Question

You are the manager in a market composed of eight firms, each of which has a 12.5 percent market share. In addition, each firm has a strong financial position and is located within a 100 -mile radius of its competitors.

a. Calculate the premerger Herfindahl-Hirschman index (HHI) for this market.

b. Suppose that any two of these firms merge. What is the postmerger HHI?

c. Based only on the information contained in this question and on the Horizontal Merger Guidelines described in this chapter, do you think the Justice Department (or FTC) would attempt to block a merger between any two of the firms? Explain.

Short answer

1. HHI=1250
2. HHI=1562
3. FTC would challenge but might allow the merge

Step-by-step solution

To find the HHI for this market

The Herfindahl-Hirschman index (HHI) is calculated with equation:

$\mathrm{HHI}=10,000\times {\mathrm{w}}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{w}}_{\mathrm{i}}^2$where${\mathrm{w}}_1$ represents company's share of a market.

Since we have 8 companies with the same market share which is $12.5\%,$the for this market is:

$\begin{array}{c}\text{HHI}=10,000\times 8\times {0.125}^2\\ =10,000\times 8\times 0.015625\\ =1,250\end{array}$

To find the market after the merge.

After two companies merge and combine their market shares, we now have 7 companies on the market and one of them has a market share which is twice bigger than the rest. This means that 6 companies have market share of 12.5%, and one company (the one that merged two companies) has a market share of 25%.

The $\mathrm{HHI}$ for this market after the merger is:

$\begin{array}{c}{\text{HHI}}_{\text{post-merge}}=10,000\times \left(6\times {0.125}^2+{0.25}^2\right)\\ =10,000\times (0.09375+0.0625)\\ =10,000\times 0.15625\\ =1,562.5\end{array}$

To find the Herfindahl-Hirschman index

Since the difference in Herfindahl-Hirschman index (HHI) before and after the merger is larger than 200 (which rises antitrust concerns),

$\begin{array}{l}{\mathrm{HHI}}_{\mathrm{post}-\mathrm{merge}}-{\mathrm{HHI}}_{\mathrm{pre}-\mathrm{merge}}\\ =1,562.5-1,250\\ =312.5312.5>200\end{array}$

Thus, the FTC would probably challenge the merge.

However, the post mergeris in the category of moderately concentrated markets (between 1,500 and 2,000 ), the FTC could allow the merge if there would be no more merges that would rise antitrust concerns.

To sum up, Justice Department (or FTC) would challenge but might allow the merge according to Horizontal Merger Guidelines