Question

They purport to measure the relative size of the firms in an industry. Industries in which a few firms supply the majority of the market output are said to have relatively high concentration. Those in which most firms supply only a small fraction of the total market are said to have relatively low concentration. Passenger car and light truck manufacturing is an example of a high concentration industry while most large scale agriculture commodity markets (i.e. wheat, corn) have low concentration. The four-firm concentration ratio and Herfindahl-Hirschmann index (HHI) are two measures of concentration.

4. An industry consists of three firms with Sales of $200,000, $500,000 and $400,000.

a. Calculate the Herfindahl-Hirschmann Index (HHI) for this industry.

b. Calculate the four-firm concentration ratio (C₄).

c. Based on the FTC and DOJ Horizontal Merger Guidelines described in Chapter 7, explain specifically whether
    you think the Department of Justice would attempt to block a horizontal merger between two firms with sales of
    $200,000 and $400,000. Calculate the new concentration ratios that would result if this merger were to occur to
    justify your answer.

Answer 1

Solution:

Market share percent for first firm = 200000/(200000+500000+400000) = 2/11 = 18.18%

Market share percent for second firm = 500000/(200000+500000+400000) = 5/11 = 45.45%

Market share percent for third firm = 400000/(200000+500000+400000) = 4/11 = 36.36%

a. Herfindahl-Hirschmann Index (HHI) = sum of square of market share percent of all firms

= 18.18^2 + 45.45^2 + 36.36^2 = 3718

b. Four firm concentration ratio = summation of percentage market share of top four firms

= 18.18+45.45+36.36 = 99.99 or 100% due to rounding up

c. If merger takes place then new HHI = 10000{(6/11)^2 + (5/11)^2} = 5040.31. Since HHI increases on merger, department of justice will try to block this merger.

New Four firm concentration ratio = 54.54+45.45 = 99.99 or 100% due to rounding up.