Question

Irene earns 8 dollars an hour. She has no nonlabour income. She has 30 hours a...

Irene earns 8 dollars an hour. She has no nonlabour income. She has 30 hours a week available for either labor or leisure.

Her utility function is U(c, r) = cr2, where c is dollars worth of goods and r is hours of leisure. How many hours per week will she work?

a. 8 b. 13 c. 15 d. 10 Please explain the answer step by steps. Thank you!

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Answer #1

Solution

Irene earns 8 dollars an hour. She has no nonlabour income. She has 30 hours a week available for either labor or leisure.

Let x = hours of labour

30 - x = hours of leisure

U = (8x).(30 - x)2

Utility will be maximized when: dU/dx = 0

dU/dx = 8.(30 - x)2 -16x.(30 - x) = 0

Solve for 'x':

x = 10 (option d)

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