Chapter 13, Problem 1P

To determine

The four-firm concentration ratio and Herfindahl index.

Explanation of Solution

The four-firm concentration ratio helps to identify the extent of the market share handled by the four largest firms in the industry. The four largest firms’ market shares are 23%, 22%, 18% and 12% respectively. The four-firm concentration ratio can be calculated by adding the market shares of the four largest firms in the industry as follows:

$\begin{array}{c}\text{Four-firm concentration ratio}=\left[\begin{array}{l}\left({\text{Market share}}_{\text{Firm 1}}\right)+\left({\text{Market share}}_{\text{Firm 2}}\right)\\ +\left({\text{Market share}}_{\text{Firm 3}}\right)+\left({\text{Market share}}_{\text{Firm 4}}\right)\end{array}\right]\\ =\left[\left(23\right)+\left(22\right)+\left(18\right)+\left(12\right)\right]\\ =75\end{array}$

Thus, the four-firm concentration ratio is 75%.

The Herfindahl index can be calculated by squaring the market share of each firm and summing them together.  We have the market shares of the industry as follows: 23, 22, 18, 12, 11, 8 and 6. The Herfindahl index can be calculated as follows:

$\begin{array}{c}{\text{Herfindahl index}}_{\text{Industry A}}=\left[\begin{array}{l}{\left({\text{Market share}}_{\text{Firm 1}}\right)}^2+{\left({\text{ share}}_{\text{Firm 2}}\right)}^2+{\left({\text{ share}}_{\text{Firm 3}}\right)}^2\\ +{\left({\text{ share}}_{\text{Firm 4}}\right)}^2+{\left({\text{ share}}_{\text{Firm 5}}\right)}^2+{\left({\text{ share}}_{\text{Firm 6}}\right)}^2\\ +{\left({\text{ share}}_{\text{Firm 7}}\right)}^2\end{array}\right]\\ =\left[{\left(23\right)}^2+{\left(22\right)}^2+{\left(18\right)}^2+{\left(12\right)}^2+{\left(11\right)}^2+{\left(8\right)}^2+{\left(6\right)}^2\right]\\ =\left[529+484+324+144+121+64+36\right]\\ =1072\end{array}$

The HHI index of the industry is 1072.

When the top three firms are combined to form a single firm, the four-firm concentration ratio as well as the Herfindahl index will change as follows:

The four-firm concentration ratio helps to identify the extent of the market share handled by the four largest firms in the industry. The four largest firms’ market shares are 63%, 12%, 11% and 8%, respectively. The four-firm concentration ratio can be calculated by adding the market shares of four largest firms in the industry as follows:

$\begin{array}{c}\text{Four-firm concentration ratio}=\left[\begin{array}{l}\left({\text{Market share}}_{\text{Firm 1}}\right)+\left({\text{Market share}}_{\text{Firm 2}}\right)\\ +\left({\text{Market share}}_{\text{Firm 3}}\right)+\left({\text{Market share}}_{\text{Firm 4}}\right)\end{array}\right]\\ =\left[\left(63\right)+\left(12\right)+\left(11\right)+\left(8\right)\right]\\ =94\end{array}$

Thus, the new four-firm concentration ratio is 94%.

The Herfindahl index can be calculated by squaring the market share of each firm and summing them together.  We have the market shares of the industry as follows: 63, 12, 11, 8 and 6. The Herfindahl index can be calculated as follows:

$\begin{array}{c}{\text{Herfindahl index}}_{\text{Industry A}}=\left[\begin{array}{l}{\left({\text{Market share}}_{\text{Firm 1}}\right)}^2+{\left({\text{Market share}}_{\text{Firm 2}}\right)}^2+{\left({\text{Market share}}_{\text{Firm 3}}\right)}^2\\ +{\left({\text{Market share}}_{\text{Firm 4}}\right)}^2+{\left({\text{Market share}}_{\text{Firm 5}}\right)}^2\end{array}\right]\\ =\left[{\left(63\right)}^2+{\left(12\right)}^2+{\left(11\right)}^2+{\left(8\right)}^2+{\left(6\right)}^2\right]\\ =\left[3969+144+121+64+36\right]\\ =4334\end{array}$

The new HHI index of the industry is 4334.

Economics Concept Introduction

Concept introduction:

Four-firm concentration ratio: The four-firm concentration ratio is the total market share handled by the four largest firms in the industry. It helps to identify the extent of the market controls of the four largest firms in the industry.

Herfindahl index: The Herfindahl index is the measure of the concentration of the market. The concentration in the market can be calculated by squaring the market share of each competing firms in the industry and summing them. Usually the HHI value ranges from 0 to 10,000.