Consider the case of two identical firms, each with a cost function C(yi)=yi^2/1+10yi where i = 1 or 2. These are the only two firms in the market for this good. The market demand is P = -2Q +280
a) If they act as a monopolist, their combined MC = Q/2 +10. Find the monopoly P, Q, and profit for each firm. Assume each firm is producing ½ the total output.
b) Consider the following problem for firm 1. Assume firm 2’s output is fixed at the quantity in (a). We know than, in general, firm 1’s total revenue is a function of how much each firm produces(since price is a function of total output), but with firm 2’s output fixed, we can write firm 1’s TR as only a function of firm 1’s output. Use this to write a function for firm 1’s profit as a function of only firm 1’s output. Use a first order condtion to find the profit maximizing quantity for firm 1 to produce and verify it is not the quantity found in (a)
c) Figure the profit for each firm from the following situations:
i) firm 2 produces the the quantity in (b) and firm 1 produces the quantity in (a)
ii) both firms produce the quantity in (b)
d) Write the information found in (a) – (c) into a normal form game for the two firms. What is the dominant strategy? Explain why this game is an example of a prisoner’s dilemma.