9 Irene earns 8 dollars an hour She has no nonlabor income S

9. Irene earns 8 dollars an hour. She has no nonlabor 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

Solution

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)