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Heterogeneous-cost Cournot Competition (view source)
Revision as of 21:35, 10 November 2013
, 21:35, 10 November 2013no edit summary
Now we can solve for <math>\;q_i^*</math>. Substituting this into the original first-order condition gives:
:<math>$q_i^* = \frac{\left ( A - c_i(n+1) + \sum_{i=1}^n c_i \right )}{B (n+1)}</math>
==Market clearing price and profits==
And then substitute into <math>\;p=A-BQ</math> to get:
:<math>p^* & = \frac{A + \sum_{i=1}^n c_i}{n+1}</math>
Now find firm profits by subsituting both <math>\;q_i^*</math> and <math>\;p^*</math> into <math>\;\pi_i = q_i \left ( p(Q) - c_i \right)</math>:
:<math>\pi_i^* &= \frac{1}{B }\left (\frac{A - c_i(n+1) + \sum_{i=1}^n c_i }{(n+1)} \right )^2</math>
==Comparison to other solutions==
