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 $U(x, y)=x+6 y$, 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?

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 $U(x, y)=x+6 y$, 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?

Accepted Answer

∻Solution∻ ‖ a ⋮ Utility Function: Izaak's utility function is given by $U(x, y) = x + 6y$, where $x$ is money spent on pizza and $y$ is hours spent fishing. With an income of $45$, he can allocate his budget between pizza and fishing. ‖‖ b ⋮ Utility Maximization: To find the optimal consumption, we need to consider the constraint $x + p \cdot y = 45$, where $p$ is the price of pizza. Assuming pizza is free (or $p=0$), he can spend all his income on fishing hours. ‖‖ c ⋮ Fishing Hours Without License: Without a license, Izaak can fish for a maximum of 3 hours, giving him a utility of $U(x, 3) = x + 6 \cdot 3 = x + 18$. If he spends all his income on pizza, $x = 45$, so $U(45, 3) = 45 + 18 = 63$. ‖‖ d ⋮ Fishing Hours With License: If he buys a fishing license, he can fish for up to 8 hours, giving him a utility of $U(x, 8) = x + 6 \cdot 8 = x + 48$. Again, if he spends all his income on pizza, $U(45, 8) = 45 + 48 = 93$. ‖‖ e ⋮ Willingness to Pay: The difference in utility between fishing with a license and without is $93 - 63 = 30$. Therefore, Izaak is willing to pay up to $30 for the fishing license to achieve the higher utility. ‖ ∻Answer∻ ⚹ Izaak is willing to pay $30 for a fishing license. ⚹ ∻Key Concept∻ ⚹ Willingness to pay is determined by the increase in utility from an additional option. ⚹ ∻Explanation∻ ⚹ Izaak's utility increases by $30 when he can fish for more hours, which reflects his maximum willingness to pay for the fishing license. ⚹◊What is the marginal utility of fishing for Izaak when he is at his maximum allowed fishing time of 3 hours per day?⍭ Generate me a similar question◊

Sia