The market demand curve for a pair of duopolists is given as P = 21 − 2Q, where Q = Q1 + Q2. The constant per unit marginal cost is $9 for each duopolist. Find the equilibrium price, total quantity and profit for each firm, assuming the firms act as a Stackelberg leader and follower, with firm 1 as the leader.
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The market demand curve for a pair of duopolists is given as P = 21 − 2Q, where Q = Q1 + Q2. The constant per unit marginal cost is $9 for each duopolist. Find the
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- Cournot duopolists face a market demand curve given by P = 60 – 1/2Q, where Q is total market demand in units. Each firm can produce output at a constant marginal cost of $15/unit. a) What is the equilibrium price and quantity produced by each firm? b) What if the firm's engaged in Bertrand competition? c) What if one of the firms chose its quantity before its competitor? What is the name for this sort of competition? d) Which of the three forms of competition gives the greatest social surplus?Tom is a monopolist input supplier to Dic and Harry. Tom's marginal cost is 1. Dic and Harry are duopolists with production function q = x1/2. No firm has fixed costs. The demand for the final product is given by Q = 100 – p. a) Assume Dic and Harry buy the input from Tom at price k. What are their cost functions? b) Find the Cournot equilibrium quantities. c) What price, k, should Tom set? -Suppose the inverse demand function for two Cournot dupolists is given by P= 10 – (Q1+Q2) and their cost are zero.a) What is each firm marginal revenue?b) What are the reaction function for the two firmsc) What are the Cournot equilibrium outputd) What is the equilibrium price?
- The inverse demand function in an industry with two firms is given as p = 50 – 2y, where y is the industry demand and p is the price. The firms have different technologies at their production plants with costs given as c(y1) = 10y, and c2[y2) = 14y2, where y = y,+ y2. 1. Assuming the firms are Cournot duopolists, find the equilibrium price, quantity and profit for each firm (if needed, have 2 digits after decimal point). 2. Assuming the firms act as a Stackelberg leader and follower, with firm 1 as the leader, find the equilibrium price, quantity and profit for each firm. 3. If the firms merge into one firm and become a monopoly in the industry, what will be the output of the merged firm? Comment on what would happen to the production plants under one ownership. Find the equilibrium price and profit. 4. Compare and comment on the total industry profits in these three market structures. 5. Assuming the firms are Bertrand duopolists, what is likely to happen? Explain verbally (no need to…consider two firms who are acting as cournot duopolists. the inverse demand function is represented by P=100-(q1+q2). here p is the price. q1 and q2 are the output levels of firms 1 and 2 marginal cost mc functions of the two firms are mc1=5 mc2= 15 find the profit of two firmsSuppose the inverse demand function for two Cournot duopolists is given by P = 10 – (Q1 + Q2) and their costs are zero. What is each firm’s marginal revenue and reaction functions? Determine the Cournot equilibrium outputs and equilibrium price. What is the implication of this model?
- Consider a Cournot duopoly. The market demand function is P = 180 – 2(q₂ + q₂), where P is the market price, q₂ is the output produced by Firm 1 and q₂ is the output produced by Firm 2. The two firms have a constant marginal cost c = 30. What is the total output in this market? Round your answer to the nearest integer (e.g. 50)Imagine any market divided by 2 Cournot oligopolists who have identical costs Marginal cost = Average cost = 200. About this market, ask yourself: a) If the demand curve for this market is given by Q = 1250 - 2.5P, where Q is the total quantity demanded in the market and P is the selling price, both given in units, what is the reaction curve of the oligopolists? b) What will be the quantity produced and the selling price of the oligopolists? c) A strategist considers that a good marketing campaign would be able to expand the Demand of this market to Q = 1,500 - 2.5P and that in this way, oligopolists could produce the same amount and make significantly greater profits. Such a campaign would generate a reduction in profits in the order of 70,000. Is it worth making this investment in marketing?Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function: P=600−QC−QD�=600−��−�� where QC�� and QD�� are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCC=25,000+100QCTC�=25,000+100�� TCD=20,000+125QDTC�=20,000+125�� Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change). For Company C, the long-run equilibrium output is , and the selling price is . For Company D, the long-run equilibrium output is , and the selling price is . At the equilibrium output, Company C earns total profits of , and Company D earns total profits of
- Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function: P=200− Q A − Q B where Q A and Q B are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TC A =1,500+55 Q A + Q A 2 TC B =1,200+20 Q B +2 Q B 2 Assume that the firms form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits). In such a case, Company A will produce units and sell at . Similarly, Company B will produce units and sell at . At the optimum output levels, Company A earns total profits of and Company B earns total profits of . Therefore, the total industry profits are . At the optimum output levels, the marginal cost of Company A is and the marginal cost of Company B is . The following table shows the long-run equilibrium if the firms act independently, as in the Cournot model…Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function: P= 200-Qa-Qb where QAQA and QBQB are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCa=1,500+55Qa+Qa2 TCb=1,200+20Qb+2Qb2 Assume that the firms form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits). In such a case, Company A will produce units and sell at $ . Similarly, Company B will produce units and sell at $ . At the optimum output levels, Company A earns total profits of $ and the marginal cost of Company B earns total profits of $ . Therefore, the total industry profits are $ . At the optimum output levels, the marginal cost of Company A is $ and the marginal…Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function:P=1000−QC−QDwhere QC and QD are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCC=15,000+50QC TCD=10,000+75QD Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change). Please, find the equilibrium output of firm C.
