Izaak likes to eat pizza and to sh. The more shing he does the happier he is, up
ID: 1190456 • Letter: I
Question
Izaak likes to eat pizza and to sh. The more shing he does the
happier he is, up to 8 hours a day. If he shes longer than 8 hours he gets a sore back and is
less happy than if he hadn't shed 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 shing. 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 shing licenses to sh only 3 hours a day. But if you buy
a shing license, you can sh as many hours as you wish. How much is Izaak willing pay for
a license?
Explanation / Answer
U = x+3y
Before buying license:
x = 40 (entire money will be spent on pizza) and y = 3 hours
Therefore, U = x+3y = 40+3(3) = 49
After buying license:
x = 40-d (pizza will be bought form income left after buying license) and y = 8 hours
Therefore, U’ = (40-d)+3y = 40-d+3(24) = 64-d
Utility before and after buying license should be equal. That is,
U = U’
49 = 64-d
d = 64-49
d = 15
Thus, Izaak should pay a maximum of $15 for license.
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