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 (i.e., each firm assumes that the other firm’s output will not change). Cournot Equilibrium Price Output Profits ($) (units) ($) Company A 145 30 300 Company B 145 25 675 Total Industry 55 $975 Compare the optimal solutions obtained in this exercise with the Cournot equilibrium given in the preceding table. What happens to the optimal selling price, total industry output, and total industry profits when the two firms form a cartel instead of acting independently? Increase Decrease No change Selling price Total industry output Total industry profits

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−

−

where

and

are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are

=1,500+55

=1,200+20

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 (i.e., each firm assumes that the other firm’s output will not change).

Cournot Equilibrium

	Price	Output	Profits
($)	(units)	($)
Company A	145	30	300
Company B	145	25	675
Total Industry		55	$975

Compare the optimal solutions obtained in this exercise with the Cournot equilibrium given in the preceding table. What happens to the optimal selling price, total industry output, and total industry profits when the two firms form a cartel instead of acting independently?

	Increase	Decrease	No change
Selling price
Total industry output
Total industry profits

Definition Video Definition Point where the demand and supply curves intersect. At the equilibrium price the quantity supplied of a good is equal to the quantity demanded. When the market is not in equilibrium, market surplus or market shortage occurs. The region that is above the price equilibrium indicates market surplus and the region below the price equilibrium indicates market shortage. Video

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