In a duopoly, the price is below the monopoly price and above the competitive price; the duopoly quantity is above the monopoly quantity and below the competitive quantity. The prices and exchange quantity from experiments can be compared to the predicted price and quantity from the Cournot model.

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Market Inverse Demand

The market inverse demand is p = D^-1(Q) = 45 - Q, where the market output Q is the sum of the outputs q₁ by Firm 1 and q₂ by Firm 2.

Marginal cost for Firm 1

The marginal cost for Firm 1 is MC₁(q₁) = 3 + 2 q₁

and the cost function for Firm 1 is C₁(q₁) = 3 q₁ + q₁².

Profit function for Firm 1

The profit function for Firm 1 can be determined from its revenue, which is p q₁ = D^-1(Q) q₁, and its cost C₁(q₁). Combining these results in p₁(q₁, q₂) = (45 - (q₁ + q₂)) q₁ - 3 q₁ - q₁².

Response function for Firm 1

The derivative of the profit function is d p₁/dq₁ = 42 - 4 q₁ - q₂.

When this is equated to 0 and solved for q₁ the result is so the first-order condition is q₁* = 21/2 - ¼ q₂.

Response function for Firm 2

By following a similar procedure for Firm 2 to the one above for Firm 1, the response function q₂* = 21/2 - ¼ q₁ for Firm 2 is obtained.

Equilibrium outputs and price

The equilibrium outputs are obtained by solving the two equations q₁* = 21/2 B - ¼ q₂ and q₂* = 21/2 - ¼ q₁ simultaneously. This results in

q₁* = q₂* = 42/5.

The equilibrium price is therefore p* = D^-1(84/5) = 28.2.