Minnie Applesauce is shopping for a summer lake cottage.Minnie hates mosquito bites, but the cheapest lake cottages have the most mosquitos.The price of a lake cabin is related to b, the number of mosquito bites you can expect per hour, according to the formula p = $20,000 - 100b.Minnie's utility function is u = x - 5b², where x is her expenditure on all goods other than her lake cabin.If Minnie makes her best choice of lake cabin, how many mosquito bites per hour will she get? A)10 B)5 C)20 D)25 E)None of the above.

Question

Quizplus · Accepted Answer

The correct answer is A.The optimal number of mosquito bites per hour is 10. This is because Minnie's utility function is u = x - 5b^2, where x is her expenditure on all goods other than her lake cabin and b is the number of mosquito bites per hour. The price of a lake cabin is related to b according to the formula p = $20,000 - 100b. Minnie's budget constraint is x + p = $20,000. Substituting the formula for p into the budget constraint, we get x + $20,000 - 100b = $20,000. Solving for x, we get x = 100b. Substituting this into the utility function, we get u = 100b - 5b^2. Taking the derivative of this with respect to b, we get du/db = 100 - 10b. Setting this equal to zero and solving for b, we get b = 10.

Minnie Applesauce Is Shopping for a Summer Lake Cottage