The market demand is p=50-Q. There are two firms who behave as Cournot duopolist

Question

The market demand is p=50-Q. There are two firms who behave as Cournot duopolists. For simplicity assume the marginal cost is zero
A) write down the profit function of each firm B) find the reaction functions of each firm The market demand is p=50-Q. There are two firms who behave as Cournot duopolists. For simplicity assume the marginal cost is zero
A) write down the profit function of each firm B) find the reaction functions of each firm
A) write down the profit function of each firm B) find the reaction functions of each firm

Explanation / Answer

In the Cournot model of oligopoly, firms choose a level of output given the output choices of rival firms. In a homogenous products oligopoly, Cournot firms exhibit market power and set a price above the perfectly competitive price and provide a level of output below the perfectly competitive level. Thus, in the Cournot model price is above the perfectly competitive price.

Let us assume Qa is first firm's quantity and Qb is second firm's quantity.

For First firm, MRaA = MC

That implies 50 – 2Qa - Qb = 0.

We could either calculate second firm's profit-maximization condition (and solve two equations in two unknowns), or, inferring that the equilibrium will be symmetric since each seller has identical costs, we can exploit the fact that Qa = Qb in equilibrium.

Thus 50 – 2Qa - Qa = 0

or Qa = 50/3. Similarly, Qb = 50/3.

Total market output under Cournot duopoly is Q d = Qa + Qb = 100/3,

and the market price is P d = 50 – Qd = 50-100/3 = 50/3.

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