final387s03ans - Econ 387L Macro II Spring 2003 University...

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Econ 387L: Macro II Spring 2003, University of Texas Instructor: Dean Corbae Final Exam Answers Consider the following cash-in-advance economy where f rms are monopolistically competitive and must set prices for their goods one period in advance. The cash-in-advance constraints mean that expected in F ation cause agents to inef f ciently economize on money holdings. The monopolistic competition means that equilibrium output falls short of the ef f cient level. Sticky prices mean that unanticipated money changes have real effects. Thus the government faces a tradeoff between the costs of expected in F ation and the bene f ts of unexpected in F ation. Speci f cally, the economy consists of a representative family (composed of a worker/shopper household and a continuum of f rms indexed by i [0 , 1] )anda government. Each f rm produces a distinct, nonstorable good i with the technology y t ( i )= n t ( i ) where n t ( i ) is the labor input at f rm i. The representative household (HH) consumes a basket of goods (call it c t ) and supplies labor to each of the f rms (call the total labor supply n t ). HH preferences are given by X t =0 β t ½ c α t α n t ¾ (1) where 0 <β< 1 , 0 <α< 1 and the composite goods are de f ned by c t = ·Z 1 0 c t ( i ) ( θ 1) di ¸ θ/ ( θ 1) (2) where 1 and n t = Z 1 0 n t ( i ) di. The HH trades bonds as well as money. Bonds costing B t +1 /R t dollars at time t return B t +1 dollars at time t +1 where R t is the gross nominal interest rate between t and t (i.e. the nominal bond price Q t =1 /R t ). Bonds are available in zero net supply so B t +1 =0 must hold in equilibrium. Let M t +1 be a HH’s choice of money balances in period t and M s t +1 is the government supply of money. The money supply evolves according to M s t +1 = x t M s t via government lump sum taxes/transfers τ t =( x t 1) M s t (note that this is also the government budget constraint). We assume the growth rate of the money supply lies in the set x t [ β, x ] where x> 1 so that the government might actually shrink the money supply. Timing in any period is given by: 1. The HH enters t with M t and B t chosen at t 1 . Each f rm enters t taking as given nominal price for its goods P t ( i ) chosen at t 1 . 2. The HH receives/pays nominal transfer/tax τ t and its bonds mature (generating nominal balances of M t + τ t + B t ). 3. The HH purchases B t +1 bonds and pays B t +1 /R t out of its nominal balances. 1
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4. The shopper must use its nominal balances to purchase consumption goods from each of the f rms Z P t ( i ) c t ( i ) di M t + τ t + B t B t +1 /R t . (3) 5. The f rm hires n t ( i ) worker hours, pays nominal wages W t n t ( i ) to the worker, and chooses next period’s price P t +1 ( i ) to maximize future pro f ts. 6. The f rm brings home any current nominal pro f ts D t ( i )= P t ( i ) y t ( i ) W t ( i ) n t ( i ) .
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This note was uploaded on 08/06/2008 for the course ECON 387 taught by Professor Corbae during the Spring '07 term at University of Texas.

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final387s03ans - Econ 387L Macro II Spring 2003 University...

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