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Imposing the profit maximizing condition of MR

# Imposing the profit maximizing condition of MR - => Q1 =...

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Imposing the profit maximizing condition of  MR  =  MC  , we conclude that Firm 1's  reaction curve is:  100 - 2 * Q1* - Q2 = 10 => Q1* = 45 - Q2/2  That is, for every choice of  Q   2  ,  Q   1   *  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  Q   1   *  . Note that we substitute  Q   2   *  for  Q   2  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
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Unformatted text preview: => Q1* = 92/3 By the same logic, we find: Q2* = 86/3 Again, we leave the actual computation of Q 2 * as an exercise for the reader. Note that Q 1 * and Q 2 * differ due to the difference in marginal costs. In a perfectly competitive market, only firms with the lowest marginal cost would survive. In this case, however, Firm 2 still produces a significant quantity of goods, even though its marginal cost is 20% higher than Firm 1's. An equilibrium cannot occur at a point not in the intersection of the two reaction curves. If such an equilibrium existed, at least one firm would not be on its reaction curve and would therefore not be playing its optimal strategy. It has incentive to move elsewhere, thus invalidating the equilibrium....
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