2. Two firms compete by setting quantities simultaneously (Cournot Competition) in a market where demand is described by p = 100 - 2(q₁ + 9₂). The marginal cost of production for Firm 1 and Firm 2 is $6 and $10 respectively. a. Derive the reaction function of each firm. b. Compute the Cournot equilibrium quantities. Note: answers may be fractions.
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- (Cournot competition with different marginal costs) Our best estimate for total marketdemand in a given market is P 1000-2Q. Two firms (1 and 2) are competing in this market in quantities, choosing Q1 and Q2 simultaneously. Firm 1 has marginalcost equal to c1 = 100 and Firm 2 produces at marginal cost c2 = 200. (a) Write down the profits of both firms and and their best response functions. (b) Find the Cournot - Nash equilibrium in quantities, and calculate equilibrium profits for both firms. (c) Suppose that each firm has the option, at a previous stage, to invest in an R&D project that will reduce its marginal cost of production by 50% if successful. What is the value of this innovation to each firm? Given that R&D costs and successprobabilities are equal, which one has greater incentives to invest in R&D ? You can think in terms of per - period profits to set aside timing issues.Consider a Cournot Oligopoly. One firm has costs C1(Q1) = 12Q1 while the other firm’s cost function is C2(Q2) = 10Q2. The demand for both firms’ products Q=Q1 +Q2 isQD(P)=200−2P. (a) Determine the equilibrium price P, the market shares s1, s2, and the quantities Q1, Q2 produced by both firms. (b) Suppose more firms with the lower cost technology, i.e., with cost function Ci(Qi) = 10Qi enter the market. How many firms with this technology must be in the market such that firm 1’s profit becomes negative. In other words, suppose there is one firm with the high costs, and n firms with the low costs. At what level n will profits of the high-cost firm be negative?Suppose the market demand for ECO textbooks at the University is given by ?=1000−2?Q=1000−2P. The Marginal Cost of a textbook is $50. Suppose there are only two textbook publishers, both printing the exact same textbook. They compete in a Cournot manner. Suppose each firm produces ?=450q=450. Is this an equilibrium? Explain your reasoning, show all the steps of your working clearly. Keep your responses short and precise. Under 250 words is a good rule of thumb.
- Consider the payoff matrix below representing two firms engaged in Bertrand Competition. Firm A is player 1 and Firm B is player 2. High price Low price High price 10, 12 -1, 13 Low price 12, 2 0, 3 What is Firm A's dominant strategy? Question 14Answer a. High price b. Low price c. Firm A does not have a dominant strategyTwo firms are competing in a Bertrand setting. The demand and costs equations are: Q1 = 88–4P1+2P2, Q2 = 88–4P2+2P1; MC1 = 9; and MC2 = 10. Instructions: Use no decimals. Do not round values if used for other calculations. d. Profits Firm 1 = $ and profits Firm 2 = $ e. If Firm 1 instead produces P1 = 16, the optimal P2 = . f. When one of the firms set a P < P-Duopoly, the best strategy for the other firm is to set: A. a P-BRF, and continue with this strategy afterward with the risk of economic profits = 0. B. a P-BRF, and after this one time, then continue with P-Duopoly. C. a P > P-Duopoly from now on, until the market reaches P-Monopoly. D. also P < P-Duopoly one time, then set P-Monopoly.Suppose two firms, Firm A and Firm B, are competing by setting quantities (Cournot competition). Firm A has a constant marginal cost of $10 per unit; Firm B has a constant marginal cost of $15 per unit. Assume fixed costs are equal to 0 for both firms. Hint: since fixed costs are zero and the marginal cost is constant, MC = AC. The two firms choose between producing 50 units or 100 units. If the total output is 100 units, the price is $20 per unit; if total output is 150 units, the price is $15 per unit; if total output is 200 units, the price is $10 per unit. Based on the information provided, fill in the firms’ profits in the payoff matrix below with Firm A choosing the row and Firm B choosing the column. QB=100 QB=50 QA=100 , , QA=50 , , The resulting equilibrium is for Firm A to produce ____ (50 or 100)units and Firm B to produce_____ (50 or 100) units.
- Two firms produce the samecommodity, both with zero cost. The demand for this commodity is D(P) = 100−P.The two firms can each produce at most 50 units. They compete on price andrationing is efficient: if pi < pj then the demand that j faces is Dj(p) = D(pj) − qi,where qi is the quantity supplied by firm i. That is, the lower price firm gets to sellfirst. Is the price list p = (p1, p2) = (0, 0) a Nash equilibrium? Prove your assertion.In a duopoly market firms face the market demand curve P=280-Q where Q=q1+q2. Each firm has a marginal cost of 40 taka per unit. What is the Cournot equilibrium?Two firms are producing identical goods in a market characterizedby the inverse demand curve P = 60 - 2Q, where Q is the sum of Firm 1's and Firm 2's output, q1 + q2. Each firm's marginal cost is constant at $12, and fixed costs are zero. Answer the following questions, assuming that the firms are Cournot competitors. In this case, the market price is $
- Two firms produce a homogeneous good and compete in price. Prices can only take integer values. The demand curve is Q = 6 p, where p denotes the lower of the two prices. The lower - priced firm meets all the market demand. If the two firms post the same price p, each one gets half the market demand at that price, i. e., each gets (6p)/2. Production cost is zero.a) Show that the best response to your rival posting a price of 6 is to post the monopoly price of 3. What is the best response against a rival's price of 4? of 5?Three firms, A, B and C engage in Bertrand price competition in a market with inverse demand given by P = 123 − 2Q. Whenever a firm undercuts the rivals’ price, it gets the entire demand. If firms charge the same lowest price in the market, they share the market. If a firm charges a price more than any rival, it has zero market share. Suppose there are no fixed costs, and the marginal costs of the firms are: c(A) = 91, c(B) = 83 and c(C) = 43. Find a Nash equilibrium of this game. What are each firm’s prices and profits? Explain solution. Suppose firm B leaves the market. Draw each firm’s best response on a diagram and find a Nash equilibrium of this duopoly game. Suppose the above game in part 2 between firms A and C was the stage game of an infinitely repeated game. Would it be possible for the two firms to collude or form a cartel in this case?An oligopoly firm faces a kinked demand curve with the two segments given by: P = 230 – 0.5Q and P = 280 – 1.5Q. The firm currently has a constant marginal cost, MC of $150. Calculate how much higher the marginal cost must be before the firms would change the profit-maximizing output and therefore the price.