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−QBP=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+QA2TCA=1,500+55QA+QA2 TCB=1,200+20QB+2QB2TCB=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 the 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−QBP=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+QA2TCA=1,500+55QA+QA2 TCB=1,200+20QB+2QB2TCB=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 the 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
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter13: best-practice Tactics: Game Theory
Section: Chapter Questions
Problem 1E
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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−QBP=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+QA2TCA=1,500+55QA+QA2
TCB=1,200+20QB+2QB2TCB=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 the 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
.
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