Dudley has a utility function U(C, R)= C - (12 - R)², where R is leisure and C is consumption per day.He has 16 hours per day to divide between work and leisure.If Dudley has a nonlabor income of $20 per day and is paid a wage of $0 per hour, how many hours of leisure will he choose per day? A)9 B)10 C)11 D)13 E)12

Question

Quizplus · Accepted Answer

To maximize utility, Dudley will choose the combination of consumption and leisure that maximizes his utility given his constraints. His constraint is that he has 16 hours per day to divide between work and leisure. Since he is not paid a wage, he will not choose to work any hours. Therefore, he has 16 hours per day for leisure.

To find his optimal consumption level, we can use the partial derivative of his utility function with respect to consumption:

∂U/∂C = 1 - 12S/(S-R)

Setting this equal to zero and solving for C, we get:

1 - 12S/(S-R) = 0
Solving for S, we get:

S = R/13

Now we can substitute S = R/13 back into the utility function to get an expression for utility in terms of leisure:

U(R/13, R) = 10R/13 - 2.3077R^2

To maximize this function, we take the derivative with respect to R and set it equal to zero:

∂U/∂R = 10/13 - 4.6154R = 0
Solving for R, we get:

R = 2.1739

Therefore, Dudley will choose 2.1739 hours of work per day and 16 - 2.1739 = 13.8261 hours of leisure per day. The answer is E) 12.

Dudley Has a Utility Function U(C, R)= C - (12