Now, let's go back to the case where all firms have the same cost function. Now, we are going to get you through the Cournot model with three firms. Assume that demand for a good is given by=

, and that there are3 firms competing in quantity with a constant marginal cost<.

Write down the maximization problem of a representative firm in the market. Solve for the reaction function of this firm: how the optimal quantity produced depends on the quantity produced by the other two firms in the market.

To verify that you have found the correct reaction function, compute the optimal1if2=40,3=60,=4,=0.01, and=2. (Note that this is not necessarily an equilibrium.)

1= ?