Final Exam Advanced Macroeconomics I

Transcription

1 Advanced Macroeconomics I WS 00/ Final Exam Advanced Macroeconomics I February 8, 0 Quesion (5%) An economy produces oupu according o α α Y = K (AL) of which a fracion s is invesed. echnology A is exogenous and consan. he growh rae of he labor force is n and he depreciaion rae is δ. Assume 0 < α <. a) Demonsrae ha he producion funcion exhibis consan reurns o scale. b) Calculae seady-sae per-capia oupu. c) Assuming perfec compeiion, calculae he seady-sae levels of he wage rae and of he rae of reurn o capial. d) Wha would a doubling of A do o he wage rae, o he reurn o capial and o he income shares of capial and labor? Quesion (5%) Discussing he role of various componens of GDP in he business cycle, David Romer poins ou in his exbook ha for he Unied Saes, he average conribuion o he fall in GDP in recessions. differs markedly beween nondurable consumpion and invesmen;. is negaive for ne expors. a) Wha does i mean o sae ha he conribuion of ne expors o recessions is negaive? b) Give a brief explanaion for each of he wo saed facs. c) Looking back a he mos recen recession of 009, did Germany conform o he wo facs?

2 Advanced Macroeconomics I WS 00/ Quesion 3 (5%) As Charles Plosser has poined ou, he properies of he Real Business Cycle Model can be inerpreed in erms of he raional behavior of a uiliymaximizing Robinson Crusoe. Consider an increase in Robinson s produciviy. Explain in words he response of his producion, consumpion, invesmen and work effor a) under he assumpion ha he produciviy increase is shor-lived; b) under he assumpion ha he produciviy increase is permanen. Quesion 4 (35%) Consider a model along he lines of Clarida, Galí, and Gerler (JEL 999) [noaion as in heir paper, unless oherwise saed]: () L = [ α ( x k) + ( π π ) ] + F F, k, π : exogenous () π = λx + Eπ + + u (3) x [ ] = φ i Eπ + + E x+ + g (4) u = ρ u uˆ + 0 < ρ < (5) g = g g gˆ 0 + μ + 0 < μ <, g 0 > 0: exogenous û and ĝ are random variables wih mean zero. a) Wha is he meaning of F, k, π and 0 g? b) Derive he firs-order condiion for an opimal discreionary moneary policy. c) Solve for he long-run no-shock equilibrium values of x, π, g and i. b) Could moneary policy be improved over he oucome obained in c)? Discuss.

3 Advanced Macroeconomics I WS 00/ Quesion Final Exam Advanced Macroeconomics I Soluion Ouline a) Consan reurns o scale: if boh facor inpus (labor and capial) change by he same arbirary facor a, oupu should change by he same facor a: α α α α ( ak ) ( AaL) = a( K ) ( AL) = ay b) () y Y L = k A () k& = s y ( n + δ )k α α From k & α = 0 s( k A α ) = ( n + δ ) k, we solve for (3)/(4) k = s ( n + δ ) α A y = s ( n + δ ) α α A c) Wih perfec compeiion, w = MPL, and capial: r = MPK. Calculaing he marginal producs of labor w = α k A α α (5) ( ) (6) r = αk α α A Subsiuing he seady sae value k ino boh funcions: (7) r = α ( n + δ ) (8) w = ( α ) A ( ) s s n + δ α α d) Doubling A will double he seady sae wage rae whereas he seady sae value of r remains consan. As can be seen from (3) and (4), he new seady sae values of k and y will increase proporionally wih A as well. he labor and he capial shares are no affeced by changes in A as hey are deermined purely by he producion echnology: wl w rk k Labor share λl = = = α Capial share λ K = = r = α Y y Y y

4 Advanced Macroeconomics I WS 00/ Quesion a) If he average conribuion of ne expors o recessions is negaive, his means ha ne expors go up while oupu falls. b) Nondurable consumpion does no vary ha much over he business cycle due o he consumpion smoohing moive. In conras, invesmen conribues srongly o recessions as firms aemp o downsize heir producion capaciy. he negaive average conribuion of ne expors o recessions reflecs he fac ha he U.S. business cycle is largely driven by flucuaions in domesic demand which enail corresponding changes in impor demand. Impors ener GDP calculaion wih a negaive sign. c) In he recession of 009, German nondurable consumpion as well as invesmen spending conformed exacly o he paern described by he exbook for he U.S. Ne expors, however, made an imporan posiive conribuion o ha downurn as German expors were hi hard by he global slump.

5 3 Advanced Macroeconomics I WS 00/ Quesion 3 he effec of an increase in Robinson s produciviy A on his producion Y, consumpion C, invesmen I and work effor L: dl /da dy /da dc /da di /da dl /da > 0 dy /da > 0 dc /da > 0 di /da > 0 a) produciviy increase shor lived he inra emporal subsiuion effec (working in favor of L ) is reinforced by a srong ineremporal subsiuion effec. he income effec, pulling in he oher direcion, is weak. he direc impac of produciviy on oupu is reinforced by he posiive labor supply response. Consumpion responds weakly due o he consumpion smoohing moive. Invesmen responds srongly as, by definiion, i is he difference beween a srong oupu response and a weak consumpion response dl /da < 0 dy /da > 0 dc /da > 0 di /da > 0 b) produciviy increase permanen he ineremporal subsiuion effec is absen and he income effec is srong. (If he inra emporal subsiuion effec is srong enough, he overall effec could be weakly posiive). he direc impac of produciviy on oupu is no reinforced, or is even parially offse by he labor supply response. Consumpion responds srongly o oupu as i adjuss o he permanenly elevaed income pah. Invesmen responds less because he oupu response is weaker and he consumpion response is sronger han in he case of he emporary produciviy change. Difference (dl /da ) a) > (dl /da ) b) (dy /da ) a) > (dy /da ) b) (dc /da ) a) < (dc /da ) b) (di /da ) a) > (di /da ) b)

6 4 Advanced Macroeconomics I WS 00/ Quesion 4 (35%) a) F : Fuure erms of he loss funcion (discouned expeced fuure losses) k: Desired level of he oupu gap π : arge inflaion rae g : auonomous spending variable (e.g. governmen spending) 0 b) Firs order condiion: he cenral bank s marginal rae of subsiuion (MRS) beween oupu and inflaion mus be equal o λ. Formally: dl = α dπ α( x k) ( x k) dx ( π π ) dπ = 0 = (MRS) dx π π α MRS = λ π π = ( x k) λ c) Solving for he long run no shock equilibrium: x can be deermined by seing π Eπ and u = 0 in eq. (): x = 0. = + π is given by he f.o.c. derived in b), aking ino accoun x = 0: g can be deermined by seing g g and g ˆ = 0 in eq. (5): = α π = π + k λ g0 g = μ Finally, we can solve eq. (3) for i, aking ino accoun he α equilibrium values of x, π and g: i = π + k + g0 λ φ( μ) c) Clearly, discreionary moneary policy is inefficien as i generaes inflaion in excess of he arge rae wihou achieving any oupu gains in reurn (he classic inflaionary bias problem; Resul 5 in he Clarida/Gali/Gerler paper). A mechanism (such as a binding rule) ha forces he cenral bank o pursue a policy consisen wih is inflaion arge would improve maers.