In the first problem set, you solved the consumer problem for the utility function (₁,₂)= ₁+2√7₂. 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 pi changes). (b) Suppose that the price of Good 1 increases from pi to p while the price of Good 2 remains unchanged. Let u 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 and ¹. How do they compare? (e) Instead of a change in p₁, suppose that the price of Good 2 increases from pa to pl 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 (₁,₂)= ₁+2√7₂. 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 pi changes). (b) Suppose that the price of Good 1 increases from pi to p while the price of Good 2 remains unchanged. Let u 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 and ¹. How do they compare? (e) Instead of a change in p₁, suppose that the price of Good 2 increases from pa to pl 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

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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