Two firms, A and B, have complete control of the supply of mineral water and both have zero costs. The market (inverse) demand function is given by: P = 200 – 10Q, where Q = qA (output of seller A) + qB (output of seller B). Their best reply functions (BRP) are given by: qA = 10 - .5qB qB = 10 - .5qA

a) Find the Cournot solution for the market price and output of mineral water and illustrate with a simple graph.

b) The marginal revenue function facing a monopolist is given by: MR = 200 – 20Q Demonstrate that firms A and B have an incentive to cooperate and maximize joint profits.

c) Assume each firm can select two output strategies—specifically the strategies from parts (a) and (b). Denote these alternative output strategies qa and qb. Compute and payoff/profit matrix showing the four possible outcomes.

d) Does the game that you developed in preceding part have a determinate outcome—i.e., is there a dominant strategy? Explain.