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How Do You Calculate Hhi



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Question
how would i calculate the HHI for an industry using the market share values?
market share values, include top 4,8,20,50 firms market share, how do i calculate the HHI?

Answer
HHI is the Herfindalh index and it is computed as sum of square sof market shares of firms. I.e. take top 4 firms, find their market shares square each of them add them up.



Question
Why is the largest possible value of the Herfindahl-Hirschman Index (HHI) 10,000?
A. An HHI of 10,000 corresponds to a monopoly--that is, a single firm with 100% market share. B. An HHI of 10,000 corresponds to 100 firms with 1% market share each. C. The Justice Department assigns a value of 10,000 to the most concentrated industry, and then calculates the HHI of other industries as a percentage. D. If the HHI of an industry is greater than 10,000, the Justice Department automatically regulates it.

Answer
A. It's purely math based. Within an industry a firm is assigned a number that is one to one related to it's marke share. This number is squared for each firm and then all these numbers are summed together. Now consider a monopoly. It has 100% of the market so gets 100 assigned to it. The rest of the firms have 0% so are assigned 0. Squaring gives you 10,000 to the first firm while the rest get 0 each. Summing gives you 10,000. Now say that one other firm gets x% of the market away from the monopoist. Then the HHI is HHI = (100-x)^2 + x^2 = 10,000-200*x + x^2 + x^2 = 10,000-200*x + 2*x^2 Now x is a very small number. So when it's squared it's even smaller. Adding double a very small number is adding very little still. And taking away 200*x is subtracting a rather large number when compared to 2*x^2. So HHI falls. From the design of the HHI then, only a monopoly can ever achieve 10000.



Question
I need help with the Herfindahl Index?
1 calculate the pre-merger H-index for all ten firms 2 calculate the post-merger H-index for the nine remaining firms to determine the impact of this merger industry's h-index 3 compare the results of the two calculations Top ten firms selling cars and light trucks in the US in October 2008 and their market share : GM 20% Toyota 18% Ford 16% Chrysler 11% Honda 10% Nissan 7% BMW 3% Volkswagen 3% Hyundai 3% Mazda 2% Will give full points.

Answer
1. Square each firm's market share and add them all together. (20)^2 + (18)^2 + (16)^2 ... (3)^2 + (3)^2 + (2)^2 = 1281. 2. Whatever two firms you're supposed to merge, do that, and repeat the calculation above. For example, if GM and Toyota merge, the calculation becomes: (38)^2 + (16)^2 ... (3)^2 + (3)^2 + (2)^2 = 2001. 3. In the example above, GM merging with Toyota significantly decreases the amount of competition in the industry. By comparison, if Hyundai and Mazda merge, the HHI becomes 1293. While this is a decrease in competition, it is a very small decrease.




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