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

Answer 1

Four firm concentration ratio :- In case of four firm concentration ratio, In a defined industry top four firm market shares are summed up .Let say S i is the sale of firm i and St is represent the total sale of the industry

so four concentratio ratio C4 = w1+w2+w3+w4

where w i = ratio of si and st i-e Si/St

In Four firm concentration ratio the foreign producer are excluded and it is applied only in relevant market.

In Herfindahl -Hirschman Index denoted as HHI the sum of squared market share of the firm is taken in a given inustry which is multiplied by 10,000

mathematically

HHI = 10,000* summation of wi

where wi = si/st

The Rothschild Index denoted by R is used to measure the elasticity of the emand of industry for a particular prouct which is relative to the individual firm. Simply R is the ratio of elasticity of demand of total market to elasticity of emand of product of iniviual firm.It will can be zero if all firm are producing same in an industry

The learner Index where is bsically is for pricing behaviour to conductIt is enoted by L

L = (P-MC )/P

Means it is the difference betwen the price P and marginal cost MC as a fraction of the price of product .mATHEMATICALLY IT RANGE FROM 0 TO 1 when It is zero it means the firm has no power in market and 1 indicate weak price in competition which means that firm has power in market .

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