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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
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- Consider two Stackelberg firms, Firm Alpha and Firm Omega, each with marginal costs of 50 and each facing the market inverse demand curve: P = 500 – Q. Firm Alpha moves first, Firm Omega moves second. How many MORE units does Firm Alpha produce than Firm Omega due to first mover advantage?Suppose the inverse demand function for two firms in a homogeneous-product Stackelberg oligopoly is given by P = 50 − (Q1+Q2) and cost functions for the two firms are C1(Q1) = 2Q1 C2(Q2) = 2Q2 Firm 1 is the leader, and firm 2 is the follower.1. What is firm 2’s reaction function?2. What is firm 1’s output?3. What is firm 2’s output?4. What is the market price?Consider a market with two firms. Call them firm 1 and firm 2. The demand function describing the market is P = 216 – 0.4Q. Firms are initially identical, with the cost function C(q) = 140 + 40q. Calculate the total profits in the market. Under what conditions, the two firms may succeed to collude? How much would each firm earn if they could collude?
- Suppose there are two pharma companies (A and B) vying to develop the first vaccine to cure AIDS. Assume a fixed MC across the two firms MCA = MCB = 4. Assume further that they both face a market demand of P = 12 -0.00004Q and Q=QA +QB. Assume firm B's reaction function is: QB = 125,000 - 0.5QA. Compute for: Firm A's Revenue or RA Firm A's Marginal revenue MR Output for firm A or QA and output for firm B or QB Market Q* and P*2.- Each of two firms, firms 1 and 2, has a cost function C(q) = 0.5q; the demand function for the firms' output is Q = 1.5 - p, where Q is the total output. Firms compete in prices. That is, firms choose simultaneously what price they charge. Consumers will buy from the firm offering the lowest price. In case of tying, firms split equally the demand at the (common) price. The firm that charges the higher price sells nothing. (Bertrand model.) (a) Formally argue that there could be no equilibrium in prices other than p1 = p2 = 0.5 (b) Solve the same problem, but this time assuming that firms compete in quantities.Now, suppose that firm 1 has a capacity constraint of 1/3. That is, no matter what demand it gets, it can serve at most 1/3 units. Suppose that these units are served to the consumers who are willing to pay the most. Thus, even if it sets a price above that of firm 1, firm 2 may be able to sell some output. (c) Obtain the (residual) demand of firm 2 (as a function of its own…Consider an industry with two firms, each of which has a constant marginal cost of 20. The inverse demand facing this industry is P(Y) = 220 −Y, where Y = y1 + y2 is the total output. 1. What is the competitive level of output? (Recall: price equals marginal cost at the competitive equilibrium.) 2. What is the output of each firm in the Cournot equilibrium? 3. What is the output of each firm in the Stackelberg equilibrium when firm 1 is the follower and firm 2 is the leader?
- The diagram below shows the demand, marginal revenue, and marginal cost of a monopolist. 120 110- 100- 90- A 80- 70 60- 50- 40- 30- 20 10 O @_ 0 1 2 3 16 4 Profit-maximizing output: Profit-maximizing price: $ 5 7 units MR 6 MC T 7 8 a. What price and output would prevail if this firm's product was sold by price-taking firms in a perfectly competitive market? 9 Quantity D T 10 11 (11, 0) 14 15 b. Determine the profit-maximizing output and price for the monoplist. Price: $ 68 Output: 5 units c. Calculate the deadweight loss of this monopoly.PROBLEM IV. Consider an industry consisting of two firms (i = 1,2) that are engaged in a Bertrand price competition. The demand function for the product of firm i is given by qi = 24 – 9p; + 6p;. The marginal cost of production for each firm is zero. Q12. The collusive price of the products is (a) 4 (b) 5 (c) 1 (d) 6 (e) 221. In the industry, only two firms (Firm 1 and Firm 2) operate and they produce a homogenous good. They collude: they maximize their joint profit and split it equally between them. Firm I has the total cost of producing q; units of output given by the function TC(q)-8q1. The total cost of producing q: units of output for Firm 2 is TC(q)-q. Only integer quantities are allowed (no fractions). The market demand for the good is Q(P)-72-P, where Q is the quantity demanded and P is the unit price of the good. How many units of the good do cach firm produce in the equilibrium? A. Each firm produces 14 units. B. Firm I produces 32 units, and Firm 2 produces 2 units. C. Firm 1 produces 28 units, and Firm 2 produces 4 units. D. Each firm produces 16 units. E. None of the above
- Consider a market with the demand curve Q(P) = 3700– 100P. Two companies compete in Bertrand setting, where the first company has a marginal cost of $10 and a capacity of 100 units, and the second firm has a marginal cost of $20 and a capacity of 1000 units. Assume that fixed costs are zero. a) Show that both firms will sell in this market at a price above $20. b) Assume that the first firm is capacity constrained. From the perspective of the second firm, find the quantity sold in the market and the price set by the second firm. c) Now, using the result from the previous part, from the perspective of the first firm, find the quantity sold in the market and the respective price set by the first firm.3 In a Cournot market with two firms, the inverse market demand curve is P=50-2Q, where Q=q1+q2(Firm 1’s output is ; Firm 2’s output is ). Both firms have a constant marginal cost of 14. If Firm 2 produces 12 units of output, how much should Firm 1 produce? Group of answer choices 3 6 0 12C2) Consider an industry with only two firms: firm A and firm B. The industry's inverse demand is P(Q) = 400 - ¹1/Q, 10 where P is the market price and Q is the total industry output. Each firm has a marginal cost of $10. There are no fixed costs and no barriers to exit the market. a) Suppose that the two firms engage in Cournot competition. Find the equilibrium price PNE in the industry, the equilibrium outputs QANE and QBNE, as well as the profits NEA and NEB for each firm. marks] b) Suppose the two firms engage in Stackelberg competition, with firm A moving first, and firm B moving second. Find the equilibrium price PS in the industry, the equilibrium outputs QS and QBS, as well as the profits π and TSB for each firm. в c) For this subquestion only, suppose that firm B has a fixed cost of $200 000: What will firm B's optimal decision be, and what will be the resulting market structure? Now assume that instead of having two firms in the market, we have a monopoly facing the inverse…
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