A given market was initially segmented evenly among 22 firms (Phase 1). Five yea

Question

A given market was initially segmented evenly among 22 firms (Phase 1). Five years later, the market was still segmented evenly among competing firms, but there were now only 9 firms (Phase 2). Eventually 7 firms emerged with equal portions of the market (Phase 3), but a move toward deregulation of the industry has prompted two of the firms to merge. (Note: The HHI is measured in units of %2. For example, 50% x 50% = 2,500%2 (or, in decimal form, 0.50 x 0.50 = 0.25). To make the conversion from decimal to percentage form mathematically, multiply the answer by 10,000; using the same example, this yields 0.50 x 0.50 x 10,000 = 2,500.)

Determine the Herfindahl-Hirschman Index for the first phase. Round your answer to two decimal places.

Determine the Herfindahl-Hirschman Index for the second phase. Round your answer to two decimal places.

Determine the Herfindahl-Hirschman Index for the third phase. Round your answer to two decimal places.

Determine the Herfindahl-Hirschman Index with two merging firms. Round your answer to two decimal places.

Explanation / Answer

Herfindahl-Hirschman Index for the first phase

22 firms with equal share of the market (each firm’s share = 100/22 =4.54%)

HHI = S1^2 + S2^2+……………………..S22^2

= (0.045 * 0.045 *10,000)^2 + (0.045*0.045)^2…….

= 445.5

Herfindahl-Hirschman Index for the second phase

9 firms with equal share of market (each firm’s share =100/9 =11.11% )

= (0.111*0.111*10,000)*9

=122.22

Herfindahl-Hirschman Index for the third phase

= (11.11%)^2 + (11.11)^2+ (11.11%)^2 + (11.11)^2 + (11.11%)^2 + (11.11%)^2+ (11.11%)^2 + (22.22%)^2 + (22.22%)^2

=(0.0123*10,000)* 7 + 987.456

=1851.48

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