final387s03ans

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

This preview shows pages 1–3. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 ) .
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 7

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online