Answered: Assume that two companies (A and B) are…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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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