Suppose Fiat recently entered into an Agreement and Plan of Merger with Case for $4.3 billion. Prior to the merger, the market for four-wheel-drive tractors consisted of five firms. The market was highly concentrated, with a Herfindahl-Hirschman index of 2,765. Case’s share of that market was 22 percent, while Fiat comprised just 12 percent of the market. If approved, by how much would the post merger Herfindahl-Hirschman index increase?

Herfindahl-Hirschman index or simply the HH Index measures a market's level of competitiveness based on the number of firms participating in the industry.

HH Index has a maximum of 10,000 points for a market that is dominated by one firm and continues to reduce and tend towards 0 as the number of firms with equal sizes in the industry increases. In other words, the increase in an industry's HH Index is a function of the decrease in the number of firms in the industry and the disparities in sizes among the firms in the industry.

For acceptable levels of HH Index, the general consideration is that a market with HH Index between 1,500 and 2,500 has a moderate concentration, while any market with HHI higher than 2,500 points is highly concentrated.

To the Question,

the Success of the Merger between Fiat and Case would reduce the number of firms in the market and this will lead to an increased HHI,

The formula for increase in HH Index=

=10,000 (Maximum HHI Points) [(22% (Case's Market Share + 12% (Fiat's Market Share)^2 - (22%)^2- (12%)^2]

= 10,000 [(0.22 + 0.12)^2 - (0.22)^2 - (0.12)^2]

=10,000 (0.0528)

=528 Points

This means the Post Merger HH Index will increase by 528 Points from 2,765 to 3, 293 (2,765+528)