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 ...
Education
- BEng (Hons) , Birla Institute of Technology and Science, India
- MSc (Hons) , Birla Institute of Technology and Science, India
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