Suppose that two firms with zero marginal costs are facing the inverse demand P=240-Q. Show that it is more advantageous to be the leader and announce your output decision first.

11 8. Suppose an industry produces an undifferentiated product  for  which market  demand  is given by  X   = A- P.  There are many  potential producers for this product, each of whom has a production function of the form: Fixed costs of F must be paid for being in business, and the marginal cost of a unit of production is a constant k . We imagine that firms decide whether to enter the industry under the supposition that,  after  all the firms that are going to enter do so, competition will be according to the Cournot model. That is, if N firms are in the market each has Cournot conjectures.  An equilibrium  is achieved with  N  firms in the industry if each firm, having its Cournot conjectures, does no worse than break even, whereas if another firm entered and made this an N + 1 firm Cournot oligopoly, all the firms would lose money. What is the equilibrium in this case? What (if anything) would be…

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An industry has a demand function of QP(p) = 500 – 250p. Suppose now that each firm has a constant marginal cost equal to 1. a. If there are n identical firms, what would be the profit of each under Cournot competition? 5. What would be the profit of each if they collude? c. If the firms face that demand function each period, what discount factor is required to support collusion? d. What happens to the required discount factor as n grows?

In the Stackelberg model, the firm that sets output first has an advantage. Explain why using your own words.

Two firms, A and B, sell the same good X in a market with total demand Q = 100 – P. The two firms compete on quantities and decides how much to produce simultaneously. Firm A cost function is C(qA) = 40qA. Firm B cost function is C(qB) = 60qB. 1. Find the best reply functions of both firms and represent them in a graph. 2. Find the quantity produced by each firm in a Nash equilibrium. 3. Find the firms and consumers surplus. 4. Compare the surplus of firms found above with the surplus arising when both firm cooperate to sustain a monopoly outcome. 5. Assume now that A and B compete as in a Stackelberg model. A chooses first and B chooses after observing the choice of A. Find equilibrium quantities produced by each firm and the market equilibrium price.

Consider a market where two firms produce the same product, and compete by choosing the price to charge consumers. There are no capacity constraints and no fixed costs. Consumers purchase from the firm that charges the lowest price, Pmin Aggregate demand is given by Q(Pmin) = 600 – 30pmin. Both firms have marginal costs of c = 15. What is the aggregate quantity produced in this market? And what price do consumers pay? (a) p₁ = = 15, p2 = 20, Q = 150 (b) P1 = P2 = 15, Q = 150 (c) P₁ = P₂ = 20, Q = 0 (d) p₁ = 10, P2 = 15, Q = 300 (e) None of the above options is correct.

A market is served by two firms in Cournot competition, each with a constant marginal cost of $100. The market inverse demand curve is P = 2,000 – 50 Q, where Q is the total market output produced by the two firms, q 1 + q 2. What is Firm 1's reaction function? A. q1 = 400 – 100q2 B. q1 = 19 – 0.5q2 C. q1 = 400 – 0.2P D. q1 = 210 – q2

Assume there are two firms, firm A and B, engaged in Cournot competition. The industry demand curve is given by P = 220 - Q, where Q = QA + QB denotes industry output. Each firm faces a marginal cost of production equal to $16. In equilibrium, what will be the output level of firm A?