A13.1 Roger’s Lobsters serves buy-by-the-pound lobster dinners every Monday night. In order to attract customers, Roger’s Lobsters can take out radio ads on local radio stations. If Roger’s Lobsters buys these advertisements, the demand for its Monday night buy-by-the-pound lobster special increases.

The demand function for Roger’s Lobsters Monday night specials is Q = 80 + 4A - 0.8P where Q is the number of pounds of lobster that Roger’s Lobsters sells each Monday night, P is the price per pound of lobster, and A is the number of radio ads that Roger’s Lobsters purchases each week. Solving the demand function for P as a function of Q and A gives the inverse demand function for Roger’s Lobsters’ Monday night special:

P = 100 + 5A - 1.25Q Roger’s Lobsters’ total cost of selling lobster, including the cost of advertising, is TC1Q2 = 1.25Q2 + 30A2 - 10A

a. What are the profit-maximizing quantity of pounds of lobster that Roger’s Lobsters sells and the profit-maximizing number of radio advertisements that Roger’s Lobsters buys each week?

b. What is Roger’s Lobsters’ profit-maximizing price for a pound of lobster?

c. How much economic profit (or loss) does Roger’s Lobsters make each week?