Intermediate Microeconomic Theory
1. Consider an industry with two firms producing an identical product. Each firm has a marginal cost of 10 and a fixed cost of 20. Market (inverse) demand for the product is given by:
P = 50 ? Q
Where Q is the total quantity produced by both firms (in other words, P = 50 ? q1 ? q2).
(a) Assume that each firm can choose a value of q from {10, 13, 16, 18}. Draw and fill-in the pay off matrix for the simultaneous move game.
(b) What is the Nash EQLM of the matrix in (b)? What is each firm’s strategy? What will be the market price?
(c) Assume still that each firm can choose a value of q from {10, 13, 16, 18}. What will be the EQLM outcome of the sequential move game in which firm 1 moves first? Explain in one or two sentences.
(d) Assume now that each firm can choose any positive value of p. What is the EQLM outcome of the simultaneous move game? What will be the market quantity? Explain in one or two sentences.
(e) Assume now that each firm can choose any positive value of p. What is the EQLM outcome of the sequential move game in which firm 1 moves first? What will be the market quantity?
Explain in one or two sentences.
2. Amy (A) and Beau (B) compete as Cournot duopolists in a market where (inverse) demand is given by:
P = 70 ? 2Q
Amy and Beau face a constant marginal cost of 10 and zero fixed costs. Assume that each firm can choose a value of q from {10, 15}.
(a) Draw and fill-in the payoff matrix for the simultaneous move game.
(b) What is the Cournot EQLM price?