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Determine the reaction function for each firm. P= 100-2(Q1 + Q2); C1 (Q1) =12Q1; C2 (Q2) =20 Q2
We determine the equilibrium in Cournot Duopoly by calculating the intersection of the reaction curves of the two firms. A reaction function of a firm gives the profit maximising level of its output given a certain level of second firm’s output. To determine the reaction function of a firm, we differentiate its profit experssion with respect to its output and equate what we get after differentiateing to zero. Let $ denote the profit expression. Determining the reaction function of firm 1:…

$1 = 100Q1-2Q1^2-2Q1Q2-12Q1) Differentiating the above wrt Q1, we get, (d$1/dQ1= 100-4Q1-2Q2-12) Equatingthe above equation to zero and then rearranging, we get: (Q1 = (88-2Q2)/4) This is first firm’s reaction curve. Folowing the same steps for firm 2, we get, (Q2= (80-2Q1)/4) as the reaction function of firm 2.

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