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QUESTION 1 Consider the standard utility maximization problem: maxU = U(x, y) subject to P x +P y = B, where P and y P denote the price of goods x and y, respectively, and B represents the consumer's available income. (a) Write the (b) Assume that U = xy, P = 1, P = 4 and Lagrangian function and obtain the first-order conditions. B=120. Find along with the optimal levels of purchase x and y. Calculate U Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. (c) Using the

QUESTION 1 Consider the standard utility maximization problem: maxU = U(x, y) subject to P x +P y = B, where P and y P denote the price of goods x and y, respectively, and B represents the consumer's available income. (a) Write the (b) Assume that U = xy, P = 1, P = 4 and Lagrangian function and obtain the first-order conditions. B=120. Find along with the optimal levels of purchase x and y. Calculate U Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. (c) Using the

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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QUESTION 1 Consider the standard utility maximization problem: maxU = U(x, y) subject to P x +P y = B, where P and y P denote the price of goods x and y, respectively, and B represents the consumer's available income. (a) Write the (b) Assume that U = xy, P = 1, P = 4 and Lagrangian function and obtain the first-order conditions. B=120. Find along with the optimal levels of purchase x and y. Calculate U Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. (c) Using the
Transcribed Image Text:QUESTION 1 Consider the standard utility maximization problem: maxU = U(x, y) subject to P x +P y = B, where P and y P denote the price of goods x and y, respectively, and B represents the consumer's available income. (a) Write the (b) Assume that U = xy, P = 1, P = 4 and Lagrangian function and obtain the first-order conditions. B=120. Find along with the optimal levels of purchase x and y. Calculate U Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. (c) Using the
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