714s10_fin_sol

714s10_fin_sol - Noah Williams Department of Economics...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Economics 714 Department of Economics Macroeconomic Theory University of Wisconsin Spring 2010 F INAL A NSWER K EY by Tim Lee 1. Let’s begin by defining a CE. D EFINITION 1 A competitive equilibrium is an allocation { c t } t = 0 and sequence of prices { p t } t = 0 such that (i) Given prices, allocation solves consumers’ problem: max c t t = 0 β t u ( c i t ) s.t. t = 0 p t c i t t = 0 p t e i t = t = 0 p 2 t + i - 1 ( 1 + g ) 2 t + i - 1 for i = 1, 2 , (ii) Markets clear, i.e. c 1 t + c 2 t = e 1 t + e 2 t = ( 1 + g ) t . (a) Attaching the Lagrange multiplier λ i on each consumers’ budget constraint, the consumers’ f.o.c.’s are β t u 0 ( c i t ) = λ i p t c i t = f ( λ i p t / β t ) , (1) where f ( · ) is the inverse function of marginal utility. Normalizing p 0 = 1, the two budget constraints and market clearing conditions form the following system t = 0 p t f ( λ 1 p t / β t ) = k = 0 p 2 k ( 1 + g ) 2 k t
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

714s10_fin_sol - Noah Williams Department of Economics...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online