Question

Suppose that the most popular car dealer in your area sells 10 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?

Answer 1

a. The largest possible Herfindahl index (HHI) in this scenario is 10,000.

b. The four-firm concentration ratio (CR4) would be 40%.

Step-by-step explanation:

a. Herfindahl index (HHI):

HHI measures the concentration of market share in an industry.

In this case, the most popular dealer holds 10% of the market share.

If all other dealers have the same or less share (10% or less), the remaining market share would be equally distributed among them.

Assuming there are a total of 10 car dealers (including the most popular one), each of the remaining 9 would have 10% / 9 ≈ 1.11% share.

To calculate the HHI, we square the market share of each dealer and add them up:

HHI = (10^2) + (1.11^2) * 9 ≈ 100 + 9.99 ≈ 109.99

Since HHI is typically reported in whole numbers, we round up to the nearest thousand:

Largest possible HHI = 109.99 ≈ 10,000

b. Four-firm concentration ratio (CR4):

CR4 measures the market share held by the top four firms in an industry.

In this scenario, the top four firms would be the most popular dealer (10%) and the next three with the largest share (assuming they all have 1.11% each).

CR4 = (10% + 3 * 1.11%) = 10% + 3.33% ≈ 40%

Therefore, in this hypothetical scenario where the most popular dealer holds 10% of the market share and all others have the same or less, the HHI could reach a maximum of 10,000, and the top four firms would control 40% of the market.

Answer 2

1. Herfindahl index = 400

2. 40%

Step-by-step explanation:

1. Remember, the Herfindahl index is an index used to determine the level of market concentration in an industry. Assuming the total car dealer firms are four in number, we can derive the largest value that the Herfindahl index could possibly take for car dealers in the area using the formula:

`HHH=S1^(2) + S2^(2) + S3^(2) + S4^(2) +... Sn^(2)`

Thus, the HHH =
`10^(2) + 10^(2)+ 10^(2) +10^(2) = 400`

2. The four-firm concentration ratio is calculated by summing the individual market share percentage; 10% + 10% + 10% + 10% = 40%