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What is the Lerner Index for the monopoly described




What is the Lerner Index for the monopoly described below?;Suppose that the (inverse) market demand curve for a new drug, Adipose-Off, designed to painlessly reduce body fat, is represented by the equation P=100-2Q, where P is the price in dollars per dose and Q is the annual output. (The marginal revenue curve is thus given by the equation MR=100-4Q). Suppose also that there is a single supplier of the drug who faces a marginal cost, as well as average cost, of producing the drug, equal to a constant $20 per dose. What are the monopolist's profit-maximizing output and price? What is the resulting deadweight loss relative to the competitive outcome?;Calculate the Lerner Index for the monopoly described in the question above.;Solution;Monopolist profit maximizing output and price is where MR = MC;20 = 100- 4Q;-80 = -4Q;20 = Q;P= 100 -2 (20);P= 100 - 40;P = $60;Therefore output is 20 and price is 60 in a monopoly.;Consumer surplus = (1/2 x 40 x 20);= 400 and;Producer surplus = (1/2 x 60 x 20);= 600;Total surplus = 400 + 600;= 1000;In a competitive market, price equals marginal cost;20 = 100- 2Q;-80 = -2Q;40 = Q;So in the competitive market output is 40 and price is $20;Consumer surplus = (1/2 x 80 x 40);= 1600 and;Producer surplus = (1/2 x 20 x 40);= 400;Total surplus = 1600 + 400;= 2000;so the deadweight loss = 2000 - 1000;= 1000


Paper#33437 | Written in 18-Jul-2015

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