Dudley’s utility function is U(C,R) = C − (12 − R)2, where R is the amount of leisure he has per day. He has 16 hours a day to divide between work and leisure. He has an income of $20 a day from nonlabor sources. The price of consumption goods is $1 per unit.
(a) If Dudley can work as many hours a day as he likes but gets zero wages for his labor, how many hours of leisure will he choose?
(b) If Dudley can work as many hours a day as he wishes for a wage rate of $10 an hour, how many hours of leisure will he choose?____. How many hours will he work? ___
(c) If Dudley’s nonlabor income decreased to $5 a day, while his wage rate remained at $10, how many hours would he choose to work?
(d) Suppose that Dudley has to pay an income tax of 20 percent on all of his income, and suppose that his before-tax wage remained at $10 an hour and his before-tax nonlabor income was $20 per day. How many hours would he choose to work?