Consider a duopoly where firms sell an homogeneous product and compete in price (Bertrand competition). The cost function of firm 1 is C1 = 20 + 5Q and the cost function of firm 2 is C2 = 8Q. The demand for the product is Q = 100 - 4P. What is the optimal price of Firm 1?
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- A common characteristic of oligopolies is a. interdependence in pricing decisions. b. independent pricing decisions. c. low industry concentration. d. few or no plant-level economies of scale.Consider a market that is a Bertrand oligopoly with 5 firms in the market. Each of these firms produce an identical product and each have the same cost function of C(Q) = 80Q. The inverse market demand for this product is P = 2480 – 2Q. How much does EACH firm produce at the equilibrium price?Two identical firms currently serve a market. Each has a cost function of C(q) = 30q. Market demand is P(Q) = 80 − 0.01Q. The firms compete by setting prices simultaneously as in Bertrand competition. Let PB represent the equilibrium Bertrand duopoly price.The firms have proposed to merge, and they announce that this merger will result in considerable cost savings. The firms’ new cost function will have the form Cm(q) = cq + 100, 000. Note that the merged firm has positive fixed costs while the unmerged firms do not. (a) What is the merged firm’s profit-maximizing price if the merger is approved? Is it possible for the cost savings (via c < PB) to be sufficiently large for the merged firms’ profit-maximizing price to be below the duopoly equilibrium price? (b) Suppose that the Department of Justice permits the merger with the requirement that the new (post-merger) price must be no greater than the pre-merger price. Under what circumstances are the firms willing to go through with…
- Consider a market that is a Bertrand oligopoly with 5 firms in the market. Each of these firms produce an identical product and each have the same cost function of C(Q) = 80Q. The inverse market demand for this product is P = 2480 – 2Q. What is the equilibrium market price?Consider a Cournot duopoly. The market demand function is P = 180 – 2(q₂ + q₂), where P is the market price, q₂ is the output produced by Firm 1 and q₂ is the output produced by Firm 2. The two firms have a constant marginal cost c = 30. What is the total output in this market? Round your answer to the nearest integer (e.g. 50)Consider a Bertrand duopoly. Market demand is P(Q)=41-3Q, and each firm faces a marginal cost of $4 per unit. How much is the sum of firms' total revenue in the Nash equilibrium?
- Consider a two-firm duopoly facing a linear demand curve: P = 1,600 – Q. Assume MCA = MCB = AC = 100. where: P = price Q = total output of the market, thus, Q = QA + QB Find the profit-maximizing output (Cournot equilibrium output) Find the Cournot equilibrium price of Firm A and Firm B.Consider a Bertrand duopoly. Both firms produce an identical good at the same constant marginal cost of $0.80. Demand is given by Q=100−P. If the two firms charge the same price, they share market demand equally. The firms are located in Singapore, where the smallest currency denomination is $0.05. The firms thus can only choose prices in increments of $0.05. a) Suppose that both firms choose the same price, P. What is the profit of a firm as a function of P? b) Now suppose that one firm unilaterally deviates from the arrangement in (a) by charging a price $0.05 lower than P. What is that firm’s profit as a function of P? c) A Nash equilibrium occurs when no firm has an incentive to deviate by lowering its price. Using your answers in (a) and (b), set up an inequality that characterizes the Nash equilibrium. Then solve for the Nash equilibria in this game. (Hint: there are three equilibria)Suppose a market is served by two firms (a duopoly). The market demand function given by P = 1200 - Q_{1} - Q_{2} where Q_{1} is the output produced by firm and Q_{2} is the output produced by firm 2 . Firm cost of production is given by the function C(Q_{t}) = 120Q_{t} and firm 2's cost of production is given by the function C(Q_{2}) = 120Q_{2} The average cost of firm 1 is given by A*C_{1} = 120 and the average cost of firm 2 is given by A*C_{2} = 120 Marginal profit function for firm 1: Delta pi 1 Delta Q 1 equiv1080-2Q 1 -Q 2; (d*pi_{2})/(Delta*Q_{2}) = 1080 - Q_{1} - 2Q_{2} Marginal profit function for firm 2: What will be the equilibrium profit levels earned by the Stackelberg leader firm and the Stackelberg follower firm?
- The inverse market demand in a homogeneous-product Cournot duopoly is P = 100 – 2(Q1 + Q2) and costs are C1(Q1) = 20Q1 and C2(Q2) = 30Q2. a. What is the reaction function for each firm? b. What is each firm’s equilibrium output? c. What is the equilibrium market price? d. What is the profit each firm earns in equilibrium?A homogeneous product duopoly faces a market demand function given by p = 300 - 3Q,where Q = q1 + q2. Both firms have constant marginal cost MC = 100. What is the Bertrand equilibrium price and quantity in this market?Consider a Duopoly model, in which two firms decide a quantity simultaneously. The market demand is given by P=50 - Q, where Q is the total output (Q=Q1+Q2). Each firm has an identical cost function, TCi=6Qi, i=1, 2. If Firm 1 believes Q2=10, Firm 1 should sell Q1= ____ units in order to maximize its profit.