What’s the minimum number of firms you can have in order to have a competitive market? HHI index is F1^2 + F2^2 + … Fk^2, where Fi is the market share of the top 50 firms in the industry (or all companies if they are less than 50). HHI = 10,000, if there is only one firm (monopoly) because 100^2 = 10,000. HHI = 2500, if there are 4 firms each with 25% market share. You get the point. If HHI < 1000 then the market is competitive. When does this happen? I.e., what is the minimum k which makes HHI < 1000? I just made up this question and I’m not sure if it is easy or hard, nor do I know if it makes sense (yet) 
When they all face a horizontal demand curve:))
I like it when that happens…lets all tilt our demand curves sideways and drive those bastards out of business.
Like a consumer strike? starving?
Stop driving your car and see if gas prices keep going up! But lets get back to HHI.
@Map @dreary It doesn’t make too much sense to ask only for k, because of the k different Fi-values…
Think again.
i am open for new knowledge… If you have got a solution tell us - in my opinion the question itself is questionable.
10 each with 10 percent
I understand the caluculus but what do you want to tell with the result? If you have less than 10 firms in a market the market can’t be competetive?
Many factors must be taken into account to determine which market structure describes a particular market. Just taking in account results of HHI would give misleading results. both HHI and concentration ratio should be used to determine market structure, as results would give a better picture.
gameday0, do you have a formula for this? The answer should, strictly speaking, be more than 10, but we can say 10.
HHI < 1800
Nope, HHI < 1000 for competitive markets.