Consider an individual who receives utility from consumption, c, and leisure, l. The individual has L time to allocate to work, n, and leisure. The individual’s consumption is a function of how much he works. In particular, c = root n. The individual’s maximization problem is  max U =ln(c)+θl subject to c = √n n+l=L where θ > 0. Solve the maximization problem. Hint: Substitute both constraints into the objective function.

Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section6.A: Indifference Curve Analysis
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Consider an individual who receives utility from consumption, c, and leisure, l. The individual has L time to allocate to work, n, and leisure. The individual’s consumption is a function of how much he works. In particular, c = root n. The individual’s maximization problem is 

max U =ln(c)+θl

subject to c = √n

n+l=L

where θ > 0. Solve the maximization problem. Hint: Substitute both constraints into the objective function.

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