Solution_Winter2007

Solution_Winter2007 - Econ 51 Final Exam Suggested Solutions 1 General Equilibrium(27 points a i(3 points These are log utilities so all we need to

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

View Full Document Right Arrow Icon
Econ 51: Final Exam - Suggested Solutions 1. General Equilibrium (27 points) a. i. (3 points) These are log utilities, so all we need to do is to equate MRSs. This gives us b i a i = b j a j for each i; j . In addition, to be feasible, we must have the sum of the bananas equal to 5 N and the sum of the apples equal to 10 N . These two allocation that satisfy b i a i = 1 2 for all i . ii. (3 points) Normalize p a = 1 and denote p b = p . We will clear the apple market. Excess demand by each individual (they are all identical) is given by z i a ( p ) = 1 2 10+5 p 1 10 = 2 : 5 p 5. Total excess demand in the market is simply z a ( p ) = N (2 : 5 p 5). To clear the market, we must have p = 2. Allocation for each agent is then given by (10 ; 5), that is the initial endowment. The solution does not depend on N . This is because, essentially, the general equilibrium already assumes very many identical agents of each type, so having N types that are all identical is exactly like an economy with a single individual. b. i. (3 points) Now the MRSs must also be equal the MRT, which is 1. Thus, we must have b i a i = 1 for all i . To achieve this, the production plan for the ±rm must make total number of apples equal total number of bananas. This is achieved by a production plan of ( y a ; y b ) = ( 2 : 5 N; 2 : 5 N ). ii. (3 points) We know that the ±rm will be in business (due to the shortage in bananas), so prices must be p a = p b = 1 (we normalized the price of apples as before). At these prices, allocations to each individual are (7 : 5 ; 7 : 5). The ±rm’s production plan is ( y a ; y b ) = ( 2 : 5 N; 2 : 5 N ). For the same reason as in part a.ii, the answer doesn’t depend on N . iii. (2 points) It won’t change any of the answers. The overall production plan in the industry will remain the same (for both parts), and it can be arbitrarily split between the two ±rms, as they make zero pro±ts anyway. That is, production plans must satisfy ( y A a ; y A b ) = ( x; x ) and ( y B a ; y B b ) = ( w; w ) such that x; w ± 0 and x + w = 2 : 5 N . iv. (2 points) It won’t change any of the answers. The overall production plan in the industry will remain the same (for both parts), and it can be arbitrarily split between the two ±rms, as they make zero pro±ts anyway. That is, production plans must satisfy ( y A a ; y A b ) = ( x; x ) and ( y B a ; y B b ) = ( w; w ) such that x; w ± 0 and x w = 2 : 5 N . c.
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.

This note was uploaded on 03/19/2011 for the course ECON 51 taught by Professor Tendall,m during the Winter '07 term at Stanford.

Page1 / 4

Solution_Winter2007 - Econ 51 Final Exam Suggested Solutions 1 General Equilibrium(27 points a i(3 points These are log utilities so all we need to

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