Demand is assumed to be unit-elastic: X(p) = 1/p. There are m ≥ b2 firms operating in the market with constant marginal cost levels c1 ≤ c2 ≤ ……. ≤ cm. They engage in Cournot competition. a. Show that the equilibrium price implies Lerner indexes Where si is the market share of firm i. b. Using the equilibrium price, show that the profit of firm i is equal to (si)2. c. Show that the industry profit is equal to the Herfindahl index H = Σi(si)2. d. What is the effect of a specific taxt on equilibrium price? How does this tax affect the industry profit and the Herfindahl index?

ENGR.ECONOMIC ANALYSIS
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Demand is assumed to be unit-elastic: X(p) = 1/p. There are m ≥ b2 firms operating in the market with constant marginal cost levels c1 ≤ c2 ≤ ……. ≤ cm. They engage in Cournot competition.

a. Show that the equilibrium price implies Lerner indexes

Where si is the market share of firm i.

b. Using the equilibrium price, show that the profit of firm i is equal to (si)2.

c. Show that the industry profit is equal to the Herfindahl index H = Σi(si)2.

d. What is the effect of a specific taxt on equilibrium price? How does this tax affect the industry profit and the Herfindahl index?

 

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