Problem 1 / 25 Problem 2 / 25 Problem 3 / 30 Problem 4 / 20 TOTAL / 100

Transcription

1 Deparmen of Economics Universiy of Maryland Economics 325 Inermediae Macroeconomic Analysis Final Exam Suggesed Soluions Professor Sanjay Chugh Spring 2009 NAME: TA S NAME: The Exam has a oal of four (4) problems and pages numbered one (1) hrough welve (12). Each problem s oal number of poins is shown below. Your soluions should consis of some appropriae combinaion of mahemaical analysis, graphical analysis, logical analysis, and economic inuiion, bu in no case do soluions need o be excepionally long. Your soluions should ge sraigh o he poin soluions wih irrelevan discussions and derivaions will be penalized. You are o answer all quesions in he spaces provided. You may use wo pages (double-sided) of noes. You may no use a calculaor. Problem 1 / 25 Problem 2 / 25 Problem 3 / 30 Problem 4 / 20 TOTAL / 100

2 Problem 1. Moneary Neuraliy or Nonneuraliy? (25 poins). Suppose firms need o use only labor in order o produce oupu, and oupu in period is given by y = An, where A is a echnology shock and n is he number of hours of labor. Firms choose heir labor in a profi maximizing way every period. Suppose he represenaive consumer s period- uiliy funcion is given by M ln( Bc ) + ln l+ ln, where, as always, l = 1 n denoes leisure, B denoes a preference P shock, and M / P is real money. Noe ha raher han supposing here are 168 unis of ime available, here we are supposing ha here is only one uni of ime available (hence, boh n and l will be fracions beween zero and one). Finally, assume he labor supply curve is always upward-sloping (i.e., i never bends backwards), and ha he labor ax rae is always zero. a. (7 poins) In he diagram below, show he effec on he consumer s opimal choice of consumpion and leisure in period due o a simulaneous rise in A and rise in B. Clearly label your diagram, and explain precisely any and all effecs perinen here. consumpion Soluion: Wih he represenaive firm maximizing profi, we know ha he real wage equals he marginal produc of labor. In his case (wih he linear producion echnology), he marginal produc of labor is simply A, which means he slope of he budge line in he above diagram (which is he real wage) is A. The rise in A means he budge line becomes seeper, pivoing around he fixed poin on he leisure axis. Nex, consider he MRS beween consumpion and leisure. We know he MRS beween consumpion and leisure (i.e., he slope of he indifference curve) is ul / u c. Wih he given uiliy funcion, ul = 1/ l and uc = B/( Bc) = 1/ c. Noe ha he B erm drops ou of he marginal uiliy of consumpion here (you had o use he chain rule o fully differeniae). Thus, he MRS is unaffeced by he preference shifer in his case, meaning he indifference map is unaffeced. 1

3 Problem 1 coninued b. (7 poins) Suppose insead of he preference and TFP shocks in par a, here were a posiive money shock (and no oher shocks) a he end of period (as we described in class i.e., he acual M urns ou o be differen han he planned M ). Suppose boh nominal prices and nominal wages are compleely flexible. In he diagram below, skech he effec on he consumer s opimal choice of consumpion and leisure in period due o he surprise exra quaniy of money in he economy. Clearly label your diagram, and explain precisely any and all effecs perinen here. (Hin: The consumpion-money opimaliy condiion is relevan for he analysis here.) consumpion iniial opimal choice leisure Soluion: Recall he consumpion-money opimaliy condiion wih log-log uiliy (derived Pc i in class and on Problem Se 7): = (again, noe ha he preference shifer B does M 1 + i no appear). A surprise rise in M in he RBC view is me wih an adjusmen in jus (all) prices, since he choice regarding consumpion represens an opimal choice. Thus P rises. Bu in he above diagram, he slope is W/P (he nominal wage divided by he nominal price level). In order o leave he planned opimal consumpion choice unaffeced, he slope of he budge line mus remain he same, which requires ha W rises by he same percenage as he rise in P. Graphically, hen, nohing changes: he budge line is unaffeced, and opimal choice remains unchanged. 2

