Pfizer and Moderna are duopolies in the COVID-19 vaccine market with slightly different products. The demand functions for their products are

Pfizer (I): q_I = 15 - 2P_I + P_A

Moderna(A): q_A = 15 - 2P_A + P_I

Assuming marginal cost of production is 4 for both Pfizer and Moderna.

(a) (5 points) Derive Pfizer and Moderna's profit in a static Cournot equilibrium.

(b) (5 points) Suppose Pfizer and Moderna merge into a single firm (a monopoly of the COVID-19 vaccine) but still produce the same two products and therefore, face the same demand functions and marginal costs given above. What would be the maximal total profit of the merged firm?

(c) (10 points) Suppose instead of merging, Pfizer and Moderna engage in an infinitely repeated competition. Each round both firms set quantities q_I and q_A simultaneously. They can produce either the monopolistic quantity you found in part (b) or the Cournot equilibrium quantity you found in part (a). Prices for each product and the profit for each firm are calculated each round using the same demand functions given above.

Consider the following "grim-trigger" strategy: "I'm going to produce the monopolistic quantity of my product in Round 1, and continue to produce that quantity each round, unless my opponent produces the Cournot equilibrium quantity, in which case I will switch to the Cournot equilibrium quantity the next round and continue to produce that quantity forever." If both firms have the same discount factor (0 < < 1), find , the minimal , such that as long as > , then "both firms choosing the monopolistic quantity every round" is the equilibrium path when both firms follow the "grim trigger" strategy.