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

1. To maximize the Herfindahl Index means to have an industry with as much concentration as possible. That calls for firms that are as big as possible. With the largest firm controlling only 10%, the way to have the rest of the industry be as concentrated as possible would be for there to be 9 other firms that each also controlled 10% of the market (for a total of 10 firms each controlling 10%). In that situation, the Herfindahl index would be 1000 (= 10*(102)) and the four-firm concentration ratio would be 40% (= 4*10%)

Explanation:

Consider the following example: Suppose that the most popular car dealer in your area sells 10 percent of all vehicles. If all other car dealers sell either the same number of vehicles or fewer in the market then the largest number of dealers possible is 10. This follows from the fact that the largest share any dealer can have is 10%, and the sum of all dealer shares must equal 100% of the market, we therefore have a maximum number of firms at 10 (= 100%/10%).Given that the maximum number of firms in the market equals 10, at a maximum concentration share of 10% for all firms, the largest Herfindahl index possible is 1000 (=10 (number of firms) x 102(percentage squared for each firm)). This logic also implies that the four-firm concentration ratio (largest possible) is 40% (= 4 (largest four firms, could be any of the ten) x 10% (share of the market))

**In the second question please provide the table, i am unable to understand which value is for which variable**