Consider a two-person exchange economy in which initial endowments for both individuals are such that (e1 = e1) = (1,1). Suppose the two individuals have the following indirect utility functions: V1 (x, y) = ln M1 - a ln Px - (1-a) ln Py V2 (x, y) = ln M2 -b ln Px - (1-b) ln Py Where Mi is the income level of person i and Px and Py are the prices for goods x and goods y, respectively. a) Calculate the market clearing prices.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter13: General Equilibrium And Welfare
Section: Chapter Questions
Problem 13.5P
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Consider a two-person exchange economy in which initial endowments for both individuals are such that (e1 = e1) = (1,1). Suppose the two individuals have the following indirect utility functions:

V1 (x, y) = ln M1 - a ln Px - (1-a) ln Py

V2 (x, y) = ln M2 -b ln Px - (1-b) ln Py

Where Mi is the income level of person i and Px and Py are the prices for goods x and goods y, respectively.

  1. a) Calculate the market clearing prices.
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