Chapter 11: Problem 1

Is it true that a merger between two firms that are not already in the top four by size can affect both the four-firm concentration ratio and the Herfindahl-Hirshman Index? Explain briefly.

Short Answer

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In conclusion, a merger between two firms that are not already in the top four by size can affect the Herfindahl-Hirshman Index (HHI) but has no impact on the four-firm concentration ratio (CR4). This is because the HHI considers the market shares of all firms in the industry, while the CR4 only focuses on the top four firms' market shares. In our example, the HHI decreased after the merger, indicating a slight reduction in industry concentration, while the CR4 remained unchanged.

Step by step solution

Concept of the Four-Firm Concentration Ratio (CR4)

The four-firm concentration ratio (CR4) measures the market share held by the top four largest firms in a specific industry. This helps to understand the level of market concentration and competitiveness in that industry. A higher CR4 ratio indicates a highly concentrated industry, whereas a lower CR4 ratio suggests more competition among many firms.

Concept of the Herfindahl-Hirshman Index (HHI)

The Herfindahl-Hirshman Index (HHI) is a measure of the concentration of an industry by considering the market shares of all firms in that industry. It is calculated by summing the squares of the market shares of all firms. Similar to the CR4, a higher HHI indicates a highly concentrated industry with limited competition.

Example of a merger between two smaller firms

Let's consider an industry with 6 firms. Market shares are as follows: 1. Firm A – 30% 2. Firm B – 25% 3. Firm C – 20% 4. Firm D – 10% 5. Firm E – 10% 6. Firm F – 5% Now, let's assume that Firm E and Firm F decide to merge. The market shares of the firms after the merger would be as follows: 1. Firm A – 30% 2. Firm B – 25% 3. Firm C – 20% 4. Firm D – 10% 5. Firm EF (merged) – 15%

Effects on the Four-firm concentration ratio (CR4)

Before the merger, CR4 = market share of the top four firms (A, B, C, and D) = 30% + 25% + 20% + 10% = 85%. After the merger, CR4 stays the same since the newly merged firm does not surpass any of the top four firms in terms of market share. Therefore, the merger does not have an impact on the CR4.

Effects on the Herfindahl-Hirshman Index (HHI)

Before the merger, HHI = \( (0.3^2) + (0.25^2) + (0.2^2) + (0.1^2) + (0.1^2) + (0.05^2) =\) 0.135 After the merger, HHI = \( (0.3^2) + (0.25^2) + (0.2^2) + (0.1^2) + (0.15^2) =\) 0.13 The HHI has decreased after the merger, signifying that the industry's concentration has reduced slightly. In conclusion, a merger between two firms that are not already in the top four by size can affect the Herfindahl-Hirshman Index but has no impact on the four-firm concentration ratio (CR4).