Izaak likes to eat pizza and to fish. The more fishing he does the happier he is

Question

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 + 3y, where x is money spent on pizza and y is hours per day spent fishing. His income is $40 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?

Explanation / Answer

Money spent on Pizza

$40 (Total Income) = x + 3 x 8 (hours)

x = 40 - 24 = $ 16

Now in this linear utility equation MRS = Slope of line = 3

P1/P2 = MRS

16/P2 = 3

P2 = $5.33(approx)

Izzak is willing to pay max $5.33

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