. How much utility does the individual receive if she consumes C = 100 and works h = 7 hours? b. Calculate the rate at which the individual is willing to sacrifice an additional leisure hour when she is already working 4 hours. c. What is this individual’s optimal amount of consumption and leisure?

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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Assume an individual has a utility function of this form

                                    U(C, L) = 20 + 4(C*L)1/2

This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2.  The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10.

 

a. How much utility does the individual receive if she consumes C = 100 and works h = 7 hours?

b. Calculate the rate at which the individual is willing to sacrifice an additional leisure hour when she is already working 4 hours.

c. What is this individual’s optimal amount of consumption and leisure?

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