Question

Based only on the knowledge that the premerger market share of two firms proposing to merge was 30 percent each, an economist working for the Justice Department was able to determine that, if approved, the postmerger HHI would increase by 1,800. Which of the following equations is a general rule explaining how the Herfindahl-Hirschman index is affected when exactly two firms (Firm i and Firm j) in the market merge, where Si is the market share of firm i and Sj. is the market share of firm j? (Hint: Compare a2 + b2 with (a + b)2.)

Answer 1

The general rule for how the Herfindahl-Hirschman Index (HHI) is affected when two firms merge is calculated using the formula HHI Change = 2 * Si * Sj, where Si and Sj are the market shares of the merging firms.

Step-by-step explanation:

The equation that explains how the Herfindahl-Hirschman Index (HHI) is affected when two firms in the market merge, using their market shares Si and Sj, is:

HHI Change = 2 * Si * Sj

Considering that the premerger market share of each firm was 30%, and Si equals Sj, the equation becomes:

HHI Change = 2 * Si * Si

Given that we know the HHI will increase by 1800, we have:

1800 = 2 * Si * Si

1800 = 2 * (30)^2

1800 = 2 * 900

1800 = 1800

This confirms that the formula for the change in HHI due to a merger of two firms with market shares Si and Sj is 2 * Si * Sj, since it accurately predicts the change in HHI in this case.

Answer 2

A merger is an agreement that unites two existing companies into one new company. There are several types of mergers and also several reasons why companies complete mergers. Mergers and acquisitions are commonly done to expand a company's reach, expand into new segments, or gain market share.

When firms merge together, we have a synergy effect.

A synergy arises in a merger or acquisition when the combined value of the two firms is higher than the pre-merger value of both firms combined. For example, if firm A has a value of $500M, firm B has a value of $75M, and the merged firm has a value of $625M, there is a $50M synergy for this merger.

Synergy effect explains 2(a + b) can be greater than 2a + 2b. 2a + 2b is the market share of the two companies before merger which is $500m + $75m = $575m compared against the newly formed company's value after merger which is $625m. The synergy effect is additional $50m.

This is caused by cost reductions, due to efficiencies in the newly combined firm. Alternatively, they may arise due to new net incremental revenues brought about by the merged firm.