Question #42478

suppose that a worker's utility function is given by the following functions; U=CL/3, where C is weekly consumption and L is leisure measured in hours each week. assume a working week is 5 days and that the working day lasts 8 hours. consider a worker with non-labour income of $50 a week and no other sources of income.
a. determine this worker's optimal number of weekly hours of work and weekly consumption when his market wage is $5 an hour.
b. what happens to hours of labour supply if non-labour income rises to $400 a week? explain why?

Expert's answer

U=CL/3,

Working week is 5 days, working day lasts 8 hours. There is 168 hours per week.

non-labour income is $50 a week

a.To determine this worker's optimal number of weekly hours of work and weekly consumption when his market wage is $5 an hour, we should find the point, where utility is maximized, U = CL/3 = max. CL/3 is maximized, when consumption almost equals total leisure hours. When L = 148, C = 20*$5 + $50 = $150, so U = 150*148/3 = 2400.

b.If non-labour income rises to $400 a week, utility is maximized, when you work all 40 hours per week, then C = 40*$5 + $400 = $600, so U = 600*(168 - 40)/3 =25600.

Working week is 5 days, working day lasts 8 hours. There is 168 hours per week.

non-labour income is $50 a week

a.To determine this worker's optimal number of weekly hours of work and weekly consumption when his market wage is $5 an hour, we should find the point, where utility is maximized, U = CL/3 = max. CL/3 is maximized, when consumption almost equals total leisure hours. When L = 148, C = 20*$5 + $50 = $150, so U = 150*148/3 = 2400.

b.If non-labour income rises to $400 a week, utility is maximized, when you work all 40 hours per week, then C = 40*$5 + $400 = $600, so U = 600*(168 - 40)/3 =25600.

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