Econ808midans.02

Econ808midans.02 - Department of Economics The Ohio State...

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

View Full Document Right Arrow Icon
Department of Economics The Ohio State University Midterm Questions and Answers–Econ 808 Profs. Levin and Peck March 7, 2002 1. (30 points) In the village of Debreuvia, there are 150 consumers and one physical com- modity per state of nature. For i = 1, . .. , 150, consumer i is a von Neumann- Morgenstern expected utility maximizer with (Bernoulli) utility of certain con- sumption given by u i ( x i ) = log( x i ) . For i = 1, . .. , 100, consumer i lives in the highlands, and has an endowment of 1 is all states of nature. For i = 101, . .. , 150, consumer i lives in the ‡ood plain. When a ‡ood occurs, all consumers living in the ‡ood plain receive an endowment of 0 .T h e probability of a ‡ood is 1 10 . When a ‡ood does not occur (probability 9 10 ), all consumers living in the ‡ood plain receive an endowment of 1 . (a) (10 points) If the entire village of Debreuvia trades state-contingent commodities, de…ne a competitive equilibrium for this economy. (b) (20 points) Calculate the competitive equilibrium price vector and allo- cation. Answer: (a) There are two states of nature, corresponding to a ‡ood (state 1) and no ‡ood (state 2). A competitive equilibrium is a price vector, ( p 1 ;p 2 ) ,andan allocation, ( x 1 i ;x 2 i ) 150 i =1 , such that (i) for i = 1, . .. , 100, ( x 1 i 2 i ) solves max[ 1 10 log( x 1 i )+ 9 10 log( x 2 i )] subject to p 1 x 1 i + p 2 x 2 i · p 1 + p 2 ; (ii) for i = 101, . .. , 150, ( x 1 i 2 i ) solves max[ 1 10 log( x 1 i 9 10 log( x 2 i )] subject to p 1 x 1 i + p 2 x 2 i · p 2 ; (iii) markets clear: 150 X i =1 x 1 i · 100 150 X i =1 x 2 i · 150 : 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
(b) Normalizethepriceofconsumptioninstate2(no‡ood)tobe1, p 2 =1 . First, we calculate the demand function for those living in the highlands (i=1, ... , 100). The …rst order conditions are x 2 i 9 x 1 i = p 1 p 1 x 1 i + x 2 i = p 1 +1 ; which we solve for the demand functions x 1 i = p 1 10 p 1 x 2 i = 9( p 1 +1) 10 : Next, we calculate the demand function for those living in the ‡ood plain (i=101, . .. , 150). The …rst order conditions are x 2 i 9 x 1 i = p 1 p 1 x 1 i + x 2 i ; which we solve for the demand functions x 1 i = 1 10 p 1 x 2 i = 9 10 : Market clearing for consumption in state 2 (no ‡ood) implies 100( 9( p 1 10 )+50( 9 10 )=150 : Solving for p 1 ,wehave p 1 = 1 6 . The C.E. allocation is given by ( x 1 i ;x 2 i )=( 7 10 ; 21 20 ) for i = 1, . .. , 100, ( x 1 i 2 i 3 5 ; 9 10 ) fori=101 ,.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/17/2008 for the course ECON 808 taught by Professor Peck during the Spring '02 term at Ohio State.

Page1 / 6

Econ808midans.02 - Department of Economics The Ohio State...

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

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