Two Companies (A and B)are Duopolists That Produce Identical Products

question 21

Essay

Two companies (A and B)are duopolists that produce identical products.Demand for the products is given by the following demand function:

P = 10,000 - 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 = 500,000 + 200Q_A + .5Q_A²
TC_B = 200,000 + 400Q_B + Q_B²

Assume that the firms form a cartel to maximize total industry profits (sum of Firm A and Firm B profits).Determine the optimum output and selling price for each firm.

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Definitions:

Market Demand

The total quantity of a good or service that all consumers in a market are willing and able to purchase at a given price.

Tax Revenue

Income that is gained by governments through taxation, used to fund public services and government obligations.

Demand Curve

A graphical representation of the relationship between the price of a good and the quantity demanded, typically downward sloping to the right.

Tax

Mandatory monetary contributions or taxes levied by a government on people or organizations to support government spending.