Question

Suppose that the most popular car dealer in your area sells 10 percent of all vehicles. 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? In that same situation, what would the four-firm concentration ratio be?

Assume that the most efficient production technology available for making vitamin pills has the cost structure given in the following table. Note that output is measured as the number of bottles of vitamins produced per day and that costs include a normal profit.

a. What is ATC per unit for each level of output listed in the table?

Output	TC	MC	ATC
51,000	$175,000	$0.65
101,000	225,000	1.15
151,000	262,500	1.74
201,000	375,500	2.50

b. Is this a decreasing-cost industry? Yes or No

c. Suppose that the market price for a bottle of vitamins is $1.74 and that at that price the total market quantity demanded is 317,100,000 bottles. How many firms will there be in this industry?

    

d. Suppose that, instead, the market quantity demanded at a price of $1.74 is only 151,000. How many firms do you expect there to be in this industry?

    

e. Review your answers to parts b, c, and d. Does the level of demand determine this industry’s market structure?

Answer 1

(a) The Herfindahl index increases as the market share of each firms increases. The highest possible market share in this case is 10% or 0.1. Hence, there would be 9 other car dealers whose share would be 0.1. The HI (in percentage terms) would be as or or or or . To calculate the index without the percent, we have or or .

The stated HI is maximum, as if we break even one share as 0.09 and 0.01 or 0.08 and 0.02, etc, instead of 0.1, we would have inequality. For example, , and the HI would decrease.

The four firm index would be maximized in a similar manner, and would be as , for s_i be the highest market share of top four firms. We have or .