Suppose Cournot duopolist firms operate with each having a cost of 30q_i (i = 1,2)so that each firm's marginal cost is 30.The inverse market demand curve is P = 120 - Q where Q = q₁ + q₂.At the Nash-Cournot equilibrium,the total quantity,Q,is

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The profit maximization condition for each firm is to set their marginal cost equal to their market share times the derivative of the inverse demand function with respect to total quantity, which is: 
MC = (qS1U1B1iS1U1B0 + qS1U1B2iS1U1B0)/2 
30 = (qS1U1B11S1U1B0 + qS1U1B21S1U1B0)/2 
60 = qS1U1B11S1U1B0 + qS1U1B21S1U1B0

Thus, at the Nash-Cournot equilibrium, each firm produces 30 units and the total quantity is 60 units.

Suppose Cournot Duopolist Firms Operate with Each Having a Cost