Consider a firm composed of 5 workers,each with a utility function of the form $U ( l ) = w l - l ^ { 2 }$ where l is hours worked and w is the wage.Suppose the firm can monitor the number of hours worked by each worker and pays them $w = 20$ per hour.How many hours will each worker choose to work?
A)2 hours.
B)4 hours.
C)8 hours.
D)10 hours.

Question

Quizplus · Accepted Answer

To find out the number of hours each worker will choose to work we need to maximise their utility function with respect to the number of hours worked.

Each worker's utility function is given by:

U(l, w) = wl - 0.5l^2

Taking the derivative of the utility function with respect to l, we get:

dU/dl = w - l

Setting this equal to zero to find the critical point:

w - l = 0

l = w

This indicates that each worker will choose to work as many hours as their wage rate.

Since the firm pays each worker $10 per hour, the number of hours each worker will choose to work is:

l = $10

l = 10 hours

Therefore, the answer is choice D, 10 hours.

Consider a Firm Composed of 5 Workers,each with a Utility U(l)=wl−l2U ( l ) = w l - l ^ { 2 }U(l)=wl−l2

Consider a Firm Composed of 5 Workers,each with a Utility $U ( l ) = w l - l ^ { 2 }$