In lecture we saw the Cournot competition model for two firms with the same cost function....

In lecture we saw the Cournot competition model for two firms with the same cost function. Now, we are going to consider asymmetric cost functions. Assume that demand for a good is given by p=a−bQd (Qd is quantity demanded), and that there are 2 firms competing in quantities. Both have no fixed costs and a constant marginal cost. Firm 1 has a marginal cost c1, and firm 2 has a marginal cost c2. We have that a>c1>c2.

Find the reaction functions of firms 1 and 2 in this market: how the optimal quantity produced depends on the quantity produced by the other firm.

To verify that you have found the correct reaction functions, compute the optimal q1 if q2=100, a=4, b=0.01, c1=2, and c2=1. (Note that this is not necessarily an equilibrium.)

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Rahul Sunny answered 1 year ago

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