The inverse demand curve for a Stackelberg duopoly is P = 10,000 - 6Q. The leader's cost structure is CL(QL) = 15QL. The follower's cost structure is CF(QF) = 25QF. 1.1. Determine the reaction function for the follower. 1.2. Determine the equilibrium output levels for both the leader and the follower. 1.3. What are the profits for the leader? For the follower?
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- Two firms are engaged in duopoly competition in a market with demand Q = 120 - p and zero costs. The reaction function for firm i given firm j's output q i = 60 - 1 2 q j . What is the payoff to firm i if the two firms engaged in collusion to maintain monopoly output and prices. Assume that each firm gets half the monopoly profit.Consider a Stackelberg duopoly with the following inverse demand function: P = 1,200 − 3Q1 − 3Q2. The firms' marginal costs are identical and are given by MCi = 6. Based on this information, the Stackelberg follower's reaction function is Multiple Choice: Q2 = 398 − 0.5Q2. Q2 = 199 − 0.5Q1. Q2 = 398 − 0.5Q1. Q2 = 199 − 0.5Q2.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…
- A duopoly faces an inverse market demand of P(Q) = 240−Q.Firm 1 has a constant marginal cost of MC1 (q1) = $10.Firm 2's constant marginal cost is MC2 (q2) = $20.Assume fixed costs are negligible for both firms. Calculate the output of each firm, market output, and price if there is (A) a collusive equilibrium or (B) a Cournot equilibrium. (A) Collusive equilibrium (Enter your responses rounded to two decimal places) The collusive equilibrium occurs where q1 equals ?and q2 equals ? Market output is ? The collusive equilibrium price is ? (B) Cournot equilibrium (Enter your responses using rounded to two decimal places) The Nash-Cournot equilibrium occurs where q1 equals ? and q2 equals ? Market output is ? The equilibrium occurs at a price of ?A duopoly faces an inverse market demand of P(Q) = 150−Q.Firm 1 has a constant marginal cost of MC1 (q1) = $30.Firm 2's constant marginal cost is MC2 (q2) = $60.Assume fixed costs are negligible for both firms. Calculate the output of each firm, market output, and price if there is (A) a collusive equilibrium or (B) a Cournot equilibrium. (A) Collusive equilibrium (Enter your responses rounded to two decimal places) The collusive equilibrium occurs where q1 equals ?and q2 equals ? Market output is ? The collusive equilibrium price is ? (B) Cournot equilibrium (Enter your responses using rounded to two decimal places) The Nash-Cournot equilibrium occurs where q1 equals ? and q2 equals ? Market output is ? The equilibrium occurs at a price of ? The market demand curve faced by Stackelerg duopolies is: Qd = 12,000 - 5P where Qd is the market quantity demanded and P is the commodity's price in dollars. Firm A's marginal cost is: MCa = 0.08qa where MCa is Firm A's marginal cost in dollars and qa is the quantity of output produced by Firm A. Firm B's marginal cost equation is: MCb = 0.1qb where MCb is Firm B's marginal cost in dollars and qb is the quantity of output produced by Firm B. Because of Firm A's lower marginal cost, Firm B has conceded the power to move first to Firm A. a. Given Firm B will move second, what is the equation for Firm B's reaction function with qb expressed as a function of qa? b. Given Firm A can move first, what quantity of output will Firm A produce? c. What quantity of output will firm B produce? What price will be established for the commodity?
- The inverse demand for a homogeneous-product Stackelberg duopoly is P = 12,000 −5Q. The cost structures for the leader and the follower, respectively, are CL(QL) = 4,000QL and CF (QF) = 5,000QF.a. What is the follower’s reaction function? QF = − QLb. Determine the equilibrium output level for both the leader and the follower.Leader output: Follower output: c. Determine the equilibrium market price. $ d. Determine the profits of the leader and the follower.Leader profits: $ Follower profits: $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 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.
- 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 two firms that compete according to the Cournot model. Inverse demand is P (Q) = 16 − Q. Their cost functions are C (q1) = 2q1 and C (q2) = 6q2 (a) Solve for Nash equilibrium quantities of each firm (b) Suppose firm 2 becomes more inefficient and its cost function changes to C (q2) = xq2 where x > 6. How large must x be to cause firm 2 to not want to produce anything in equilibrium?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?