1. Consider a market with three firms (i = 1, 2, 3), which have identical marginal costs c = c2 = C3 = 0. The inverse demand function is given by p =1- Q, where Q = 91 + 92 + q3. a. Compute the Cournot equilibrium, i.e., the market price and quantity. b. Assume that two of the three firms merge. Show that the profit of merging firms decreases. c. What happens to the market price if all three firms merge compared to part (a)?
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- Question 3 The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has al cost of production of C₁= 15*Q₁ and firm 2 has a cost of production of C₂=20*Q₂. 1) Suppose firm 1 and firm 2 compute simultaneously in quantities. What are the Cournot quantities and prices? What are the profits of firm 1 and 2? 2) Suppose firm 1 and firm 2 compete simultaneously in prices. What are the Bertrand quantities and prices? What are the profits of firm 1 and 2? 3) Suppose that firm play a Stackelberg game. First firm 1 sets the quantity in t=1, then, knowing which quantity firm 1 has set, firm 2 chooses the quantity in t=2. What are the Stackelberg quantities and prices? What are the profits od firm 1 and 2? Compared to part a) which firm benefits and which firm loses?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…Consider an industry with two firms, each of which has a constant marginal cost of 20. The inverse demand facing this industry is P(Y) = 220 −Y, where Y = y1 + y2 is the total output. 1. What is the competitive level of output? (Recall: price equals marginal cost at the competitive equilibrium.) 2. What is the output of each firm in the Cournot equilibrium? 3. What is the output of each firm in the Stackelberg equilibrium when firm 1 is the follower and firm 2 is the leader?
- The diagram below shows the demand, marginal revenue, and marginal cost of a monopolist. 120 110- 100- 90- A 80- 70 60- 50- 40- 30- 20 10 O @_ 0 1 2 3 16 4 Profit-maximizing output: Profit-maximizing price: $ 5 7 units MR 6 MC T 7 8 a. What price and output would prevail if this firm's product was sold by price-taking firms in a perfectly competitive market? 9 Quantity D T 10 11 (11, 0) 14 15 b. Determine the profit-maximizing output and price for the monoplist. Price: $ 68 Output: 5 units c. Calculate the deadweight loss of this monopoly.QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)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
- The marginal cost of a product is fixed at MC = 20. The demand for the product is Q = 100 - 2P. (a) Now consider a Cournot model with two firms that are choosing quantities simultaneously. What is the best reply (best response) function for each firm? What is theNash equilibrium? What is the total surplus? (b)What do you expect the total surplus would be with three firms? Why? (You do not need to calculate an exact value. You can say ”total surplus is at least 100”, or ”total surplus is at most 80”)Consider a market with the demand curve Q(P) = 3700– 100P. Two companies compete in Bertrand setting, where the first company has a marginal cost of $10 and a capacity of 100 units, and the second firm has a marginal cost of $20 and a capacity of 1000 units. Assume that fixed costs are zero. a) Show that both firms will sell in this market at a price above $20. b) Assume that the first firm is capacity constrained. From the perspective of the second firm, find the quantity sold in the market and the price set by the second firm. c) Now, using the result from the previous part, from the perspective of the first firm, find the quantity sold in the market and the respective price set by the first firm.Economics 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. Now suppose the two firms engage in Stackelberg market competition. Assume firm 1 is the leader (first-mover) and firm 2 is the follower firm (second-mover). Marginal profit function of Stackelberg leader: 900−Q1 QUESTION 14: What will be the market price in this Stackelberg model? Group of answer choices $480 $650 $720 $900 QUESTION 15: Can you calculate the profit earned by the…
- Consider the Cournot competition between two firms with different marginal costs. For firm 1, let the cost function be: C1(q1)-3*q1 For firm 2, let the cost function be: C2(q2)-6*q2 The inverse demand function is: P(Q)=12-Q, where Q=q1+q2 In this game, write down the profit functions for firm 1 and firm 2 (as functions of q1 and q2). Then, find the Nash equilibrium quantities for firm 1 and firm 2. In the NE, which firm produces more: the one with the low or the high marginal cost? Note: To get credit, you need to show your calculations and explain your answer.Two firms - firm 1 and firm 2 - share a market for a specific product. Both have zero marginal cost. They compete in the manner of Bertrand and the market demand for the product is given by: q = 20 − min{p1, p2}. 1. What are the equilibrium prices and profits? 2. Suppose the two firms have signed a collusion contract, that is, they agree to set the same price and share the market equally. What is the price they would set and what would be their profits? For the following parts, suppose the Bertrand game is played for infinitely many times with discount factor for both firms δ ∈ [0, 1). 3. Let both players adopt the following strategy: start with collusion; maintain the collusive price as long as no one has ever deviated before; otherwise set the Bertrand price. What is the minimum value of δ for which this is a SPNE. 4. Suppose the policy maker has imposed a price floor p = 4, that is, neither firm is allowed to set a price below $4. How does your answer to part 3 change? Is it now…C2) Consider an industry with only two firms: firm A and firm B. The industry's inverse demand is P(Q) = 400 - ¹1/Q, 10 where P is the market price and Q is the total industry output. Each firm has a marginal cost of $10. There are no fixed costs and no barriers to exit the market. a) 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 NEA and NEB for each firm. marks] b) Suppose the two firms engage in Stackelberg competition, with firm A moving first, and firm B moving second. Find the equilibrium price PS in the industry, the equilibrium outputs QS and QBS, as well as the profits π and TSB for each firm. в c) For this subquestion only, suppose that firm B has a fixed cost of $200 000: What will firm B's optimal decision be, and what will be the resulting market structure? Now assume that instead of having two firms in the market, we have a monopoly facing the inverse…