Q1: What is the price-equillibrium under the assumption of the two companies colluding? What is the profit for each firm? Q2: Derive the output reaction curves for both firms and calculate the price-output equllibrium under this assumption. What is the profit for each firm?
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Q1: What is the price-equillibrium under the assumption of the two companies colluding? What is the profit for each firm?
Q2: Derive the output reaction
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- 2) Assume that there are 2 firms producing an identical product. Both firms have the same total cost function TC(q) =q2. The inverse demand function for the firms' output is p=120 Q, where Q is the total output and p is price. 1. What are the equilibrium price, output and profits of each firm if they are competing with each other? (Hint: Consider the equilibrium in a Cournot game.) 2. What happens if they form a cartel? Calculate the equilibrium price, output, and profits for the cartel? 3. If a single firm cheated, what would its output and profits be, assuming the other firm maintains the cartel price? Calculate the new outputs and profits for bath firms: 4. Discuss why it is hard to enforce a cartel. Explain using words. DO NOT do any calculations. DO NOT draw any graphs. 5. What can the cartel members do to enforce the cartel agreement? Propose a method. Describe the method using words. DO NOT do any calculations. DO NOT draw any graphs.There are only two driveway paving companies in a small town, Asphalt, Inc. and Blacktop Bros. The inverse demand curve for paving services is ?= 2040 ―20? where quantity is measured in pave jobs per month and price is measured in dollars per job. Assume Asphalt, Inc. has a marginal cost of $100 per driveway and Blacktop Bros. has a marginal cost of $150. Answer the following questions: Determine each firm’s reaction curve and graph it. How many paving jobs will each firm produce in Cournot equilibrium? What will the market price of a pave job be? How much profit does each firm earn?Suppose that there are two firms producing a homogenous product and competing in Cournot fashion and let the market demand be given by Q = 360-- Assume for simplicity that each firm operates with zero total cost. Suppose that two firms collude. How much more profit each firm can obtain relative to Cournot competition? 8000 14400 7200 16000
- 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?Use the orange points (square symbol) to plot the initial short-run industry supply curve when there are 10 firms in the market. (Hint: You can disregard the portion of the supply curve that corresponds to prices where there is no output since this is the industry supply curve.) Next, use the purple points (diamond symbol) to plot the short-run industry supply curve when there are 15 firms. Finally, use the green points (triangle symbol) to plot the short-run industry supply curve when there are 20 firms. PRICE (Dollars per pound) 100 90 80 70 80 50 40 30 20 10 0 0 125 250 375 500 825 750 875 1000 1125 1250 QUANTITY (Thousands of pounds) Demand Because you know that competitive firms earn Supply (10 firms) True Supply (15 firms) If there were 10 firms in this market, the short-run equilibrium price of rhodium would be $ would . Therefore, in the long run, firms would False Supply (20 firms) per pound. From the graph, you can see that this means there will be ? per pound. At that price,…
- Suppose the iceberg lettuce industry is a Cournot duopoly with two firms: Xtra Leafy (a) and Yummy Farms (y). Xtra Leafy produces q units of output and Yummy Farms produces qy units of output. Aggregate market output is Q = x + y. The (inverse) market demand schedule is: p = 176 - 2Q Both firms have identical cost structures: MC = MC₁ = ATC₂ = ATC₁ = $12 Find Xtra Leafy's Cournot reaction function of the form: 9x = a + bay Where "a" is the reaction function's intercept and "b" is its slope. Note: Please review the formatting instructions above. If any value is negative, be sure to include its negative sign. a. a= b. b = Hint: One of your answers will be negative. Think about why.Additional Problem 3: Assume two companies (C and D) are Cournot duopolists that produce identical products. Demand for the products is given by the following linear demand function: ? = 600 − ?C − ?D where ?C and ?D are the quantities sold by the respective firms and P is the price. Total cost functions for the two companies are ??C= 25,000 +100?C 2 ??D = 20,000 + 125?D c. Determine the equilibrium price and quantities sold by each firm. d.Determine the profits for the market as well as eachfirm.Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function:P=1000−QC−QDwhere QC and QD are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCC=15,000+50QC TCD=10,000+75QD Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change). Please, find the equilibrium output of firm C.
- If each firm acts to maximize its profits, taking its rival’s output as given (i.e., the firmsbehave as Cournot oligopolists), what will be the equilibrium quantities selected by each firm?What is the total output, and what is the market price? What are the profits for each firm?(I) Duopoly with homogeneous product: quantity and price competition Consider a market with two firms (firms 1 and 2). The (inverse) demand curve is: p = 30 - 2q where q= q1 + q2 Suppose Firm 1 has a marginal cost (c1) of 6 and Firm 2 has a marginal cost (c2) of 12. Assume neither firm has a fixed cost. (1) Suppose firms choose quantities sequentially: Firm 1 chooses q and after that decision is known Firm 2 chooses q2. Calculate the SPNE. (2) Suppose firms choose prices sequentially: Firm 2 chooses its price first and after that decision is known Firm 1 chooses its price. What is the SPNE? Justify.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?
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