Consider a Cournot model of a market with of two firms with differentiated products. Firm 1 has Cournot best response function qi(q2) = (150-3q2)/10 and has constant marginal cost of 100. Firm 2 has Cournot best response function q2(q) = (100-2q1)/3 and has constant marginal cost of 50. What are the firms' marginal revenue functions? 20. Firm I's Cournot equilibrium output level is 21. Firm l's Cournot equilibrium output level is
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- 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…Suppose that Raleigh and Dawes are the only sellers of bicycles in the UK. The inverse market demand function for bicycles is ?(?)=200−2?. Both firms have the same total cost function: ??(?)=12? and the same marginal cost: ??(?)=12.Suppose this market is a Stackelberg oligopoly and Raleigh is the first mover.a) Write down a formula for the reaction function of Dawes.b) Calculate the equilibrium quantity that each firm produces and the equilibrium price in the market.c) At the Stackelberg equilibrium, how much profit does each firm make?Suppose now that the two firms decide to act like a single monopolist.a) What will the total quantity of bicycles sold in the market be and what will the equilibrium price be? Represent the profit maximisation problem on a graph and indicate the price and quantity at the equilibrium.b) Calculate the total profit made by the two firms when they act like a monopoly. Compare it with the total profit they were making in the Stackelberg oligopoly.c) For the…Suppose that Raleigh and Dawes are the only sellers of bicycles in the UK. The inverse market demand function for bicycles is P(Y)=200-2Y. Both firms have the same total cost function: TC(Y)=12Y and the same marginal cost: MC(Y)=12. Suppose this market is a Stackelberg oligopoly, and Raleigh is the first mover. Write down a formula for the reaction function of Dawes. Calculate the equilibrium quantity that each firm produces and the equilibrium price in the market. Give typing answer with explanation and conclusion
- Ugly Dolls Inc. (UD) is a firm in Mytown that sells its products on a market under monopolistic competition. The cost function of UD is represented by TC = 100+10Q. Lately, because of the UD is making a big amount of profit, some firms enter the market to compete. Assume that Mytown engages in free trade in the dolls markets with Yourtown, who also faces a market with monopolistic competition. Because of this we can expect that, (a) The numbers of firms operating in this market will not change. (b) At equilibrium the profit of firms will increase. (c) The quantity of types of dolls available to consumers will increase. (d) All the above answers are correct.Q4. Consider two firms competing in a Cournot fashion. Each firm has MC=10 and the market demand is given by P=100-Q, where Q is the total market output. What is firm 1's Response function? a. q1=45-.5q2 b. q1=30 c. q2=45-.5q1 d. firm 1 will set p=MCBonus question Competition à la Cournot with homogenous goods and asymmetric incomplete information. Consider a duopoly that competes à la Cournot (choosing quantities simultane- ously), facing inverse demand function p(Q) = a – Q where Q = q1 + 92, where the cost function for firm 1 is c1 (91) = cqı with c > 0 which is common knowledge for both firms. The cost function for firm 2 is not common knowledge and can be c2(42) = Cí42 with probability 0 € (0, 1) or c2(92) = CL92 with probability 1- 0, where CL < CH- The notation Cz means low cost and CH means high cost. Firm 2 can be a new entrant to the industry, or could have just invented a new technology. Firm 2 knows its marginal cost which means it has private information since it know if it is Cz or CH. Firm 1 on the other hand does not know the marginal cost of firm 2 (we don't either) and therefore it has less information than firm 2 and therefore constitutes asymmetric information. Firm 2 may want to choose a different (presumably…
- 1. Return to our Cournot competition model with two firms. Suppose now that the products aren't quite identical. In fact, both firms face different demand functions, a – b(q1 + dq2) a – b(dqn + 42) Pi = P2 = where d is some umber between 0 and 1 that specifies how similar the products are. Everything else about the model remains the same. (a) Calculate the best response functions for each firm. How does the slope of those best responses change with d? What happens when d = 0 or d = 1? (b) Calculate the equilibrium prices and quantities in this market. (Note: the firms are not identical).There are two firms that are producing identical goods in a market characterized by 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 cost are 0. Answer the following question, assuming that the firms are Cournot competitors. a. Calculate each firm's reaction function and illustrate them graphically (15 points) b. How much output does each firm produce? (12.5 points) c. What is the market price? (7.5 points) d. How much profit does each firm earn? What is the industry profit? (10 points)Reference the following information about the market demand function for questions 1 to 15. These questions are on different types of market structures – monopoly, perfect competition, Cournot oligopoly market, and the Stackelberg oligopoly market. The market demand function is given the following equation: P = 2000 – Q where Q is the industry’s output level. Suppose initially this market is served by a single firm. Let the total cost function of this firm be given the function C(Q) = 200Q. The firm’s marginal cost of production (MC) is equal to the firm’s average cost (AC): MC = AC = 200. What is the difference in the industry output levels produced by the perfectly competitive industry (Qc) and the monopoly (Qm) industry? Group of answer choices Qc - Qm = 900 units Qc - Qm = 1800 units Qc - Qm = - 900 units Qc - Qm = 600 units
- You are given the market demand function Q = 1500-1000p, and that each duopoly firm's marginal cost is $0.20 per unit, which implies the cost function: C(qi) = 0.20qi, assuming no fixed costs for i = 1, 2. The cooperative Cournot quantities are q₁ and 92 = The cooperative Cournot price is $ (round to the nearest penny). Calculate the cooperative Cournot profits: firm 1 $ and firm 2 $ (enter your responses as whole numbers). (round both responses to the nearest cent).The inverse market demand curve for salmon is given by P(Y) = 100 – 2Y, and the total cost function for any firm in the industry is given by TC(y) = 4y. a. Suppose that two Cournot firms operated in the market. What would be the reaction function for Firm 1 and the reaction function of Firm 2? (Notes: The marginal cost is not zero). If the firms were operating at the Cournot equilibrium point, what would the industry output and price be? b. For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the graphTwo 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...