4 Problem 1 coninued c. (7 poins) Consider again he same money shock from par b. Suppose he nominal wage is compleely rigid (i.e., i can never change), bu nominal goods prices are compleely flexible. In he diagram below, skech he effecs on he consumer s opimal choice of consumpion and leisure in period due o he surprise exra quaniy of money in he economy. Clearly label your diagram, and explain precisely any and all effecs perinen here. (Hin: The consumpion-money opimaliy condiion is relevan for he analysis here.) consumpion Soluion: The logic proceeds as in par c unil he discussion abou he nominal wage. In order o leave he consumpion choice unchanged, we saw in par c ha W had o rise by he same percenage as P. Bu here W is sicky, so he budge line mus roae somehow. Wih a rise in P and W unchanged, he real wage is lower, so he budge line pivos downward, meaning opimal consumpion is lower here. Thus, in his case expansionary moneary policy ends up causing consumpion o fall because of he sickiness in nominal wages. a. (4 poins) The RBC view is capured by which scenario, par b or par c? The New Keynesian view is capured by which scenario, par b or par c? Soluion: The RBC view is par b (all prices are flexible), he NK view is par c (some prices in his case wages are sicky). 3

5 Problem 2. Quasi-Linear Uiliy in he Consumpion-Leisure Framework (25 poins). In he saic (i.e., one period) consumpion-leisure framework, suppose he represenaive consumer has he following uiliy funcion over consumpion and leisure, ucl (,) = ln() c + Al, where, as usual, c denoes consumpion and l denoes leisure. In his uiliy funcion, ln( ) is he naural log funcion, and A is a number (a consan) smaller han one ha governs how much uiliy he individual obains from a given amoun of leisure. Suppose he budge consrain he individual faces is simply c= (1 ) w n, where is he labor ax rae, w is he real hourly wage rae, and n is he number of hours he individual works. (Noice ha his budge consrain is expressed in real erms, raher han in nominal erms.) a. (5 poins) Does his uiliy funcion display diminishing marginal uiliy in consumpion? Briefly explain. Soluion: Marginal uiliy wih respec o consumpion is he slope of he uiliy funcion when viewed as a funcion of consumpion alone. The given funcion is logarihmic in consumpion, and he naural log funcion, is sricly increasing and sricly concave, meaning he slope wih respec o consumpion is always decreasing and asympoes o zero. Hence, his funcion does display diminishing marginal uiliy in consumpion. b. (5 poins) Does his uiliy funcion display diminishing marginal uiliy in leisure? Briefly explain. Soluion: Jus as above, marginal uiliy wih respec o leisure is he slope of he uiliy funcion when viewed as a funcion of leisure alone. The given funcion is linear in leisure, hence is slope wih respec o leisure is consan. Thus, his funcion does no display diminishing marginal uiliy in leisure. c. (15 poins) Assume (as usual) he represenaive consumer maximizes uiliy. For he given uiliy funcion, plo his represenaive consumer s labor supply funcion, explaining he logic behind your ploed funcion. Also, how would a decrease in he ax rae affec he opimal amoun of labor supply (i.e., increase i, decrease i, or leave i unchanged)? Carefully explain your logic/derivaion. (Noe: Be sure o base your analysis here on he uiliy funcion ha is given above.) Soluion: The consumpion-leisure opimaliy condiion (which can be derived using a Lagrangian, which is omied here because he general derivaion proceeds exacly as we ve seen several imes) is ul A = = (1 ) w, uc 1/ c from which we ge ha Ac = (1 ) w a he consumer s opimal choice. Subsiuing he given budge consrain ino his (i.e., subsiuing for c ) we have A (1 ) w n = (1 ) w. Canceling erms and solving for n, we find 1 n =, A 4

