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

Jinal Mistry · Accepted Answer

Final Answer : A, Explanation :  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.

Definitions

Learning Objectives

Learning Objectives

Related questions