The inverse market demand for mineral water is P=200-10Q, where Q is total market output and P is the market price. Two firms, A and B, have complete control of the supply of mineral water and both have zero costs.

a. find the Cournot solution

b. find an identical output for each firm that maximizes joint profits.

assume that each firm can choose only two outputs- the one from parts a and b. denote these outputs q_a and q_b

c. compute the payoff/profit matrix showing the four possible outcomes.

d. show that this game has the same basic properties as the Advertising Game. in particular, each firm's optimal output is independent of what the other firm produces. Now consider firms playing an infinitely repeated version of this game and consider the following strategy for each firm: (I) produce q_b in period 1,(ii) produce q_b in period t if both firms produced q_b in all preceding periods, and (iii) produce q_a in period t if one or more firms did not produce q_b in some past period. assume each firm acts to maximize its sum of discounted profits where the discount rate is r.

e. find the values for r such that this strategy pair is a Nash equilibrium.

please answer questions e, d, and e.