6 Problem 2c coninued (if you need more space) which shows ha labor supply here is independen of axes, hence changes in he ax rae canno affec he quaniy of labor. The labor supply funcion, ploed wih he wage (pre- or afer-ax, i doesn make a difference) on he verical axis and n on he horizonal axis, is a verical line a he numerical value 1/ A. This (perfecly inelasic) labor supply is clearly unaffeced by changes in axes; indeed, i is compleely unaffeced by changes in changes in he pre-ax real wage w as well. Furher discussion (which was no required): The reason why labor (equivalenly, leisure) here doesn depend a all on he (pre- or afer-ax) wage is ha here is no diminishing marginal uiliy in leisure (i.e., uiliy is linear wih respec o leisure, as we saw above). When a mulidimensional uiliy funcion is linear in one argumen and has diminishing marginal uiliy in is oher argumen(s), i is said o be quasi-linear. Quasi-linear uiliy funcions give rise o demand funcions for he linear objec ha are compleely insensiive (inelasic) o price here, he demand for leisure (he flip side of which is he supply of labor) is compleely insensiive (inelasic) o he wage. 5

7 Problem 3. Financing Consrains and Labor Demand (30 poins). In our class discussion abou he way in which financing consrains affec firms profi maximizaion decisions, we focused on he effecs on firms physical capial invesmen. In realiy, mos firms spend wice as much on heir wage coss (i.e., heir labor coss) han on heir physical invesmen coss. (Tha is, for mos firms, roughly wo-hirds of heir oal coss are wages and salaries, while roughly one-hird of heir oal coss are devoed o improving or expanding heir physical capial.) For many firms, paymen of wages mus be made before he receip of revenues wihin any given period. (For example, imagine a firm ha has o pay is employees o build a compuer; he revenues from he sale of his compuer ypically don arrive for many weeks or monhs laer because of delays in he shipping process, he reail process, ec.) For his reason, firms ypically need o borrow o pay for heir ongoing wage coss. 1 Bu, because of asymmeric informaion problems, lenders ypically require ha he firm pu up some financial collaeral o secure loans for his purpose. Here, you will analyze he consequences of financing consrains on firms wage paymens using a variaion of he acceleraor framework we sudied in class. For simpliciy, suppose ha he represenaive firm, which operaes in a wo-period economy, mus borrow in order o finance only period-1 wage coss; for some unspecified reason, suppose ha period-2 wage coss are no subjec o a financing consrain. As in our sudy of he acceleraor framework in class, he represenaive firm s wo-period discouned profi funcion is P1f ( k1, n1) + Pk 1 1+ ( S1+ D1) a0 Pwn Pk 1 2 S1a1 P f( k, n ) Pk ( S + D ) a Pw n Pk S a i 1+ i 1+ i 1+ i 1+ i 1+ i and suppose now he financing consrain ha is relevan for firm profi-maximizaion is Pwn = S a The noaion is as always: P denoes he nominal price of he oupu he firm produces and sells; S denoes he nominal price of sock; D denoes he nominal dividend paid by each uni of sock; n denoes he quaniy of labor he firm hires; w is he real wage; a 0, a 1, and a 2 are, respecively, he firm s holdings of sock a he end of period 0, period 1, and period 2; k 1, k 2, and k 3 are, respecively, he firm s ownership of physical capial a he end of period 0, period 1, and period 2; i denoes he nominal ineres rae beween period 1 and period 2; and he producion funcion is denoed by f(.). Also as usual, subscrips on variables denoe he ime period of reference for ha variable. Finally, because his is a wo-period framework, we know a 2 = 0 and k 3 = 0. (OVER) 1 The commercial paper marke, abou which much has been discussed in he news media in recen monhs, is one ype of channel for such firm financing needs. 6

