Suppose the demand for a product is P = 150-Q and that the marginal cost of producing the product is $30. If two firms were initially competing in a Cournot oligopoly and then try to collude to maximize joint profits, what is the profit that firm 1 would actually get, given its best response function, assuming that firm 2 is producing the colluding quantity? (Hint: think about the "cheating" outcome)
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- 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 BSuppose 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 16000What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q= 1,800 - 1,000p. and each firm's marginal cost is $0.28 per unit? The Cournot-Nash equilibrium occurs where q, equals and 92 equals (Enter numenic responses using real numbers rounded to two decimai places.) Furthermore, the equilibrium occurs at a price of $ (Round your answer to the nearest penny.)
- Two firms in a Cournat oligpoly each have the best response function, such that the optimal quantity for each individual firm to produce must satisfy the equation: Q-27-Q/2 What quantity Q will each firm produce in the market? Type your answer...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…If firm 1 and firm 2 are the oligopolistic firms in bottled spring water production in Nomansland. The market demand is given by ? = 5000 −20?, Qd is the number of kilolitres demanded per month while P is the price of kilolitres of bottled water. The marginal cost of a kilolitre of bottled water is R10.How do I Find the Cournot equilibrium quantities and price? and how do I Find the Cournot profits and the monopolist profits?
- Try the analysis with an n-firm Cournot oligopoly in which one firm innovates to reduce cost from c to c/2. For this problem, assume n = 2, and use the demand and cost numbers used in the lecture. That is, let inverse market demand be given by P = 100 - Q, and let marginal cost be constant at 50 per unit before the innovation, and 25 per unit after the innovation. (a) Compute what the duopolist stands to gain from innovating. How does it compare to the perfectly competitive firm and to the monopolist? (b) What can you conclude about the relationship between concentration and innovationOnce more, please consider a market with eight producers that produce a total of 30,000 units. Their output is broken down below: Firm's Firm Output One 7400 Two 1800 Three 4100 Four 5200 Five 1400 Six 2800 Seven 6600 Eight 700 According to our lecture, this industry likely to be an oligopoly because is not; a small number of firms produce a large amount of the output O is; a small number of firms produce a large amount of the output O is not; production is spread out among relatively many firms is; production is spread out among relatively many firmsConsider a Cournot oligopoly with n = 2 firms. Firm 1 cost function is TC₁ (9₁) = 20 + 12q₁ + q², while firm 2 cost function is TC₂ (9₂) = 50 +8q2 + q2 . The total market demand is P(Q) = 50 — 2Q, where Q is the total quantity produced by all (active) firms in the industry. a- Compute the Cournot equilibrium total quantity, price, quantity for each firm, and profit for each firm. Which firm is making higher profits? b- Consider the situation in which a third firm (firm 3) enters the market. What is the total equilibrium quantity, price, quantity and profit for each firm if TC3 = TC₁? [hint: q₁ and q3 will be the same, since 1 and 3 are identical] c- How would your answer at point b change if instead TC3 = TC₂? Would consumers prefer firm 3 to enter with the total cost of firm 1 or firm 2? d- What would be the highest one-time cost that firm 3 would be willing to pay to enter the market and then compete in a Cournot game with total cost equal to firm 1?
- 4. Consider a Cournot Oligopoly with two firms, where firm 1 is twice as efficient as firm 2. In particular, firm l's cost function is c1(q1) = q1, while firm 2's cost function is e2(q2) = 2q2. The inverse market demand function is given by P = 100 – 5(q1 +92). (a) Find the firms' reaction (best response) functions. (b) Find the firms' equilibrium output levels and their profits. Does firm 1 make twice the profit of firm 2?Suppose the airline industry consisted of only two firms: American and Texas Air Corp. Let the two firms have identical cost functions, C(q) - 40g Assume that the demand curve for the industry is given by P= 190 -Q and that each firm expects the other to behave as a Cournot compedtor. Calculate the Coumot-Nash equilibrium for each firm, assuming that each chooses the output level that maximizes as profes when taking its rival's output as given. What are the profits of each firm? (Round all quantities and dollar amounts to two decimal places) When competing, each firm will produce units of output. In tum, each firm will earn profit of $. What would be the equilibrium quantity if Texas Air had constant marginal and average costs of $10 and American had corntant marginal and average costs of S407 It Texas Air had constant marginal and average costs of $10 and American had constant marginal and average costs of S40, American would produceunits and Texas Air Corp. would produce units. In…The inverse demand function in a market is given by P = 500- Q. The fırms that operate in this market have zero fixed costs, and constant marginal costs equal to MC = 2O. %3D