Consider a worker who consumes one good and has a preference for leisure. She maximizes the utility function u(x, L) = xL, where a represents consumption of the good and L represents leisure. Suppose that this worker can choose any L = [0, 1], and receives income w(1 - L); w represents the wage rate. Let p denote the price of the consumption good. In addition to her wage income, the worker also has a fixed income of y ≥ 0. (a) Write down the utility maximization problem for this consumer. (b) Find the Marshallian demands for the consumption good and leisure. (c) Find the indirect utility as a function of p, w, and y.

Consider a worker who consumes one good and has a preference for leisure. She maximizes the utility function u(x, L) = xL, where a represents consumption of the good and L represents leisure. Suppose that this worker can choose any L = [0, 1], and receives income w(1 - L); w represents the wage rate. Let p denote the price of the consumption good. In addition to her wage income, the worker also has a fixed income of y ≥ 0. (a) Write down the utility maximization problem for this consumer. (b) Find the Marshallian demands for the consumption good and leisure. (c) Find the indirect utility as a function of p, w, and y.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter16: Labor Markets

Section: Chapter Questions

Problem 16.2P

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