8 Problem 3 coninued The Lagrangian for he firm s profi maximizaion problem is hus P1f ( k1, n1) + Pk 1 1+ ( S1+ D1) a0 Pwn Pk 1 2 S1a1 P f( k, n ) Pk ( S + D ) a Pw n Pk S a i 1+ i 1+ i 1+ i 1+ i 1+ i + λ [ Sa Pwn] in which λ denoes he Lagrange muliplier on he financing consrain. a. (5 poins) Based on he Lagrangian above, compue he firs-order condiions wih respec o k 2 and a 1. Soluion: The firs-order condiions are simply: Pf( k, n) P P 1+ i 1+ i S2 + D2 S1+ + λs1 = 0 1+ i 2 k = 0 b. (5 poins) Based on he Lagrangian above, compue he firs-order condiions wih respec o n 1 and n 2. Soluion: The firs-order condiions are simply: P f ( k, n ) Pw λpw = 0 1 n Pf 2 n( k2, n2) Pw 2 2 = 0 1+ i 1+ i Noe for reference below ha he firs equaion here can be expressed as f ( n k, ) (1 ) 1 n1 = w1 + λ. 7

9 Problem 3 coninued Suppose ha a he beginning of period 1, he real reurn on STOCK, r STOCK, all of a sudden falls below r, he real reurn on riskless ( safe ) asses. Suppose ha before his shock occurred (i.e., in period zero ), i was he case ha r = r STOCK. c. (5 poins) Below is a graph of he invesmen (capial) marke in period 1. Does he adverse shock o r STOCK shif eiher he invesmen demand and/or he savings supply funcion? If so, explain how, in wha direcion, and why. Soluion: The invesmen demand funcion is unaffeced by he financing consrain (see he FOC on k1 above), hence exogenous changes in rstock have no effec on capial demand/invesmen demand. Furhermore, because nohing is said abou wheher financing fricions impinge on he savings supply side of he economy (i.e., on consumers consumpionsavings decisions), here is no basis for assering any shif of he savings funcion. Hence, here is no direc effec on he marke for physical capial. d. (5 poins) Below is a graph of he labor marke in period 1. Does he adverse shock o r STOCK shif eiher he labor demand and/or he labor supply funcion? If so, explain how, in wha direcion, and why. Soluion: No shif in labor supply because, as above, no saemens are made abou wheher financing fricions affec consumers behavior (which is wha would be required for a shif of he labor supply funcion). A fall in rstock will cause a RISE in λ, hence for a given level of w1, he effecive marginal produc of period-1 labor FALLS, hence he labor demand curve shifs inwards. This effec arises because λ direcly appears in he period-1 FOC on labor above. 8

10 Problem 3 coninued e. (5 poins) Below is a graph of he labor marke in period 2. Does he adverse shock o r STOCK shif eiher he labor demand and/or he labor supply funcion? If so, explain how, in wha direcion, and why. Soluion: No shif in labor supply because, once again, no saemens are made abou wheher financing fricions affec consumers behavior (which is wha would be required for a shif of he labor supply funcion). The financing consrain does NOT affec period-2 wage paymens, hence a fall in rstock has no direc effec on period-2 labor demand funcion: here is no shif in he period-2 labor demand funcion. Supply Demand Period 2 Labor Marke n 2 f. (5 poins Harder) Based on he firs-order condiions on n 1 and on k 2 you compued in par a and in par b, is i more appropriae o hink of λ here as a componen of he real ineres rae or as a componen of he real wage? Briefly, bu carefully, explain. Soluion: The muliplier λ appears as a muliplicaive facor in he real wage for period 1 see he expression derived in par b. Hence i can be hough of as a componen of he real wage. This componen of he real wage is a pure financing componen he paymen ha is refleced by λ is NOT a paymen made by firms o workers, bu raher o lenders for heir loans which ALLOW he firms o pay heir workers. From he poin of view of firms, hough, his affecs heir labor hiring decisions, hence can be hough of as par of he oal price (i.e., a componen of he wage ) of hiring workers. 9

