The inverse market demand for mineral water is P = 100 - Q, where Q is the total market output, and P is the market price. Two firms, A and B, have complete control of the supply of mineral water. Marginal costs are constant and equal to 10 for both firms (i.e., MC1=MC2=10)

1. Find the Cournot Solution.
2. Find an identical output for each firm that maximizes joint profits.

Continuing with the same problem, assume that each firm can choose only two outputsthe ones from parts a and b in question 1. Denote these outputs q_aand qb.

1. Compute the payoff matrix showing the four possible outcomes.
2. Now consider firms playing an infinitely repeated version of this game and consider the following strategy for each firm: (i) produce q_bin period 1, (ii) produce q_bin periodtif both firms produced q_bin all preceding periods, and (iii) produce q_ain periodtif one or more firms did not produce q_bin some past period. Assume each firm acts to maximize its sum of discounted profits where the discount rate isr. Find the values forrsuch that this strategy pair is a Nash equilibrium.