Consider a differentiated products market with two Bertrand competitors. Firm’s 1 demand curve is given by Q1= 20 - P1 +P2 and firm’s 2 demand curve is given by Q2= 20 – P2 +P1. Firm 1’s marginal cost is £2 and firm 2’s marginal cost is £20. What is the equilibrium price of firm 1? a. 28 b. 14 c. 11 d. 34
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Consider a differentiated products market with two Bertrand competitors. Firm’s 1
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- 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.You are the manager of BlackSpot Computers, which competes directly with Condensed Computers to sell highpowered computers to businesses. From the two businesses’ perspectives, the two products are indistinguishable. The large investment required to build production facilities prohibits other firms from entering this market, and existing firms operate under the assumption that the rival will hold output constant. The inverse market demand for computers is P=5900-Q , and both firms produce at a marginal cost of $800 per computer. Currently, BlackSpot earns revenues of $4.25 million and profits (net of investment, R&D, and other fixed costs) of $890,000. The engineering department at BlackSpot has been steadily working on developing an assembly method that would dramatically reduce the marginal cost of producing these high-powered computers and has found a process that allows it to manufacture each computer at a marginal cost of $500. How will this technological advance impact your…You are the manager of Taurus Technologies (Firm 1), and your sole competitor is Spyder Technologies (Firm 2). The two firms’ products are viewed as identical by most consumers. The relevant cost functions are C(Q1) = 120 + 8Q1 and C(Q2) = 120 + 12Q2, and the market demand curve for this unique product is given by P = 160 – 2.5Q. Given this information, the profits for firm 1 are = $__. Give typing answer with explanation and conclusion
- PROBLEM (5) (In a market with demand Q = 780 - p, there are 3 identical firms, A, B and C; each with a total cost function TC(Q) = 3(Q)^2. Calculate the market price under each of the 2 scenarios below, (i) B and C jointly form the fringe supply and A is the dominant firm in the dominant firm model. ( ii) They act as perfectly competitive firms -as if trying to maximize total surplus and minimize DWL- that is, their joint MC serves as the “market supply” for the competitive market. Please answer all the parts!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 $160 for product Y?$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?
- 1 Consider two identical firms with a unit cost of production of $10 and a market demand of p= 60-y. (a) What is firm 1’s optimal output level as a function of firm 2’s output? (b) What is firm 2’s optimal output level as a function of firm 1’s output? (c) What is the Cournot equilibrium output level for these firms? (d) What is the Cournot equilibrium price level? Show your work step by step.Exercise 13.2. A homogeneous products duopoly faces a market demand function given byP = 300 − 3Q, where Q = Q1 +Q2. Both firms have constant marginal cost MC =100.a) What is Firm 1’s profit-maximizing quantity, given that Firm 2 produces an output of 50 unitsper year?Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…
- Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…Consider two firms competing to sell a homogeneous product by setting price. The inverse demand curve is given by P = 40 − Q . Firm 1 has MC1(Q1) = 4 and firm 2 has MC2(Q2) = 4.5. Based on this information, we can conclude that the market price will be a. $4.25 and each firm will produce 18 units. b.$4 and each firm will produce 18 units. c. $4 and firm 1 will produce 36 units and firm 2 will produce 0 units. d. $4.50 and firm 1 will produce 36 units and firm 2 will produce 0 units.Brand X is one of many firms in a competitive industry where each firm has a constant marginal cost of 2 dollars per unit of output. If marginal cost for Brand X rises to 4 dollars per unit and marginal costs of all other firms in the industry stay constant, by how much does the price in the industry increase? a. 2 dollars b. 1 dollar c. 0 dollar d. 2/n, where n is the number of firms in the industry e. None of the above.
