Final answer:
When two firms in an industry merge, the new HHI index can be calculated by adding the square of the merged firm's market share to the original HHI index and then subtracting the squares of the market shares of the third and fourth firms, which have now merged.
Step-by-step explanation:
The Herfindahl-Hirschman Index (HHI) is a measure of market concentration and is calculated by summing the squares of the market shares of all firms in the industry. When two firms in an industry merge, the new HHI index can be calculated by adding the square of the merged firm's market share to the original HHI index and then subtracting the squares of the market shares of the third and fourth firms, which have now merged.
For example, let's say the market shares of the original firms were Firm A with 25%, Firm B with 20%, Firm C with 15%, and Firm D with 10%. If Firm C and Firm D merge, their combined market share would be 25%. To calculate the new HHI index, we would add 25² to the original HHI index and then subtract the squares of the market shares of Firm A and Firm B.