Assume that two companies (A and B) are duopolists that produce identical products. Demand for the products is given by the following linear demand functions: P=200-QA-QB where QA and QB are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCA = 1500+55 QA +QA2 TCB = 1200+20 QB +2QB2 Assume that the firms form a cartel and maximize total industry profits, a. Determine the optimal output and selling price for each firm. b. Determine Frim A, Firm B, and total industry profits at the optimal solution found in part (a). c. Show that the marginal cost of the two firms are equal at the optimal solution found in part (a)

Assume that two companies (A and B) are duopolists that produce identical products. Demand for the products is given by the following linear demand functions: P=200-QA-QB where QA and QB are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCA = 1500+55 QA +QA2 TCB = 1200+20 QB +2QB2 Assume that the firms form a cartel and maximize total industry profits, a. Determine the optimal output and selling price for each firm. b. Determine Frim A, Firm B, and total industry profits at the optimal solution found in part (a). c. Show that the marginal cost of the two firms are equal at the optimal solution found in part (a)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.2P

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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 - QBwhere QA and QB are the quantities sold by the respective firms and P is the sellingprice. Total cost functions for the two companies areTCA = 1500 + 55QA + Q2ATCB = 1200 + 20QB + 2Q2BAssume that the firms act independently as in the Cournot model (i.e., each firmassumes that the other firm’s output will not change).a. Determine the long-run equilibrium output and selling price for each firm.b. Determine Firm A, Firm B, and total industry profits at the equilibrium solutionfound in Part (a).
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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 - 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 areTCC = 25000 + 100QCTCD = 20000 + 125QDAssume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm’s output will not change).a. Determine the long-run equilibrium output and selling price for each firm.b. Determine the total profits for each firm at the equilibrium output found in Part (a).
Only typed answer Two firms both produce leather boots. The inverse demand equation is given by P = 340 - 2Q, where P is the price of boots in USD/pair and Q is quantity of boots in million pair. The cost function is given by: C(Q) = 40Q. If the two firms are Stackelberg oligopolists), the output of the leader is equal to: 1) 60 2) 80 3) 75 4) 900
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. The total cost functions for the two companies are TCa=1,500+55Qa+Qa2 TCb=1,200+20Qb+2Qb2 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 A, the long-run equilibrium output is and the selling price is $ . For Company B, the long-run equilibrium output is , and selling price is $ . At the equilibrium output, Company A earns total profits of $ and Company B earns total profits of $ . Therefore, the total industry profits are $ .
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 (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function: P=400−QA−QBP=400−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+110QA+QA2TCA=1,500+110QA+QA2 TCB=1,200+40QB+2QB2TCB=1,200+40QB+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 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…
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 where QCQC and QDQD 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=100Qc TCd=20,000=125Qd 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 $ .
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Albert and Johny are the only sellers of Motorbikes in Ireland. The inverse market demand function for motorbikes is P(Y)= 200- 2Y . Both firms have the same total cost function: T(C)= 12Y and the same marginal cost: M(C)=12. Suppose now that the two firms decide to act like a single monopolist. What will the total quantity of Motorbikes sold in the market be and what will the equilibrium price be? Represent the profit maximisation problem on a graph and indicate the price and quantity at the equilibrium. Calculate the total profit made by the two firms when they act like a monopoly. Compare it with the total profit they were making in the Stackelberg oligopoly. For the two firms to be willing to agree to act as a monopoly, how should they split the quantity to produce between them? We assume that if they do not agree to act like a monopoly, then the market structure is the Stackelberg oligopoly studied above. We further assume that no money transfer is possible between the two…
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