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cournot2-1

# cournot2-1 - Concentration and Profitability Assume that we...

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ECO 171 Industrial Organization Concentration and Profitability Assume that we have N firms with different marginal costs We can use the N-firm analysis with a simple change Recall that demand for firm 1 is P = (A - BQ -1 ) - Bq 1 But then demand for firm i is P = (A - BQ -i ) - Bq i Equate this to marginal cost c i A - BQ -i - 2Bq i = c i This can be reorganized to give the equilibrium condition: A - B(Q* -i + q* i ) - Bq* i - c i = 0 But Q* -i + q* i = Q* and A - BQ* = P* P* - Bq* i - c i = 0 P* - c i = Bq* i

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ECO 171 Industrial Organization Concentration and profitability (cont.) P* - c i = Bq* i Divide by P* and multiply the right-hand side by Q*/Q* P* - c i P* = BQ* P* q* i Q* But BQ*/P* = 1/ η d and q* i /Q* = s i so: P* - c i P* = s i η d Price cost margin = market share/demand elasticity
ECO 171 Industrial Organization Concentration and Profitability: generalization N firms with costs C i ( q i ) and marginal costs MC i ( q i ) Inverse demand function p=D ( Q ) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 i Q q s s Q q P MC P so Q q p Q Q P P q Q P P MC P MC q Q P P q Q q q Q q q C q q Q P Q q i i

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