Consider an industry that consists of 3 tirms facing a demand curve P = 80 - Q. All three firms have constant marginal costs and zero fixed costs. The marginal cost for firms 1 and 2 is $10, while the marginal cost for firm 3 is $20. Find the Cournot equilibrium quantities assuming that firms 2 and 3 merge. b. Calculate the equilibrium market quantity and price. Calculate the equilibrium profit for each firm,
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- 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 abovea) Suppose that the two firms engage in Cournot competition. Find the equilibrium price PNE in the industry, the equilibrium outputs QANE and QBNE, as well as the profits πANE and πBNE, for each firm. b) Suppose the marginal cost for firm B increases from $20 to $140, while everything else remains unchanged. Find the new equilibrium price PNE in the industry, the new equilibrium outputs QANE and QBNE, as well as the new profits πANE and πBNE for each firm. c) Suppose that, in addition to the marginal cost increase from $20 to $140 from sub question b), firm B also has a fixed cost of $2500, out of which $2100 may be recouped if it shuts down; everything else remains unchanged. In this case, what will firm B’s optimal output be? (Justify your answer.) What will firm A’s profit be?Two Cournot competitors face inverse demand p = 50-Q, where Q = 9₁ +92 is the total output of firms 1 and 2. Both firms have marginal cost of 2. What are the equilibrium output levels q₁ and 92? 16 and 16 25 and 25 20 and 9 36 and 3
- 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.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…1. if the total cost function for this market is TC = 500 + 10Q2 , calculate the total and marginal costs for each of the quantities in the table. what is the demand function for this market? 2. What are the profit-maximizing quantity, price, and profit for this market? 3. If there are two firms Atlas and Bowden in this market with the same earlier total cost function and they engage in Cournot competition, what is each firm's equilibrium quantity, price, and profit? [NB: round quantities to nearest integer to find equilibrium quantity, price, and profit]
- 8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output, 1.e. Qq1 +42. The inverse demand curve in the market is given by P-15-Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) If the firms could collude, what would be the total output in the mar- ket? Assuming each firm produces half of the collusive output, what is the profit of each firm?Explain in few lines Three firms are competing through prices (Bertrand competition). They are all selling the same products. The only difference is that the first two firms have a constant marginal cost equal to 2 while the third firm has a constant marginal cost equal to 5. In equilibrium the two firms with lower marginal cost will set their price just slightly below 51. marginal costs e, = c, = c, = 20. The inverse demand function is given by P = 100 - Q. where Q = q, + 4: + 93- Consider a market with three firms (i - 1, 2, 3). which have identical a) Identify the reaction functions for each firm and compute the Cournot equilibrium, i.e., the market price and quantity. b) What happens to the market price if all three firms merge compared to part (a)?
- Suppose that there are two firms in an industry and they face market demand y=400-0.5p where y=y1+y2 . The total cost functions of the firms are C1(y1)= 40y1 and C2(y2)= 2y22. a) Assume initially that the firms enter into Cournot competition. Calculate the equilibrium market price and each firm’s equilibrium output. That is, find y1c, y2sand pc.b) Calculate the equilibrium market price and each firm’s equilibrium output assuming that firm 2 is the Stackelberg leader and firm 1 is the follower. That is, find y1s, y2sand ps.Assume firms' marginal and average costs are constant and equal to c and that inverse market demand is given by P = a - bQ where a, b > 0. Suppose now the market is served by k firms that choose quantities for their identical products simultaneously. Calculate: i. ii. iii. iv. The Nash equilibrium quantities for the Cournot firms as functions of k. 2 Market output and price as a function of k Firm profit as a function of k Using your answers in i, ii, iii and iv, describe what happen to firm output, market output, market price and firm profit as the number of firms increases.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…