11 Problem 4. The Dynamics of Fiscal Policy (20 poins). Presiden Obama and his primary economic advisers have planned o pu in place large fiscal simuli over he nex few years. The precise deails of he fiscal simulus are sill o be worked ou, bu hey include boh ax cus as well as increased governmen spending in he nex few years. I is early 2009, and he new adminisraion has jus recenly been seaed. A he beginning of 2009, he lifeime consolidaed budge consrain of he governmen is: B g g g = ( g ) P 1 r (1 r )(1 r ) (1 r )(1 r )(1 r ) sr sr sr sr r2010 (1 + r2010)(1 + r2011) (1 + r2010)(1 + r2011)(1+ r2012)... Line 1: PDV of fiscal deficis Line 2: PDV of seignorage The noaion here is as in Chaper 15: denoes real lump-sum ax collecions, g denoes real governmen spending, sr denoes real seignorage revenue, r denoes he real ineres rae, B denoes nominal (one-period) governmen bonds, and P denoes he nominal price level of he economy (i.e., he nominal price of one baske of consumpion). Subscrips indicae ime periods, which we will consider o be calendar years. Noe, of course, he ellipsis ( ) in each line of he above equaion. As indicaed above, he firs line of he righ-hand-side is he presen discouned value of all fiscal deficis he governmen will ever run saring from 2009 onwards, and he second line of he righ-hand-side is he presen-discouned value of all seignorage revenue ha will ever resul from he moneary policy acions of he Federal Reserve saring from 2009 onwards. The primary economic advisers o Presiden Obama are Treasury Secreary Timohy Geihner, Naional Economic Council Chairman Lawrence Summers, and Council of Economic Advisers Chairwoman Chrisina Romer. 10

12 Problem 4 coninued In addressing each of he following issues, no quaniaive work is required a all; he following quesions all require only concepual analysis. Each issue should be addressed in no more han hree or four senences. a. (5 poins) Geihner, because of his background as Presiden of he New York Federal Reserve, implicily advocaes ha no maer wha fiscal policy acions he new adminisraion akes, hey should be designed in such a way as o have no effecs on he conduc of moneary policy whasoever. If his is so, wha ype of fiscal policy a Ricardian fiscal policy or a non-ricardian fiscal policy does Geihner advocae? Briefly explain. Soluion: The policy is Ricardian because i is being conduced in a way o ensure ha ax revenues and/or governmen spending adjus (in a PDV sense) o, by hemselves, ensure lifeime governmen budge balance. b. (5 poins) The less even-keeled ha he is, Summers commens someimes seem o imply ha he fiscal simulus measures should no ake ino accoun any consequences hey may have for he conduc of moneary policy. If he combinaion of ax cus and governmen spending ha ulimaely pan ou over he nex few years follow Summers advice, wha are likely o be he consequences for he Federal Reserve s moneary policy in 2009 and beyond? In paricular, will he Fed likely have o expand or conrac he nominal money supply? Briefly explain. Soluion: By lowering he PDV of fiscal surpluses (i.e., increasing he PDV of fiscal deficis) and given a fixed B/P (if you assumed his, his is fine; if hey made some more sophisicaed argumen (ie, FTPL) as o why B/P may NOT be fixed, hen will need o race hrough ha argumen), he PDV of seignorage revenue mus rise o balance he lifeime governmen budge consrain. Increased seignorage requires an increase (a some poin) in he nominal money supply. 11

13 Problem 4 coninued c. (5 poins) The objecive academic macroeconomis ha she is, Romer ypically poins ous in her remarks ha because fiscal policy plans (for boh axes and governmen spending) will almos surely be revised as he years unfold (ha is, fiscal policy plans adoped in 2009 can be revised in laer years), i may be impossible o know beforehand wha he evenual consequences for moneary policy of a paricular fiscal policy acion adoped a he sar of 2009 migh be. Use he governmen budge consrain presened above o inerpre wha Romer s saemens mean. Soluion: d. (5 poins) If, laer his year afer he new fiscal plans are (supposedly) clarified furher, he nominal price level of he economy behaves as shown in he following diagram on he nex page (he price level, P, is ploed on he verical axis), which of he following is he mos relevan explanaion: he fiscal heory of he price level, he fiscal heory of inflaion, or he financial acceleraor mechanism? Briefly jusify your answer. Soluion: This illusraes he FTPL because here is a one-ime jump in P (a he ime of he fiscal reform). June 2009 Time END OF EXAM 12