24. Under Cournot duopoly, two firms (A and B) produce the entire output of a particularhomogenous good. Both firms know the market demand curve is given by P = 250 -2Q, where Q is the sum of total industry output. Firm outputs are denoted by A and B.Both firms face the same costs: there are no fixed costs and marginal cost is 10 per unitfor all levels of output.(a) Explain what is meant by a 'best response' function in this context. Mathematicallyderive the best response functions for each firm.(b) Sketch both best response functions on a diagram and explain the significance of theintersection of these two best response functions.(c) Find the Nash equilibrium in quantities for this duopoly market. What are Q and P inthis Nash equilibrium? (d) Suppose the two firms were now to collude and act as a monopoly in order tomaximize their joint profits. What price and quantity would be observed? How dothe levels of consumer and producer surplus in this situation compare with thoselevels under the Cournot equilibrium?

Cournot competition is an economic model in which competing firms choose a quantity to produce…

Answered: 24. Under Cournot duopoly, two firms (A…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

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12. Two firms with differentiated products are competing in price. Firm A and B face the following demand curves: QA = 90 – 2PĄ + Pg and QB = 140 – 2Pg + PA respectively. Assume production is costless. a. Give equations for and graph each firm's reaction curve. b. If both firms set their prices at the same time, what is the Nash equilibrium price, quantity, and profit for each firm? c. Suppose A sets its price first and then B responds. What price and quantity does each firm set now? Is it advantageous to move first? d. Compare the profits from part b and c. Which firm benefits more from the sequential price choosing?
3. Two identical firms compete as a Cournot duopoly. The demand they face is P = 100 - 2Q. The cost function for each firm is C(Q) = 4Q. The equilibrium output of each firm is: a) 8 b) 16 c) 32 d) 36 How do I .solve this in detailed steps?
1. Best responses in a Cournot Oligopoly Firm A and Firm B sell identical goods Total market demand for the good is: The inverse demand function is therefore 1 P(QM) = 780 -Q=780 -0.02222QM 45 QM is total market production (i.e., combined production of firm's A and B. That is: Q(P) = 35, 100- 45P 2M = A +QB As a result, the inverse demand curve for each firm is: P(QA, QB) = 780- -1/32₁-752 45 Unlike the example in class, the two firms have different costs. = 4000A TCA (QA) TCB (QB) = 260QB = 780 -0.022220A -0.02222QB a. Using the demand function and the cost functions above, what is firm A's profit function. b. Using the profit function above and assuming that firm B produces Qg, calculate what firm A's best response is to firm B’s decision to produce QB- Note: Firm A's best response should be a function of B
QUESTION 1A) Two cournot competitors face inverse demand P = 50 - Q. Where, Q = q1+q2, is the total output of firms 1 and 2. What are the equilibrium output levels for q1 and q2, If firm 1 marginal cost is 1, and firm 2's marginal cost is 12? QUESTION 1B. Continuing with the inverse demand, P = 50 - Q, if each firm has a marginal cost of 0, what is the difference between the equilibrium price under Cournot competition and under Bertrand competition? b. C. d. a. The Cournot price is higher than the Bertrand price by 50. The Cournot price is lower than the Bertrand price by 25. The Cournot price is higher than the Bertrand price by 50/3. Equilibrium prices under Cournot and Bertrand are the same, so the difference is zero.
21. 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
Question 25 Consider two cigarette companies, PM Inc. and Brown Inc. If neither company advertises, the two companies split the market and earn $60 million each. If they both advertise, they again split the market, but profits are lower by $20 million since each company must bear the cost of advertising. Yet, if one company advertises while the other does not, the one that advertises attracts customers from the other. In this case, the company that advertises earns $70 million while the company that does not advertise earns only $30 million. What will these two companies do if they behave as individual profit maximizers? Both companies will advertise. Brown Inc. earns $40. Neither company will advertise. Brown Inc. earns $60. Both companies will advertise. PM Inc. earns $60. One company will advertise, and the other will not. Brown Inc. earns $70.
