That is, for every choice of Q2 , Q1* is Firm 1's optimal choice of output. We can perform analogous analysis for Firm 2 (which differs only in that its marginal costs are 12 rather than 10) to determine its reaction curve, but we leave the process as a simple exercise for the reader. We find Firm 2's reaction curve to be: Q2* = 44 - Q1/2 The solution to the Cournot model lies at the intersection of the two reaction curves. We solve now for Q1* . Note that we substitute Q2* for Q2 because we are looking for a point which lies on Firm 2's reaction curve as well. Q1* = 45 - Q2*/2 = 45 - (44 - Q1*/2)/2= 45 - 22 + Q1*/4 = 23 + Q1*/4=> Q1* = 92/3 By the same logic, we find: Q2* = 86/3 Again, we leave the actual computation of Q2* as an exercise for the reader. Note that Q1* and Q2
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