Charlie can work as many hours as he wishes at a local fast-food restaurant for a wage of $4 per hour. Charlie also does standup comedy. Since Charlie lives in a quiet, rather solemn Midwestern town, he is the town's only comedian and has a local monopoly for standup comedy. The demand for comedy is Q = 40 - P, where Q is the number of hours of comedy performed per week and P is the price charged per hour of comedy. When Charlie maximizes his utility, he spends at least 1 hour per week working at the restaurant and he gets at least 1 hour of leisure time. His utility depends only on income and leisure. How many hours per week does he perform standup comedy?

Question

Quizplus · Accepted Answer

Charlie maximizes his utility by equating marginal revenue from comedy to his wage rate. The demand function is Q = 40 - P, so P = 40 - Q. Total revenue is P*Q = (40-Q)Q = 40Q - Q^2. Marginal revenue is the derivative: MR = 40 - 2Q. Setting MR equal to the wage rate of $4, we get 40 - 2Q = 4, solving gives Q = 18.

Charlie Can Work as Many Hours as He Wishes at a Local