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
q_{1} by Firm 1 and q_{2} by Firm 2.
Marginal cost for Firm 1
The marginal cost for Firm 1 is
MC_{1}(q_{1}) = 3 + 2 q_{1}
and the cost function for Firm 1 is
C_{1}(q_{1}) = 3 q_{1}
+ q_{1}^{2}.
Profit function for Firm 1
The profit function for Firm 1 can be determined from its revenue,
which is p q_{1} = D^{1}(Q) q_{1}, and its
cost C_{1}(q_{1}). Combining these results
in
p_{1}(q_{1},
q_{2}) =
(45  (q_{1} + q_{2})) q_{1} 
3 q_{1}  q_{1}^{2}.
Response function for Firm 1
The derivative of the profit function is
d p_{1}/dq_{1} =
42  4 q_{1}  q_{2}.
When this is equated to 0 and solved for q_{1} the
result is so the firstorder condition is
q_{1}* = 21/2  ¼ q_{2}.
Response function for Firm 2
By following a similar procedure for Firm 2 to the one
above for Firm 1, the response function
q_{2}* = 21/2  ¼ q_{1}
for Firm 2 is obtained.
Equilibrium outputs and price
The equilibrium outputs are obtained by solving the two
equations q_{1}* = 21/2 B  ¼ q_{2} and
q_{2}* = 21/2  ¼ q_{1} simultaneously.
This results in
q_{1}* = q_{2}* = 42/5.
The equilibrium price is therefore
p* = D^{1}(84/5) = 28.2.
