Determine each firm’s revenue function. b) Determine the reaction function for each firm. c) Calculate each firm’s equilibrium output. d) Calculate the equilibrium market price. e) Calculate the profit each firm earns in equilibrium.
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The inverse demand function in a particular homogenous product Cournot duopoly is
P = 150 – 2(Q1+Q2).
Each firm produces at constant marginal costs, equal to 20 and 28, respectively. [Notethat MRi(Qi) = a-bQj-2bQi]
- a) Determine each firm’s revenue function.
- b) Determine the reaction function for each firm.
- c) Calculate each firm’s equilibrium output.
- d) Calculate the
equilibrium market price. - e) Calculate the profit each firm earns in equilibrium.
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- A homogenous-good duopoly faces an inverse market demand function of p = 150 − Q. Assume that both firms face the same constant marginal cost, MC1 = MC2 = 30. Calculate the output of each firm, the market output, and the market price in a Nash-Cournot equilibrium Re-solve part (a) assuming that the marginal cost of firm 1 falls to MC1 =20 Explain what will happen to each firm’s output, the market output, and the market price if the two firms can collude (e.g., form a cartel)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 ?OLIGOPOLY 1.- Each of two firms, firms 1 and 2, has a cost function C(q) = 30q; the inverse demand function for the firms' output is p = 120-Q, where Q is the total output. Firms simultaneously choose their output and the market price is that at which demand exactly absorbs the total output (Cournot model).(a) Obtain the reaction function of a firm.(b) Map the function obtained in (a), and graphically represent the Cournot equilibrium in this market.(c) Repeat (b), this time analytically.(d) Now suppose that firm 1's cost function is C(q) = 45q instead, but firm 2's cost is unchanged. Analyze the new solution in the market.(e) Obtain the total surplus, consumer surplus, and industry profits in both cases, and compare. What is the effect of the worsening in firm 1's cost?
- 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?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…Q2. Consider a two-firms Cournot model with constant returns to scale. Assume also that the inverse demand function is P = 100 – 2Q, with marginal cost equal to 20for both firms, where Q = q1 + q2 . c) Calculate Stackleberg equilibrium. Draw a picture of this outcome using best-response functions and isoprofit contours.Q1) Which one of the following statements about Cournot oligopoly model with N firms is incorrect? 1)The result with unspecifed N firms can be applied to N=1. 2)If N>1 and there exists a unique Nash equilibrium, then the market price cannot depend on N. 3)If the model is symmetric and there exists a unique Nash equilibrium and N approaches infinity, then the market price approaches to the marginal cost, i.e., the perfectly competitive price. 4)The result with unspecified N firms can be applied to N approaching infinity. Q2) Which of the following statements about the classic Cournot duopoly model is incorrect? 1)The products of the two firms are homogeneous. 2)It is a static game with complete information. 3)The two firms decide on their prices and let their quantities be dictated demand conditions. 4)There exist examples that have unique Nash equilibrium points.
- 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 Cournot Duopoly model. The inverse demand for their products is given byP = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given by TCi = 2Qi, for i = 1, 2.(a) In the Cournot model, what does each firm choose?(b) What is the timing of each firm’s decision?Consider the Bertrand model and answer the question below related to the content. Assume that each firm in the Bertrand Duopoly model can only choose non-negative integer quantities: 0, 1, 2, ... . Assume the demand is Q(P)=10-P and the marginal cost is 0 for each firm. Given this information, which of the following is FALSE? [Hint: Check values of profit functions.] A. If firm 2 sets price equal to 1, then the best response of firm 1 to this price is 1 B. If firm 2 sets price equal to 4, then the best response of firm 1 to this price is 4 C. If firm 2 sets price equal to 2, then the best response of firm 1 to this price is 1
