Question

Explain the difference between a four firm concentration ratio, a Herfindahl-Hirschman Index, a Lerner index, and a Rothschild index.

Based on the information given below, indicate for each of the following, whether the industry is best characterized by the model of perfect competition, monopoly, monopolistic competition, or oligopoly.

a) Industry A has a four-firm concentration ratio of 0.005% and an HHI of 75. A representative firm has a Lerner index of 0.45 and a Rothschild index of 0.34.

b) Industry B has a four-firm concentration ratio of 0.0001% and an HHI of 55. A representative firm has a Lerner index of 0.0034 and a Rothschild index of 0.00023.

c) Industry C has a four-firm concentration ratio of 100 % and an HHI of 10,000. A representative firm has a Lerner index of 0.4 and a Rothschild index of 1.0.

d) Industry D has a four-firm concentration ratio of 100% and an HHI of 5,573. A representative firm has a Lerner index of 0.43 and a Rothschild index of 0.76.

Answer 1

Rothschild Index is ratio of elasticity of demand for total market to elasticity of demand for product of an individual firm.The Rothschild Index is a value between 0 (perfect competition) and 1 (monopoly). When an industry is composed of many firms, each producing similar products, the Rothschild index will be close to zero.

Lerner's index is a  measure of the difference between price and marginal cost as a fraction of the product’s price. When Price equals marginal cost , the Lerner Index is zero; the firm has no market power. A Lerner Index closer to 1 indicates relatively weak price competition; the firm has market power.

Four firm concentration ratio is the proportion of total output in an industry produced by the four largest firms in an industry. This is one of two common concentration ratios. The four-firm concentration ratio is commonly used to indicate the degree to which an industry is oligopolistic and the extent of market control held by the four largest firms in the industry.

Herfindahl Index is a measure of concentration of the production in an industry calculated as the sum of the squares of market shares for each firm. This is one method of summarizing the degree to which an industry is oligopolistic and the concentration of market control held by the largest firms in the industry

(A) The four-firm concentration and the HHI are low, the Lerner and the Rothschild index indicate economic profits and product differentiation. It is like monopolistic competition.

(B) The four-firm concentration and the HHI are very low, the Lerner and the Rothschild index indicate small economic profits and little product differentiation. This is perfect competition.

(C) The four-firm concentration and the HHI are as high as can be, that is, there is one firm. The Lerner index tells us that there is a fair degree of markup, and the Rothschild index also indicates that there is one firm. This is a monopoly.

(D) This is  oligopoly with moderately large mark-ups, the mark-ups and the Rothschild index indicating product differentiation