Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of where q₁ is Firm 1's output, p₁ is Firm 1's price, and p2 is Firm 2's price. Similarly, the demand Firm 2 faces is 92=16 Solve for the Bertrand equilibrium. In equilibrium, P₁ equals S At these prices. 9₁ equals and P2 equals S and 92 equals 01 =180 - 20, + 182. (Enter numeric responses using integers.) =160-2p₂+1p1-
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- A homogeneous products duopoly faces a market demand function given by Q = 20-2P, where Q = Q1 + Q2. Both firms have a constant marginal cost MC = 4. 1. Suppose the two firms set their quantities simultaneously by guessing the other firm's quantity choice. Derive the equation of each firm's reaction curve and then graph these curves. 2. What is the Cournot equilibrium quantity and price in this market for each firm? 3. What would the equilibrium price in this market be if it were perfectly competitive? 4. What is the Bertrand equilibrium price in this market?Consider a duopoly market with 2 firms. Aggregate demand in this market is given by Q = 500 – P, where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MCi = 20, i=A,B. Assume the firms compete a la Cournot. 1. What are the equilibrium quantities? 2. What is the total quantity supplied on this market? 3. What is the equilibrium price in this market?The figure below shows the market conditions facing two firms, Brooks, Inc., and Spring, Inc., in the domestic market for large utility pumps. Each firm has constant long-run costs, so that MC0 = AC0. As competitors in a duopoly, there are a number of models to determine output and prices. Assume that the Bertrand duopoly model applies, so that they both set price equal to their marginal cost. Initial output in this market will be 16,000 per year (this is split between the two firms), at a price of $300. (a) At the initial equilibrium, what is total surplus (consumer surplus plus producer surplus)? Suppose that Brooks, Inc. and Spring, Inc. form a joint venture, River Company, whose utility pumps replace the output sold by the parent companies in the domestic market. Assuming that River Company operates as a monopolist and that its costs equal MC0 = AC0, what is: (b) The price? (c) The output? (d) Total profit? (e) The resulting deadweight loss from River Company operating as a…
- The figure below shows the market conditions facing two firms, Brooks, Inc., and Spring, Inc., in the domestic market for large utility pumps. Each firm has constant long-run costs, so that MC0 = AC0. As competitors in a duopoly, there are a number of models to determine output and prices. Assume that the Bertrand duopoly model applies, so that they both set price equal to their marginal cost. Initial output in this market will be 16,000 per year (this is split between the two firms), at a price of $300. Suppose that Brooks, Inc. and Spring, Inc. form a joint venture, River Company, whose utility pumps replace the output sold by the parent companies in the domestic market. Assuming that River Company operates as a monopolist and that its costs equal MC0 = AC0, what is: (b) The price?The figure below shows the market conditions facing two firms, Brooks, Inc., and Spring, Inc., in the domestic market for large utility pumps. Each firm has constant long-run costs, so that MC0 = AC0. As competitors in a duopoly, there are a number of models to determine output and prices. Assume that the Bertrand duopoly model applies, so that they both set price equal to their marginal cost. Initial output in this market will be 16,000 per year (this is split between the two firms), at a price of $300. Suppose that Brooks, Inc. and Spring, Inc. form a joint venture, River Company, whose utility pumps replace the output sold by the parent companies in the domestic market. Assuming that River Company operates as a monopolist and that its costs equal MC0 = AC0, what is: (e) The resulting deadweight loss from River Company operating as a monopoly?The figure below shows the market conditions facing two firms, Brooks, Inc., and Spring, Inc., in the domestic market for large utility pumps. Each firm has constant long-run costs, so that MC0 = AC0. As competitors in a duopoly, there are a number of models to determine output and prices. Assume that the Bertrand duopoly model applies, so that they both set price equal to their marginal cost. Initial output in this market will be 16,000 per year (this is split between the two firms), at a price of $300. Suppose that Brooks, Inc. and Spring, Inc. form a joint venture, River Company, whose utility pumps replace the output sold by the parent companies in the domestic market. Assuming that River Company operates as a monopolist and that its costs equal MC0 = AC0, what is: (c) The output? (d) Total profit?
- Consider a Cournot Duopoly model. The inverse demand for their products is given byP = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given byT Ci = 2Qi, for i = 1, 2.(a) In the Cournot model, what does each firm choose?(b) What is the timing of each firm’s decision?(c) Find the Nash equilibrium quantities (Q∗1, Q∗2)?(d) What is the equilibrium price? Just help with c and d here pleaseSuppose that two firms produce mountain spring water and the market demand for mountain spring water is given as follows: P= 254 - 91 - 92 Firm 1 and Firm 2 have a MC = 50 a) Find the Cournot-Nash equilibrium price and quantity of each firm. b) Assume now that firm 1 becomes the Stackelberg leader. What will be the market price, output by each firm? Compared to part a, who gains? c) If Firm 1 chooses a quantity, then Firm 2 chooses a quantity (having observed Firm 1's quantity), then Firm 1 has an opportunity to revise its quantity (having observed Firm 2's quantity), then payoffs are determined, does either firm stand to gain relative to the case of simultaneous quantity choice? Why or why not? (hint: there is no need to do any calculation here).H7. For q1=120-2p1-p2 and q2=120-2p2+p1, show that the duopolists have incentives to collude as well as find the -joint profit-maximizing price, output and profit and find each firm’s price, output and profit. What is the optimal defection of each firm, is collusion Nash equilibrium? Show in 2x2 matrix. Is it a prisoner’s dilemma?
- Consider a duopoly market with 2 firms. Aggregate demand in this market is given byQ = 500 – P,where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MCi = 20, i=A,B. Assume the firms compete a la Cournot. 1. Find the inverse demand in this market. Note that marginal revenue for both firms is given by MRA=500-2QA-QB, MRB=500-QA-2QB. Describe what a best-response curve is and how to find it. Derive the best-response function for each firm. What are the equilibrium quantities? What is the total quantity supplied on this market? What is the equilibrium price in this market?While there is a degree of differentiation between major grocery chains like Albertsons and Kroger, theregular offering of sale prices by both firms for many of their products provides evidence that these firmsengage in price competition. For markets where Albertsons and Kroger are the dominant grocers, thissuggests that these two stores simultaneously announce one of two prices for a given product: a regularprice or a sale price. Suppose that when one firm announces the sale price and the other announces theregular price for a particular product, the firm announcing the sale price attracts 1000 extra customers toearn a profit of $5000, compared to the $3000 earned by the firm announcing the regular price. Whenboth firms announced the sale price, the two firms split the market equally (each getting an extra 500customers) to earn profits of $2000 each. When both firms announced the regular price, each companyattracts only its 1500 loyal customers and the firms each earned $4500 in…Consider a duopolistic market with an inverse demand curve P(Q) = 460 − 4Qand constant marginal costs for each firm that are given by MC(Q) = 10.Assume fixed costs are negligible. The two identical firms are competing in this market by choosing their production quantities simultaneously. In the equilibrium, each firm produces 37.5 units and the prevailing market price is 160. How would the joint profits of these two firms change if they successfully formed a cartel? Change in joint profits: ? (Enter your answer rounded to two decimal places; include a negative sign if appropriate.)