Ann and Bruce each own a pizza store in Frostbite Falls, Minnesota. Demand for pizza is given by Q = 200 - 10P. Having the only two pizza stores in Frostbite Falls, they attempt to profitably split the market without violating the Sherman Antitrust Act. Each has the cost function C = 50 + 2Q. If Ann and Bruce behave as duopolists, how much profit do each of them earn?​ a) What are the (i) inverse demand function for pizzas and (ii) the marginal cost of producing pizzas in this market?
Every year, each duopolist decides how many pizzas to sell. They both know the local demand function, and they know how many pizzas were sold by the other rival last year. In fact, each duopolist assumes that the other seller will sell the same number this year as he/she sold last year.
b) if is the quantity of pizzas sold by Bruce last year, and as a response, Ann sells o pizzas this year, what does Ann think the price of pizzas will be this year?
c) If Q, is the quantity of pizzas sold by Bruce last year, and as a response, Ann sells QA pizzas this year, what is Ann's marginal revenue of pizzas this year?
d) What equation does Ann solve in order to find the profit maximizing output, if Ann believes that Bruce will continue to sell Q; quantity of pizzas this year?
e) Ann's Cournot reaction function tells us what Ann's profit-maximizing output this year would be as a function of Bruce's output last year. Use the equation you wrote in (d) to find Ann's reaction function.