Suppose there are two firms operating in the same market and compete over prices. the firms sell a differentiated product and their demand is given by Firm 1's demand: -1.5 p,+p2+273 Firm 2's demand: 0.5 p,-1.5 p2+293 The firms' reaction function will be of the form p1=A1+a, p2 and p2=A2+a2P1 where A1= and a1= A2= and a2= Are prices Ostrategic complements Ostrategic substitutes What are the equilibrium prices in this market P1= and p2= What are the quantities demanded from each firm and q2= What are the profits for each firm TT= and t2=
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- Consider a duopoly market with 2 firms. Aggregate demand in this market is given byt Q = 500 – P, where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MC = 20, i=A,B. « Assume the firms compete a la Cournot. e a) Find the inverse demand in this market. Note that marginal revenue for both firms is given by MRA=500-2QA-QB, MRB=500-QA-2QB. b) Describe what a best-response curve is and how to find it. c) Derive the best-response function for each firm. d) What are the equilibrium quantities? e) What is the total quantity supplied on this market? f) What is the equilibrium price in this market?2.- Each of two firms, firms 1 and 2, has a cost function C(q) = 1 2 q; 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 = 1 2. (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…1. Bertrand's original analysis predicted a perfectly competitive price and output if there were more than one firm in a market. Assume firms A and B are Bertrand competitors making identical products at identical cost C¡ = 200qi and facing inverse market demand P = 1200 – 0.1Q. Assume further that there are no capacity constraints, and that if the firms charge the same price, consumers split their purchases evenly between the firms. a. Assume A and B choose prices repeatedly and simultaneously, and that both adopt the Trigger strategy. Determine whether joint-profit maximizing is a sustainable equilibrium if the interest rate is 5% and there is a 40% probability of significant entry into the market that would eliminate future monopoly profits. b. How would your analysis change if there were four identical Bertrand competitors rather than two? Why?
- Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedulein this market is:p Qd180 150155 175130 200Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever itneeds to be to sell the total output in the market.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your workdetermining the profits in each box in the matrix.(b) Determine the Nash equilibrium of this game.(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreementbe?(d) Explain how the government might respond to such an agreement and whyOnly two firms, Acme and Stuff Inc., sell a particular product. The table below shows the demand curve for their product. Each firm has the same constant marginal cost of $10 and zero fixed cost (so MC-ATC=$10). Price Quantity Total Revenues 10 70 65 60 55 50 45 40 28889 35 30 25 20 15 10 15 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 0 If Acme and Stuff Inc are able to collude, how much will Acme produce? 6500 12000 16500 20000 22500 24000 24500 24000 22500 20000 16500 12000 6500 0Return to Figure 9.2. Suppose P0 is $10 and P1 is$11. Suppose a new firm with the same LRAC curve asthe incumbent tries to break into the market by selling4,000 units of output. Estimate from the graph what thenew firm’s average cost of producing output would be.If the incumbent continues to produce 6,000 units, howmuch output would the two firms supply to the market?Estimate what would happen to the market price as aresult of the supply of both the incumbent firm andthe new entrant. Approximately how much profit wouldeach firm earn?
- There is much evidence that large firms with considerable market power (firms such asmonopolies) may not maximize profits but may pursue quite different objectives such asgrowth or sales revenue maximization. What are the arguments put forward to defendmonopoly? Name any 5 Generally, the aim of a business is to maximize profit. Which point should a firm operateat in order to achieve maximum profit? By making use of a graph indicate clearly the pointat which a firm makes maximum profit and a point where a firm increase their output inorder to enhance profit as well as well as the points where they should reduce theirproduction if they want to enhance profitConsider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedulein this market is: p Qd180 150155 175130 200Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever itneeds to be to sell the total output in the market.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your workdetermining the profits in each box in the matrix.(b) Determine the Nash equilibrium of this game.(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreementbe?(d) Explain how the government might respond to such an agreement and why.Please
- 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…5. Tom is a monopolist input supplier to Dick and Harry. Tom's marginal cost is 1. Dick and Harry are duopolists with production function q x/2 No firm has fixed costs. The demand for the final product is given by Q 100-p. a) Assume Dick and Harry buy the input from Tom at price k. What are their cost functions? b) Find the Cournot equilibrium quantities. c) What price, k, should Tom set? d) Now suppose Dick could buy Tom's firm and stop supplies of the input to Harry so that Dick would be a monopolist. How much is Dick willing to pay for Tom's firm? e) How much is Tom willing to sell his firm for?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 12