Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of where q, is Firm 1's output, p, is Firm 1's price, and p, is Firm 2's price. Similarly, the demand Firm 2 faces is Solve for the Bertrand equilibrium. in equilibrium, p, equals $ and P₂ equals $ (Enter numeric responses using integers.) q, = 160 – 2P, + 1P2, q2 = 160-2p₂+1p₁.
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- Two firms produce identical products at zero cost, and theycompete by setting prices. If each firm charges a low price,then both firms earn profits of zero. If each firm charges ahigh price, then each firm earns profits of £30. If one firmcharges a high price and the other firm charges a low price,the firm that charges the lower price earns profits of £50, andthe firm charging the higher price earns profits of zero. (a) Which oligopoly model best describes this situation?(b) Write this game in normal form.(c) Suppose the game is infinitely repeated. Can theplayers sustain the "collusive outcome" as a Nashequilibrium if the interest rate is 50 percent? Explain. Please answer the a, b and c parts.QUESTION 4: The graph below shows the demand and costs data for a one of firms operating in a market with a highly differentiated product/All underlying work must be shown MC ATC $11.50 $10.00 $9.00 $6.00 D MR 200 400 700 s00 Quantity A) Refer to the graph above. If the firm in the graph above maximizes profit, it will produce units of output and charge price per unit. A) 400; $10 B) 600; $6 C) 900; $9 D) 600; $11.50 B) Refer to the graph above. At the profit maximizing output level, the firm from above will earn: A) zero economic profit. B) $900 total economic profit. C) $2,700 economic profit. D) $2,700 economic loss. C) Refer to your answer above. You can conclude that if there are no barriers to entry: a) new fims will enter this industry in the long run in a search of profit. b) existing firms will exit this industry in the long run because of the short-run losses. c) this industry is in long-run equilibrium, and there are no incentives to enter or exit. d) the price per unit of…2. Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of q₁ - 100 - 2p₁ + P2, where q₁ is Firm 1's output, p₁ is Firm 1's price, and p2 is Firm 2's price. Similarly, the demand function Firm 2 faces is 92 100 2p2 + P₁. Solve for the Nash-Bertrand equilibrium. =
- Suppose that identical duopoly firms have constant marginal costs of $0 per unit. Firm 1 faces ademand function of q1 = 100 – 2p1 + p2, where q1 is Firm 1’s output, p1 is Firm 1’s price, and p2 isFirm 2’s price. Similarly, the demand Firm 2 faces is q2 = 100 – 2p2 + p1. Please solve for theBertrand equilibrium.1 Consider two identical firms with a unit cost of production of $10 and a market demand of p= 60-y. (a) What is firm 1’s optimal output level as a function of firm 2’s output? (b) What is firm 2’s optimal output level as a function of firm 1’s output? (c) What is the Cournot equilibrium output level for these firms? (d) What is the Cournot equilibrium price level? Show your work step by step.6. Two firms, Firm 1 and Firm 2 and are competing in quantities. The demand they are facing is given by p=1-91-92, with p being the price of the good, and 9₁ and 92 the quantities produced by firm 1 and 2 respectively. The total cost of firm 1 is TC1 (91) = 9₁ and the one of firm 2 is TC₂ (92) = 292. (a) Find the Cournot equilibrium. (b) The government decides that it wants to make the market more competitive. As such it decides to offer to Firm 1 a license to become the leader in the market. The licence costs F, and if Firm 1 buys it, it will be allowed to choose its quantity before Firm 2. What is the maximum Firm 1 would be willing to pay for this license?
- 8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output, 1.e. Qq1 +42. The inverse demand curve in the market is given by P-15-Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) If the firms could collude, what would be the total output in the mar- ket? Assuming each firm produces half of the collusive output, what is the profit of each firm?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…demand is y = 500 1. The Corleone and Chung families are the only providers of a good in the U.S. The market 20p. The costs of production for each of them are represented by the cost functions C₁(y₁) = 10∙y₁ and C₂(y₂) = 7 y2, respectively. Suppose both families must choose their output levels simultaneously. a) Derive their reaction functions. b) Calculate the Cournot equilibrium in this market. Indicate output levels, market price, and individual profits. (Answer: y₁ = 80 units, P = 14 USD) -
- 8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output, 1.e. Q-91 +42. The inverse demand curve in the market is given by P-15-Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. "// (b) If the firms could collude, what would be the total output in ket? Assuming each firm produces half of the collusive output, the profit of each firm? the mar- what is (c) Suppose each firm produces half of the collusive output identified in part (b). Firm 1 considers a deviation from this arrangement. What would be the best deviating output of firm 1 and its deviation profit? (d) Suppose firms interact repeatedly over an infinite horizon, and firms have a common discount factor & € (0,1). Specify a trigger strategy for each firm to sustain the collusive arrangement as an…Consider the Cournot duopoly with linear demand function ? = 2000 − 2Q, where P is the price and Q = q1 + q2 is the total supply. Firm 1 and firm 2 has constant marginal cost of 600. Just answer the E, F and G, thank you bartleby! a. If firm compete in price, draw in detail the best response of each firm.b. Determine and explain the Bertrand equilibrium.c. What is the equilibrium quantity and how much profit for each firm?d. Explain the Bertrand Paradox in (c)!e. If firm 1 has capacity of production 450 and firm 2 has capacity of 200. Determine the Bertrand equilibrium.f. What is the equilibrium quantity, and how much profit for each firm?g. Is there any paradox in (f)?. The market for widgets consists of two firms that produce identical products. Competition in the market is such that each of the firms independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 is known to have a cost advantage over firm 1. A recent study found that the (inverse) market demand curve faced by the two firms is P = 280 – 2(Q1 + Q2), and costs are C1(Q1) = 3Q1 and C2(Q2) = 2Q2. a. Determine the marginal revenue for each firm. b. Determine the reaction function for each firm.