8. A consumer bas utility function u(z, y) = VIy, for two goods, X and Y, where c is some positive constant. Here, z> 0 denotes the amount of X consumed and y >0 the amount of Y comsumed. Each unit of X costs 1 dollar and each unit of Y costs 1 dollar, and the consumer has a budget for X and Y of M dollars. Use the Lagrange multiplier method to find the quantities r of X and y of Y the consumer will consume in order to maximise his utility subject to the budget constraint. (Your answers will depend on c and M.) Find the corresponding value, A, of the Lagrange multiplier. Suppose that V = u(x, y") is the maximum achievable utility. Find an explicit expression for V in terms of c and M, and verify that OM = 1.

8. A consumer bas utility function u(z, y) = VIy, for two goods, X and Y, where c is some positive constant. Here, z> 0 denotes the amount of X consumed and y >0 the amount of Y comsumed. Each unit of X costs 1 dollar and each unit of Y costs 1 dollar, and the consumer has a budget for X and Y of M dollars. Use the Lagrange multiplier method to find the quantities r of X and y of Y the consumer will consume in order to maximise his utility subject to the budget constraint. (Your answers will depend on c and M.) Find the corresponding value, A, of the Lagrange multiplier. Suppose that V = u(x, y") is the maximum achievable utility. Find an explicit expression for V in terms of c and M, and verify that OM = 1.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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