A13.3 Esteban’s Argentinian Grill is the best place to grab a steak in Sacramento, California. The restaurant uses the highest-quality meat and grills it using traditional Argentinian methods. Few customers, however, know about the restaurant. In an attempt to draw in more customers, Esteban hires an economist to determine whether taking out costly television advertisements will be profitable.

His consultant determines that the demand function for a steak at Esteban’s is Q = 560 + 2A - 2P where Q is the number of steaks that Esteban’s sells, P is the price of a steak, and A is the number of advertisements. Solving the demand function for P as a function of Q and A gives the inverse demand function for Esteban’s steaks:

P = 280 + 1A - 0.5Q Esteban’s cost of selling steak is TC = 40Q + A2

a. What are the profit-maximizing number of steaks that Esteban sells and the profitmaximizing number of television advertisements that he purchases?

b. What price does Esteban charge for a steak?