Question

1. A homogeneous good industry is composed of 3 firms. You are given the following information on output, price and marginal cost of each firm: q1 =20 q2 =40 q3 =120 p = 20.50 c1 =20 c2 =19.5 c3 =17.5 Remember that for each firm (p−ci/p) =((alpha)*i/n)) where (alpha)i is the market share of firm i and n is the price elasticity of demand.

a) Calculate the 2-firm concentration ratio.

b) Calculate the Herfindahl index.

c) Calculate the number equivalent. What does it mean?

d) Calculate the Lerner index of the largest firm.

e) Calculate the price elasticity demand of the largest firm.

Answer 1

Solution

Given Data:

Output of firms 1 , 2 and 3 are 20 , 40 and 120 ; Price is constant at 20.50 across the industry.

Marginal cost across the firms is : 20,19.50 and 17.50

a) Calculating the price elasticity and market share for each firm

P = C (n / n+1) where "P" is the profit maximizing price of the good of the firm;C = marginal cost and "n" is the

Price elasticity of Firm 1 => P / c1 = (n /n+1) i.e., (20.50 / 20) = (n/n+1)

i.e., n = -41

Price elasticity of Firm 2 => (20.50 / 19.50) = (n/n+1) i.e., n = -20.50

e.Price elasticity of Firm 3 => (20.50 / 17.50) = (n/n+1) i.e., n = -6.83

Market share of firms 1,2 and 3 are 20 / 180 , 40/180 and 120/180 i.e., 11.11% , 22.22 % and 66.66% respectively.

a. 2-firm concentration ratio is (66.66 +22.22 )% which is 88.88%

b. Herfindahl index = (11.11 ^ 2) + (22.22 ^2) +(66.66 ^ 2)

i.e., 123.43 + 493.72 +4443.55

i.e., 5060.70

It indicates that the industry is highly concentrated.

c.71.13 .It indicates that the industry is highly concentrated.

d.Lerner index is given by (P - MC) / P

i.e., (20.50 - 17.50) / 20.50 i.e.,14.63% for firm 3 as it has the largest market share.

e.Price elasticity of Firm 3 => (20.50 / 17.50) = (n/n+1) i.e., n = -6.83

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e) The price elasticity demand of the largest firm

(p-ci/p) = ((alpha) * i/n))

i.e., (