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Determining equilibrium price and quantity - Cournot model

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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-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 = 500,000 + 200QA + .5QA2
TCB = 200,000 + 400QB + QB2

Assume that the two firms act independently as in the Cournot model (that is, each firm assumes that the other firm's output will not change). Determine the long-run equilibrium output and selling price for each firm.

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Solution Summary

This solution describes the steps to calculate equilibrium price and output for the given two firms.

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In cournot competition, firms compete in quantities and tend to maximize their profit

P=10000-QA-QB

In case of company A
Total Revenue =TRA=P*QA=(10000-QA-QB)*QA=10000QA-QA^2-QAQB
Marginal Revenue=MRA=d(TRA)/dQA=10000-2QA-QB

TCA=500000+200QA+0.5QA^2
Marginal ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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