnula for die real irage ifZP：W P = MPLU-f(|AKlaL*1Wc know tiiat 0.3, XAe ailso know tFiat labor i L iricreas

34、e by 0 percent. Let( FJ-P), equal the itiiiial xalue of die real wage and (Fr/F)： equal (he final valu已 of ihe real wage. To find L I to reflecLthe l&-percetir increase in the labor force:(W. P), (M)_3)A1C 嚴(yán)(W.P)2 =(ro.3)AK,WJ( IJL)3To calculare Hi亡 percentage change m ih亡 real wage, divide ( u/F)；

35、by【了尸卜;：(W/P)5 _ Cl -O3)Aoaa.lL)-a(W/P)!(1 O.3)/fO3-3=0.972.So the real wage decreases by 2.Snr. The intuition is tlutt as supply of labor increase labor becomes relatively abundajK and capiial becomes relatively s;ar;e r 菇 ourws of rhe econotuy;Ikiicc, real decrcascs and real rciual rate increases.

36、c. e can us& the same logic as in pan (b) to seiYa*A(IJK)uJL bThereforeT ue hape:Yz _ A(l.lf()03L07可二AKLP7=CLloa=1.02Q,This equatiotii kHou e char output mcreases by about 3 percent. Notice that aY. Whin a and L stays the samef MPL and、 arc directly proportional. d. Usin# the same fbnnula. ue find i

37、tiai The chaise in ouipui i乳Yz _ CLl/IJK037K = 丄沖小-=1.1This ecjnatiDn shows that output mcreascs by 10 percent. Similarly, the rental price of capitis I iuid the rea.1 wage also increase by 10 percent;(R/P)2 _ D3fl,l/l)/4AR-O7LO7=L.l(WyPJj 0 7(1(W/P)! =0,74/CO3L-na=1.17、Suppose that the money dema n

38、d fun ctio n takes the form(M/P)d L(i,Y) Y/(5i)a. If output grows at rate g, at what rate will the dema nd for real bala nces grow(assu ming con sta nt nominal in terest rates)?b. What is the velocity of money in this economy?c. If in flati on and nominal in terest rates are con sta nt, at what rate

39、, if any, will velocity grow?d. How will a perma nent in crease in the level of in terest rates affect the level of velocity? Howwill it affect the subseque nt growth rate of velocity?a. f output Y irons at rat5 比 then real nicnev balances (M PiJ must also 呂rcnv at 圧忙 gh iven that the nominal mtenes

40、t rate i 占 a cons：antrExpressing:he money demand function in percemage change fbim, we have：% Change t I P F = S Change in Y * ? Change in(5；Khenthe notniiial interest ra：e does not change. x e havedb Change (X1;P)d = % Change in Y-0.g = % Change in Y.b. To find the velociiy of money: star 旺譏h (he q

41、iiantit;. eq nation MV = P、 and rewrite the eqcacicui es fXLP) = (l/V)Y. Since mo：iev supply and money demand should be the samg、叭v have (M/P)= (M/P)*. Fierce (I V)Y = Y 工 Therefore, the velocity of money is V = 5ic. From part b w e tua-e V = Si .where j is the nomitial interest rate. If Hie nominal

42、 interest rate E constant then the velocity cf money must be constant.d. Again, from pan b, we have V 5r, which means dm there a one-to-one reUiionship beiweenthe e亡of velocity and the t；vel will reduce the demand of laborb. In part w* we have solved for the real wage (W P as a function of K and L：L

43、 above is the labor demand. Ln equilibrium, we ha. e supp【y of labor = demand of labor. Since we ha e labor supply of L=LOOO in the economy, we plug-in L= 1.000 info the abo& equation. Similarly. * e plug-in K=l ,000. Then we can solve for 認(rèn) P.lpOOO = Cy)_3 1,000W 2As we have said, in equilibrium, e

44、mploy mein ls 1.000 isince labor 汕“1丫 = labor demand =IT o 呂芒 ihe output we plug-i ti equ ilibrium alu es of capital and labor K= 1.000 and L=l ,(XX) in rhe producr ion funccion:y=ki.L2/i= IOOOLOM13 U000The total output earned by workers is equal to marginal cotimbution oflabor to output (MPL) limes

45、 the atnouni of labor: MPL * L = (W P k L = (2 3) l*(XX) 667 units of output. No:e (liar the labor gets twa-thirtk (2/3) ofwtat output(Y = 1 tCOO). In Cobb-Douglas production functicm of the fcrm Y = KL 二 u and I- n stands for the capitafs and labors share of cucpuc, n this problem a=L 3.c. The Congress mandated a real wage of I unit cf out put t which 花 abote the equilihrmir real