Consider an industry with 6 identical firms, each facing a demand Q = 30,000 x [1/6 - 1/20 (p - p)], where Q is the output level by the firm, p is the price charged by the firm and p is the average price in the industry. Suppose each firm has a fixed cost 7500 and a marginal cost 35. What is p in a symmetric equilibrium when there is no entry or exit of any firm? (Round your answer to the nearest integer.) Your Answer:
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- Firm 1 and firm 2 are Bertrand duopoloists. Firm 1 has a marginal cost of $6.00 per unit, and firm 2 has a marginal cost of $8.01 per unit. The demand for their product is p=23.00−Q, where Q is the total quantity demanded. How much does each firm sell in equilibrium? Assume that prices can only be set to the nearest cent, firms split the market if they set the same price, and there are no fixed costs. Firm 1 production:______ Firm 2 production:______ What are the profits for each firm in equilibrium? Firm 1 profit: $______ Firm 2 profit: $______suppose there are two firms that compete in prices, say firms 1 and 2, but that the firms produce differentiated products. Suppose that the demand for firm 1 is q1(p1,p2)=10-2p1+p2 and the demand for firm 2 is q2(p2,p1)=10-2p2+p1. Also, assume that firm 1 has a constant marginal cost of c1 = 2 and firm 2 has a constant marginal cost of c2 = 3. i. Solve for the Bertrand equilibrium in prices. ii. Now, suppose firms 1 and 2 merge and firm 1 will operate both firms and they will split the resulting profits equally. Will both firms agree to this merger or do they prefer the Bertrand outcome?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.
- Firms 1 and 2 produce a homogeneous product in the market, with market demand dQ=200-p. Each firm i ci=1,2) has the cost function C CQ₂) = 40 +20- Q₂, where Qt is firm i's output. (a). what is the Cournot equilibrium output per firm and price in this market? You (b). What would the equilibrium price in this market be if the two firms collude to 9291 Set outputs to maximize total industry profits? (C). Suppose firm I is the leader and chooses output first, while firm 2 is the follower and sets output af after observing firm I's output. What would be the Noutputs and price in the S Stackelberg equilibrium?4. In 2056, there are two mining firms operating on the moon, extracting Helium 3. Once both firms have entered the market, they compete a la Cournot. The market inverse demand function is given by P(Q) = 8 - Q. Assume that both firms have the total cost functions C(q) =2+2q. Let the star superscript* denote equilibrium quantities/prices/profits. Which of the following statements is true? (a) q₁ =q2 = 4 (b) qt > 92 (c) p* = 6 (d) π₁ < π₂ (e) T₁ = π = 2 the C2.- Each of two firms, firms 1 and 2, has a cost function C(q) = 1 2 q; 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 = 1 2. (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…
- Suppose a market is served by two firms (a duopoly) The market demand function given by P = 1200 - O_{1} - O_{2} where is the output produced by firm 1 and is the output produced by firm 2 Q_{1}*Q_{2} Firm I's cost of production is given by the function C(Q_{1}) = 120Q_{1} and firm 2's cost of production is given by the function C(Q_{2}) = 120Q_{2} The average cost of firm is given by A*C_{1} = 120 and the average cost of firm 2 is given by A*C_{2} = 120 Marginal profit function for firm 1 (d*pi_{1})/(Delta*Q_{1}) = 1080 - 2Q_{1} - Q_{2} Marginal profit function for firm 2 (Delta*pi_{2})/(Delta*Q_{2}) = 1080 - Q_{1} - 2Q_{2} What will be the equilibrium profit levels earned by the stackelberg leader firm and the stackelberg follower firm?Q3. There are two firms selling differentiated products. Firm A faces the following demand for his product: e, = 20 – -P, + -P, 2. Firm B faces the following demand: 1 P. +-P, 2. 0, = 220- Assume that the marginal cost is zero both for firm A and firm B. What are the equilibrium prices of a simultaneous price competition? What would the equilibrium prices be if A is the leader and B is the follower?Suppose we have two identical firms A and B, selling identical products. They are the only firms in the market and compete by choosing quantities at the same time. The Market demand curve is given by P=477-Q. The only cost is a constant marginal cost of $16. Suppose Firm A produces a quantity of 66 and Firm B produces a quantity of 49. If Firm A decides to increase its quantity by 1 unit while Firm B continues to produce the same 49 units, what is the Marginal Revenue for Firm A from this extra unit? Enter a number only, no $ sign. Don't forget to include the negative sign if revenue decreases.
- = Suppose the inverse demand for a particular good is given by P 1200 12Q. Furthermore, there are only two firms, A and B. Firm A's marginal cost is a constant $25, and Firm B's marginal cost is a constant $20. Assume these two firms engage in Stackelberg competition, where Firm A moves first. If we assume that the firm with the lowest costs could supply the entire market, then the deadweight loss due to the market power these two firms exert through Stackelberg competition equals $_____. [Round your answer to two decimals.]Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively isPROBLEM (5) In a dominant firm market with demand Q = 30 − p, the dominant firm has MC(Q) = 2Q (that is, with TC(Q) = Q^2) and the fringe is composed of 5 identical firms, each with MC(Q) = 10Q (that is, with TC(Q) = 5Q^2). (a) Calculate the market price in the dominant firm model. Calculate the quantity produced by the fringe. (b) Now assume that the 5 fringe firms form a “union”, and act as 5 “plants” of the union firm and this union firm competes as one single firm against the dominant firm in quantities, as in Cournot competition. What is the Cournot-Nash equilibrium price and quantity in this market organization? (c) Now, the dominant firm convinces the “union” not to compete with it but instead collude (to maximize the sum of profits) to form a cartel. What is the market price and quantity? (d) Back to the problem description. If all the firms (the dominant firm and the 5 fringe firms) acted as price takers, as in the perfect competition, what would be the market equilibrium…