Chapter 12, Problem 1VQP

To determine

Calculation of Herfindahl index and the concentration ratio.

Explanation of Solution

 There are five firms in the industry namely A, B, C, D, and E. Each firms’ market share is shown in the below table.

Table 1

Firms	Market share (%)
A	22
B	22
C	22
D	22
E	12

The Herfindahl–Hirschman index can be calculated using the share of market, which is shown in the above table.

$\begin{array}{c}\text{HHI}={\text{S}}_1^2+{\text{S}}_2^2+{\text{S}}_3^2{\text{+S}}_4^2+{\text{S}}_5^2\\ ={22}^2+{22}^2+{22}^2+{22}^2+{12}^2\\ =2080\end{array}$

The Herfindahl–Hirschman index of the five firms in the industry is 2080.

The first four firm’s market concentration ration in the industry is calculated below:

$\begin{array}{c}\text{MCR}=22+22+22+22\\ =88\end{array}$ 

The market concentration ratio of the first four firms is 88 percentage.

Economics Concept Introduction

Herfindahl–Hirschman index: The HHI index uses to calculate the market concentration using the formulae.

$\text{HHI}={\text{S}}_1^2+{\text{S}}_2^2+{\text{S}}_3^2\text{+}\mathrm{...}+{\text{Sn}}^2$

Here,

S = market share of the firm

n= number of firms