Izaak likes to eat pizza and to fish.The more fishing he does the happier he is, up to 8 hours a day.If he fishes longer than 8 hours he gets a sore back and is less happy than if he hadn't fished at all.For y less than or equal to 8, his utility function is U(x, y)= x + 6y, where x is money spent on pizza and y is hours per day spent fishing.His income is $45 a day and he has no expenses other than pizza.The Bureau of Fisheries has just decided to allow people without fishing licenses to fish only 3 hours a day.But if you buy a fishing license, you can fish as many hours as you wish.How much is Izaak willing pay for a license?
A)$33
B)$30
C)$48
D)$28
E)$0

Question

Quizplus · Accepted Answer

To determine how much Izaak is willing to pay for a fishing license, we first calculate his utility from fishing for 3 hours without a license and then for 8 hours, which is his optimal fishing time. His utility function for fishing and pizza is U(x, y) = 10x + 6y, where x is the money spent on pizza and y is the hours spent fishing.Without a license, he can fish for 3 hours:U = 10x + 6(3) = 10x + 18.With a license, he prefers to fish for 8 hours:U = 10x + 6(8) = 10x + 48.His income is $45, and we assume all of it is spent on pizza (x) when not buying a license. Thus, without a license, his utility from spending all on pizza is 10(45) = 450. However, this isn't directly relevant as we're comparing utilities with different fishing hours.To find out how much he values the additional 5 hours of fishing (from 3 to 8 hours), we look at the increase in utility from those hours:Additional utility = 6(8) - 6(3) = 48 - 18 = 30.This means Izaak values the additional 5 hours of fishing at $30, which is the maximum he would be willing to pay for the fishing license to increase his fishing hours from 3 to 8.

Izaak Likes to Eat Pizza and to Fish