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Heterogeneous-cost Cournot Competition (view source)
Revision as of 22:44, 10 November 2013
, 22:44, 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==
==Comparison to other solutions==
First of all note what happens to price as the quantity provided increases with more firms competiting (i.e., we move towards Bertrand competition, where free entry drives economic rents to zero):
:<math>\lim_{n \to \infty} \left ( \frac{A + \sum_{i=1}^n c_i}{n+1} \right ) \implies p \to \min (c_i)</math>
And at the other extreme, we have monopoly pricing:
:<math>p^m = \frac{A + c_i}{2}</math>
When the firms are identical the optimal quantity function simplies to:
:<math>q_i^* = \frac{ A - c }{B (n+1)}</math>
And likewise the profit is then:
:<math>\pi_i^* = \frac{1}{B }\left (\frac{A - c}{n+1} \right )^2</math>
