In the first problem set, you solved the consumer problem for the utility function u(x₁, x₂) =₁+2√2. Throughout this question, assume that the consumer has the same utility function,and that wealth is high enough to ensure an interior solution to the utility maximizationproblem.(a) Verify that the Slutsky equation holds for cross-price changes (i.e. for Good 1 when p2changes, and for Good 2 when p₁ changes).(b) Suppose that the price of Good 1 increases from p₁ to p₁ while the price of Good 2remains unchanged. Let u and u¹ respectively denote the utilities before and after thischange. Using the Hicksian demand function from the first problem set, write expressionsfor the equivalent and compensating variations in terms of prices and utilities uº andu¹. How do they compare?(c) Instead of a change in p₁, suppose that the price of Good 2 increases from p2 to p2while the price of Good 1 remains unchanged. Write expressions for the equivalent andcompensating variations. How do they compare? Explain why the comparison does ordoes not differ from that in part (b).

Answered: Image /qna-images/answer/bf6d404c-8d59-426c-aaa3-e777aeadbc58.jpg

In the first problem set, you solved the consumer problem for the utility function u(x1, x₂) = ₁+2√2. Throughout this question, assume that the consumer has the same utility function, and that wealth is high enough to ensure an interior solution to the utility maximization problem. (a) Verify that the Slutsky equation holds for cross-price changes (i.e. for Good 1 when p2 changes, and for Good 2 when p₁ changes). (b) Suppose that the price of Good 1 increases from p₁ to p₁ while the price of Good 2 remains unchanged. Let uº and u¹ respectively denote the utilities before and after this change. Using the Hicksian demand function from the first problem set, write expressions for the equivalent and compensating variations in terms of prices and utilities uº and u¹. How do they compare? (c) Instead of a change in p₁, suppose that the price of Good 2 increases from p2 to p/2 while the price of Good 1 remains unchanged. Write expressions for the equivalent and compensating variations. How do they compare? Explain why the comparison does or does not differ from that in part (b).

In the first problem set, you solved the consumer problem for the utility function u(x1, x₂) = ₁+2√2. Throughout this question, assume that the consumer has the same utility function, and that wealth is high enough to ensure an interior solution to the utility maximization problem. (a) Verify that the Slutsky equation holds for cross-price changes (i.e. for Good 1 when p2 changes, and for Good 2 when p₁ changes). (b) Suppose that the price of Good 1 increases from p₁ to p₁ while the price of Good 2 remains unchanged. Let uº and u¹ respectively denote the utilities before and after this change. Using the Hicksian demand function from the first problem set, write expressions for the equivalent and compensating variations in terms of prices and utilities uº and u¹. How do they compare? (c) Instead of a change in p₁, suppose that the price of Good 2 increases from p2 to p/2 while the price of Good 1 remains unchanged. Write expressions for the equivalent and compensating variations. How do they compare? Explain why the comparison does or does not differ from that in part (b).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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