Consider a Bertrand Duopoly Model. Marker demand curve is given by Q = 200-P. Firm A has a marginal cost of $20 and Firm B has a marginal cost of $50. In equilibrium, what is the market price? How many units does each firm produce? Calculate each firm's profit.

Consider a duopoly with homogenous goods where Firm 1 has the following production function:  Q1 = F1(L,K) = L1/2 K1/2, where Q and K are measured in units and L in hours. Firm 2 uses labour and capital as well but has a different production function, given by Q2 = F2(L,K) = L1/3 K2/3. You may assume that the market for labour and capital is perfectly competitive and the current wage rate is £40 and the rental rate on capital is £10. Both firms sell their products on the same market with inverse demand function       P = 52 – (Q1 + Q2), where P is measured in pound sterling. Which production function(s) exhibit(s) decreasing returns to scale?  Suppose Firm 1 wishes to produce 6 units. What is the cost minimising input mix for Firm 1?  Suppose Firm 2 wishes to produce 4 units. What is the cost minimising input mix for Firm 2?  Assume both firms now have the option to produce either 4 units or 6 units. We will consider the situation where both firms simultaneously, but independently,…

Juanita owns a plot of land in the desert that isn't worth much. One day, a giant meteorite falls on her property, making a large crater. The event attracts scientists and tourists, and Juanita decides to sell nontransferable admission tickets to the meteor crater to both types of visitors: scientists (Market A) and tourists (Market B). The following graphs show daily demand (D) curves and marginal revenue (MIR) curves for the two markets. Juanita's marginal cost of providing admission tickets is zero.

In the Cournot equilibirum, what is the market price and units produced by firm 1 and firm 2?

There are two identical firms in an industry, 1 and 2, each with cost function , i = 1,2. The industry demand curve is P = 100 − 5X where industry output, X, is the sum of the two firms’ outputs (X1 + X2). (a) If each firm makes its output decisions on the assumption that the other will not react to its choices (the Cournot assumption), what is the equilibrium output for each firm? What is the equilibrium price? (b) Suppose that each firm takes it in turn to choose its level of output, on the assumption that the other’s output level is fixed. Would the process of adjustment be stable? (c) Suppose that firm 1 introduces a cost-saving innovation, so that its cost curve becomes C1 = 8X1. Firm 2’s cost curve and the industry demand curve are unchanged. What happens to the equilibrium quantity produced by each firm and to market price?  

Consider a duopoly where firms compete in prices and firms do not have any capacity constraints. Market demand is P(Q)=45-4Q, and each firm faces a marginal cost of $9 per unit. How much is each firm's total variable cost if firms equally divide the market at Nash equilibrium?

Consider a BERTRAND duopoly where each firm's price MUST BE IN WHOLE DOLLARS. Each firm incurs a $50 fixed costs and can produce any quantity without additional cost. Market demand is P(Q)=100-Q. Firm 1 has chosen $25 and Firm 2 has chosen $50. What are Firm 1's profit? Do not enter the $.

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

Consider an industry comprised of three identical firms faced with a linear cost function given by: C(qi) = cqi; for i = 1; 2; 3. Let inverse market demand be given by: P(Q) = a - bQ; where Q = q1 + q2 + q3.a. Compute the Cournot equilibrium; that is, find prices, quantities, and profits.b. Suppose that firms 1 and 2 merge, converting the market into a duopoly consisting of the “superfirm” and firm 3. Compute the new Cournot equilibrium. Once again find prices, quantities, and profits.c. Suppose that all three firms merge. Compute quantities, prices, and profits for the cartel solution.d. Suppose that firm 1 and 2 represent two members of OPEC – Saudi Arabia and Venezuela, say – while firm 3 is a non-OPEC oil exporting country – Russia, say. Describe the dynamics of OPEC. (Hint: re-interpret the solution to part 2, as 1 firm deviating from the fully cartelized solution. Is it convenient to have a partial cartel?)

Consider a Bertrand duopoly where market demand is P(Q)=5-9Q. Each firm faces a marginal cost $2 and no fixed cost. How much is the dead weight loss in a Nash equilibrium?