Consider a worker who consumes one good and has a preference for leisure. She maximizes the utility function u(x, L) = xL, where à 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 à 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.
Economics Today and Tomorrow, Student Edition
1st Edition
ISBN:9780078747663
Author:McGraw-Hill
Publisher:McGraw-Hill
Chapter7: Demand And Supply
Section7.1: Demand
Problem 4R
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4641886b-89da-403b-8f60-7233a6fc439f%2F04f04057-9f3a-4f11-865f-d6b289175c84%2Fg49cgxg_processed.png&w=3840&q=75)
Transcribed Image Text: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.
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