# Statistical distribution of firms by revenue in competitive market

I would like to produce a simple distribution of competitive market firms based on their revenues. I know the number of firms in the market n, the total market revenue TR and, therefore, also the average revenue per firm.

I had the idea that I could bin revenues and apply the Poisson distribution to populate a distribution of firms in the market based on revenue. For example, 2 firms with $$0 -$$2 M in revenues, 4 firms with $$2 -$$4 M in revenues, etc.

Is anyone familiar with any research regarding the distribution of firms' revenues in a competitive market that would provide guidance or confirmation of doing something like this?

• Although I am not familiar with the topic, I would guess using the lognormal distribution would make more sense than Poisson. Dec 28 '19 at 8:27
• What exactly do you mean by competitive market? In most theoretical models with free entry the firms have the same technology. As a result, in equilibrium they all have the same revenue. Dec 29 '19 at 8:26
• In real life defining a precise product market is very difficult. Is coke on the same market as Pepsi? What about sparkling water? There are same consumers for whom these are substitutes. These is a subject of study in antitrust cases, but in those cases usually there are only a few big firms on a market, not enough to properly fit a distribution. Dec 29 '19 at 8:27