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.© BrainMass Inc. brainmass.com October 10, 2019, 1:25 am ad1c9bdddf
In cournot competition, firms compete in quantities and tend to maximize their profit
In case of company A
Total Revenue =TRA=P*QA=(10000-QA-QB)*QA=10000QA-QA^2-QAQB
This solution describes the steps to calculate equilibrium price and output for the given two firms.