6. Two firms, Firm 1 and Firm 2 and are engaged in Cournot competition. The inverse demand they are facing is given by p = 50-q, with p being the price of the good, and q being total quantity demanded, given by q = 91 +92, where 9₁ and 92 are the productions of firm 1 and 2 respectively. The total cost of firm 1 is TC1(91) = q and of firm 2 is TC₂ (92) = 292. (a) Find the Cournot equilibrium and the price that corresponds to it. (b) Find the Lerner Index of each firm.
6. Two identical firms that have the cost function C(q) = 4qj, where j = {1,2} are competing in a homogenous good market. The two firms make simultaneous decisions on price, and they face industry demand Q(P) = 20-p. What is the Bertrand-Nash equilibrium profit of each firm? Hints for (b) and (c): Solve for each firm j's output (q;) and use the fact that II; = p;q; - C;(qj). b. Now, suppose the two firms are deciding whether to set a collusive market price of $6 (this means that they would both charge $6). Solve for their profits under this pricing scheme. a. C. d. e. If one of the firms decides to deviate from the collusive scheme and undercut its rival's price by $1, how much profit would it earn? Reproduce and then fill in the table below using your findings from parts (a)-(c). Firm 1 Collude Compete Collude ποι ποι dev, fol Firm 2 Compete oldev Bert., Bert. *col and Bert. are the collusive and Bertrand profit levels, respectively. dev is the profit level of a firm when it undercuts…
bok rint An oligopoly producing a homogeneous product is comprised of three firms that act like a cartel. Assume that these three firms have identical cost schedules. Assume also that if any one of these firms sets a price for the product, the other two firms charge the same price. As long as they all charge the same price they will share the market equally; and the quantity demanded of each will be the same. Below is the total-cost schedule of one of these firms and the demand schedule that confronts it when the other firms charge the same price as this firm. Complete the marginal-cost and marginal- revenue schedules facing the firm. erences Mc Graw Hill Output Total cost Marginal cost Price Quantity demanded Marginal revenue 0 1 23456 7 8 $0 180 300 480 720 1,020 1,380 1,800 2,280 Short Anewor LA JUL 26 $780 720 660 600 540 480 420 360 Toolbar navigation (a) What price would be charged, what output would be produced, and what profit would be made by this firm? (b) If the firms…
Please solve D and E part only. Thankyou. Consider three firms, each with cost function C(qi)=4qi, currently competing Cournot. Market demand is P = 20 – Q. a. a. Find the quantities, price, and profits of each firm in equilibrium. b. Imagine firms1 and 2 merged to become one, so after the merger there are now two firms left in the market, firm 1&2 and firm 3. Assume there are no cost efficiencies expected and assume that the two firms play Cournot as before. Find the quantities, price, and profits of each firm in equilibrium c. Was it profitable for firms 1 and 2 to merge in the first place? d. Continuing with b., imagine that firms did not play Cournot after the merger, but rather that the merged firm 1&2 became a Stackelberg leader after the merger and firm 3 became the Stackelberg follower. If this were the case, find the quantities, price, and profits of each firm in equilibrium. e. Was it profitable for firms 1 and 2 to merge in the first place? Did price…
Question 4 Consider a duopoly market with 2 firms. Aggregate demand in this market is given by 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 MCi = 20, i=A,B. Assume the firms compete a la Cournot.Note that marginal revenue for both firms is given by MRA=500-2QA-QB, MRB=500-QA-2QB. Describe what a best-response curve is and how to find it. Derive the best-response function for each firm. What are the equilibrium quantities? What is the total quantity supplied on this market? What is the equilibrium price in this market?
Suppose that two firms are Cournot competitors. Industry demand is given by: P = 200 – Q, where Q is the combined output of the two firms. If both Firm 1 and Firm 2 face constant marginal and average total costs of $20: a. Solve for the Cournot price, quantity, and firm profits. b. Suppose that Firm 1 is considering investing in costly technology that will enable it to reduce its costs to $14 per unit. How would this change the equilibrium values you found in part a? How much should Firm 1 be willing to pay if such an investment can guarantee that Firm 2 will not be able to acquire it? c. If Firm 2 tries to counteract Firm 1's new technology by changing this game to Stackelberg Competition in which they (Firm 2) moves first (after Firm 1 adopts their new technology), what will be the new equilibrium values of price, quantity and firm profits? Will this strategy work for Firm 2?

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