If a firm with a 10 percent market share merges with a firm with a 15 percent market share and the other firms have market shares of 40 percent, 15 percent, 10 percent, and 10 percent, respectively, the Herfindahl index will _____.

Question

If a firm with a 10 percent market share merges with a firm with a 15 percent market share and the other firms have market shares of 40 percent, 15 percent, 10 percent, and 10 percent, respectively, the Herfindahl index will _____.​

Quizplus · Accepted Answer

To calculate the change in the Herfindahl index after the merger, we need to first calculate the initial index:

Market share^2 of each firm:
(0.1)^2 + (0.15)^2 + (0.4)^2 + (0.15)^2 + (0.1)^2 + (0.1)^2 = 0.365

Therefore, the initial Herfindahl index is 365.

After the merger, the market share of the two merging firms will be combined:

New market share of the merged firms = 0.1 + 0.15 = 0.25

Market share^2 of each firm:
(0.25)^2 + (0.4)^2 + (0.15)^2 + (0.1)^2 + (0.1)^2 = 0.2525

Therefore, the new Herfindahl index is 252.5.

The change in the index is:

252.5 - 365 = -112.5

This means that the Herfindahl index will fall by 112.5 after the merger.

However, the question is asking for the change in the index in terms of percentages, rather than absolute values. To calculate this, we need to take the absolute value of the change, divide it by the initial index, and multiply by 100:

|-112.5| ÷ 365 × 100 = 30.8%

So the answer is not given in any option.

If a Firm with a 10 Percent Market Share Merges