For a > 0, consider a consumer whose utility function amounts to u(x1, x2) = − exp(−ax1x2). Can you take first order conditions to solve the utility maximization problem? Explain your argument. Next solve the utility maximization problem, and derive Marshallian demands and the indirect utility function. Given your calculations, state and use the duality theorem to find the expenditure function and Hicksian demand

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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For a > 0, consider a consumer whose utility function amounts to u(x1, x2) = − exp(−ax1x2). Can you take first order conditions to solve the utility maximization problem? Explain your argument. Next solve the utility maximization problem, and derive Marshallian demands and the indirect utility function. Given your calculations, state and use the duality theorem to find the expenditure function and Hicksian demand

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