# Cournot Duopoly: Determining Equilibrium Price and Quantity

Two identical firms compete in a cournot duopoly. The demand faced P= 100-2Q. The cost function firm C(Q)= 4Q. What is Nash equilibrium?

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#### Solution Preview

In Cournot competition firms compete in quantities and tend to maximize their profit. Counot model predicts that firms choose Nash equilibrium.

Let

q1 = output of Firm A

q2 = Output of Firm B.

Total Output Q=q1+q2

P = equilibrium price

P=100-2*(q1+q2) = 100-2q1-2q2

Consider Firm A

Total Revenue for Firm A, ...

#### Solution Summary

Solution describes the steps to determine equilibrium price and quantity of two identical firms in the case of cournot duopoly.

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