Suppose that the most popular car dealer in your area sells

Suppose that the most popular car dealer in your area sells 4 percent of all vehicles.

Instructions: Enter your answers as whole numbers.

a. If all other car dealers sell either the same number of vehicles or fewer, what is the largest value that the Herfindahl index could possibly take for car dealers in your area?

b. In that same situation, what would the four-firm concentration ratio be?

Solution

If the most popular car dealer sells 4% of all the vehicles and other car dealers either sell same or less, then in order to get the largest Herfindahl index we need to assume that all dealers in the market sell 4% as that will give us the maximum HHI. If we assume anything less than 4% for the other dealers than we wont get the maximum value.

Now with that information we need to find out how many dealers are going to be in market to complete the market of 100%. If every dealer has 4% of market share so the number of dealers in the market are 100/4 = 25

Hence there are 25 dealers in the market

With the above information, let\'s now find Herfindahl index and four-firm concentration.

(a) The Herfindahl index is simply the sum of the squares of the market shares for each firm within the industry.

(4)²+(4)²+(4)²+................(4)²+(4)² i.e. (4)² x 25 times

which is 16 x 25 = 400

Hence largest value that HHI can takes in this area is 400

(b) Four-firm concentration ratio sum of the market share of the 4 largest firms in the industry.

In this case market share of 4 largest firms is 4+4+4+4 = 16