QUESTION 3 An industry consists of three firms with identical costs C(q) = 18q + q 2. Market demand is Q = 150 – p. What is the industry Cournot equilibrium if firms 1 and 2 merge (to jointly produce output q12)? 912=36; q3=24; p=90 O 912=32; q3=28; p=60 O 912=93=20; p=80 O 912=25; q3=22; p=48
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- 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…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”)The Able Manufacturing Company and Better Bettors, Inc. are rival firms in the production of a calculator used by horse racing fans for handicapping (determining betting strategies). Each firm has a fixed cost of $100 and a MC = $10 in producing calculators. The demand for the industry’s product is: Q = 900 – 5P, where P is the market price and Q = Q1 + Q2. If each firm must choose how many calculators to produce and sell without knowing of its rival’s production decision, what will be the Cournot equilibrium price and quantities produced? Calculate the profit for each firm.
- Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. Suppose that the firms compete by simultaneously setting price, not simultaneously setting output. That is, suppose we consider the Bertrand model instead of the Cournot. Show that the two firms must earn lower profits. Hint: Create a two-by-two game using two different prices for each firm. One price should be the Cournot price (the Cournot is price of the good when firms produce the Cournot output you found above, which is 100 and 100, so the price is P = 400 − 100 − 100 = 200). The second price should be under 200 and over 150. Then show that the Nash equilibrium of this game is the lower of the two prices. When calculating profits, assume that each firm has equal sales (one half of demand) if they charge…Two firms produce differentiated products. Firm 1 faces the demand curve Q1 = 75 -P1 + .5P2. (Note that a lower competing price robs the firm of some, but not all, sales. Thus, price competition is not as extreme as in the Bertrand model.) Firm 2 faces the analogous demand curve Q2 = 75 -P2 +.5P1. For each firm, AC =MC = 30. suppose that firm 2 acts as a price leader and can commit in advance to setting its price once and for all. In turn, firm 1 will react to firm 2’s price, according to the profit-maximizing response found earlier, P1 = 52.5 + .25P2. In committing to a price, firm 2 is contemplating either a price increase to P2 = $73 or a price cut to P2 =$67. Which price constitutes firm 2’s optimal commitment strategy? Justify your answer and explain why it makes sense.You are the manager in a market composed of eight firms, each of which has a 12.5 percent market share. In addition, each firm has a strong financial position and is located within a 100-mile radius of its competitors.Instruction: Enter your responses rounded to the nearest penny (two decimal places).a. Calculate the premerger Herfindahl-Hirschman index (HHI) for this market.b. Suppose that any two of these firms merge. What is the postmerger HHI?c. Based only on the information contained in this question and on the U.S. Department of Justice Horizontal Merger Guidelines described in this chapter, do you think the Justice Department would attempt to block a merger between any two of the firms?multiple choice It likely will not. It may, but will likely consider other factors as well. It likely will.
- You are the manager of a firm that produces products X and Y at zero cost. You know that different types of consumers value your two products differently, but you are unable to identify these consumers individually at the time of the sale. In particular, you know there are three types of consumers (1,000 of each type) with the following valuations for the two products: Consumer Type Product X Product Y 1 $90 $60 2 70 140 3 40 160 a. What are your firm’s profits if you charge $40 for product X and $60 for product Y?$ b. What are your profits if you charge $90 for product X and $160 for product Y?$ c. What are your profits if you charge $150 for a bundle containing one unit of product X and one unit of product Y?$ d. What are your firm’s profits if you charge $210 for a bundle containing one unit of X and one unit of Y, but also sell the products individually at a price of $90 for product X and $160 for product Y?$Two firms, A and B, face an inverse market demand function of P = 1200 - 4Q. Each firm has the same cost function Ci = 20qi. Assume the A and B are Stackelberg competitors, and that A is the leader. Derive from profit functions the equilibrium prices, quantities, and profits for A and B. How does the methodology for solving the Stackelberg problem differ from the method for solving the Cournot problem? Why?The Hull Petroleum Company and Inverted V are retail gasoline franchises that compete in a local market to sell gasoline to consumers. Hull and Inverted V are located across the street from each other and can observe the prices posted on each other’s marquees. Demand for gasoline in this market is Q = 80 -9P, and both franchises obtain gasoline from their supplier at $2.75 per gallon. On the day that both franchises opened for business, each owner was observed changing the price of gasoline advertised on its marquee more than 10 times; the owner of Hull lowered its price to slightly undercut Inverted V’s price, and the owner of Inverted V lowered its advertised price to beat Hull’s price. Since then, prices appear to have stabilized. Under current conditions, how many gallons of gasoline are sold in the market, and at what price? Gallons sold: ? Price: $ ? How would prices differ if Hull had service attendants available to fill consumers’ tanks but Inverted V was only a self-service…
- You are the manager of a firm that produces products X and Y at zero cost. You know that different types of consumers value your two products differently, but you are unable to identify these consumers individually at the time of the sale. In particular, you know there are three types of consumers (1,000 of each type) with the following valuations for the two products: Consumer Type Product X Product Y 1 $90 $60 2 70 140 3 40 160 d. What are your firm’s profits if you charge $210 for a bundle containing one unit of X and one unit of Y, but also sell the products individually at a price of $90 for product X and $160 for product Y?Consider an inverse market demand P= 200 − 2Q. Suppose there are two firms in the market, firm 1 and 2 have constant marginal and average cost MC = AC= 20. Suppose that firm 1 is a Stackelberg leader, (i.e., it determines its output before firm 2.) Determine the Stackelberg equilibrium outputs and profits.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?