The expenditure function for a consumer with Cobb-Douglas preferences is e(p, u) upip a, where 0 < a < 1. Calculate the substitution matrix for the Cobb-Douglas 1-a demand system for this consumer. Verify that the diagonal terms are negative and the cross-price effects are symmetric. [Tip: for this question, remember that once you have derived the terms da¢ (p,u) and duk (p,u) i, j = 1, 2. for the symmetric matrix, you need to substitute for u with the indirect utility function, v(p, y)]

The expenditure function for a consumer with Cobb-Douglas preferences is e(p, u) upip a, where 0 < a < 1. Calculate the substitution matrix for the Cobb-Douglas 1-a demand system for this consumer. Verify that the diagonal terms are negative and the cross-price effects are symmetric. [Tip: for this question, remember that once you have derived the terms da¢ (p,u) and duk (p,u) i, j = 1, 2. for the symmetric matrix, you need to substitute for u with the indirect utility function, v(p, y)]

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.13P

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