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Consider a market where N firms produce a homogeneous product and compete by simultaneously setting quantities. The inverse demand function has the general form P PO-P(qi +q2 +q3 + + qv), where Q is total quantity produced, qi is the quantity produced by firm i and P is the market price. The demand curve is downward sloping, so P10 < 0. The total cost of firm i is given by Cig). (0) Show that P- MC qi i , where și is the market share of firm i and є dP/P is the absolute value of the price elasticity of demand (ii) Derive a weighted Lerner index for the industry as a whole, using market shares as weights, and show that it is directly related to the Herfindahl index of market concentration, H- si. Can you therefore conclude that an increase in industry concentration will cause an increase in the industry price-cost margin? Explain why or why not.

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dPC*) ク&. O P 6L P MC (Proved) weighted Larner İndex of tne indust- P-M 2. direct Propor tiomai. As si Hemce L and rise n concentration mceases pmce eoritera coSA masin

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