Practical men, who believe themselves to be quite exempt from any intellectual influences, are usually slaves of some defunct economist. (Keynes)

Many have recently said 1) US industries have become more concentrated lately, 2) this is a bad thing, and 3) inadequate antitrust enforcement is in part to blame. (See many related MR posts.)

I’m teaching grad Industrial Organization again this fall, and in that class I go through many standard simple (game-theoretic) math models about firms competiting within industries. And occurs to me to mention that when these models allow “free entry”, i.e., when the number of firms is set by the constraint that they must all expect to make non-negative profits, then such models consistently predict that too many firms enter, not too few. These models suggest that we should worry more about insufficient, not excess, concentration.

Two examples:

“Cournot” Quantity Competitio n Firms pay (the same) fixed cost to enter an industry, and (the same) constant marginal cost to make products there. Knowing the number of firms, each firm simultaneously picks the quantity it will produce. The sum of these quantities is intersected with a linear demand curve to set the price they will all be paid for their products.

n Firms pay (the same) fixed cost to enter an industry, and (the same) constant marginal cost to make products there. Knowing the number of firms, each firm simultaneously picks the quantity it will produce. The sum of these quantities is intersected with a linear demand curve to set the price they will all be paid for their products. “Circular City” Differentiated Products Customers are uniformly distributed, and firms are equally distributed, around a circle. Firms pay (the same) fixed cost to enter, and (the same) constant marginal cost to serve each customer. Each firm simultaneously sets its price, and then each customer chooses the firm from which it will buy one unit. This customer must pay not only that firm’s price, but also a “delivery cost” proportional to its distance to that firm.

Customers are uniformly distributed, and firms are equally distributed, around a circle. Firms pay (the same) fixed cost to enter, and (the same) constant marginal cost to serve each customer. Each firm simultaneously sets its price, and then each customer chooses the firm from which it will buy one unit. This customer must pay not only that firm’s price, but also a “delivery cost” proportional to its distance to that firm. [I also give a Multi-Monopoly example in my next post.]

In both of these cases, when non-negative profit is used to set the number of firms, that number turns out to higher than the number that maximizes total welfare (i.e., consumer value minus production cost). This is true not only for these specific models I’ve just described, but also for most simple variations that I’ve come across. For example, quantity competition might have increasing marginal costs, or a sequential choice of firm quantity. Differentiated products might have a quadratic delivery cost, allow price discrimination by consumer location, or have firms partially pay for delivery costs.

Furthermore, we have a decent general account that explains this general pattern. It is a lot like how there is typically overfishing if new boats enter a fishing area whenever they expect a non-negative profit per boat; each boat ignores the harm it does to other boats by entering. Similarly, firms who enter an industry neglect the costs they impose on other firms already in that industry.

Yes, I do know of models that predict too few firms entering each industry. For example, a model might assume that all the firms who enter an industry go to war with each other via an all-pay auction. The winning firm is the one who paid the most, and gains the option to destroy any other firm. Only one firm remains in the industry, and that is usually too few. However, such models seem more like special cases designed to produce this effect, not typical cases in the space of models.

I’m also not claiming that firms would always set efficient prices. For example, a sufficiently well-informed regulator might be able to improve welfare by lowering the price set by a monopolist. But that’s about the efficiency of prices, not of the number of firms. You can’t say there’s too much concentration even with a monopolist unless the industry would actually be better with more than one firm.

Of course the world is complex and space of possible models is vast. Even so, it does look like the more natural result for the most obvious models is insufficient concentration. That doesn’t prove that this is in fact the typical case in the real world, but it does at least raise a legitimate question: what theory model do people have in mind when they suggest that we now have too much industry concentration? What are they thinking? Can anyone explain?

Added 11a: People sometimes say the cause of excess concentration is “barriers to entry”. The wikipedia page on the concept notes that most specific things “cited as barriers to entry … don’t fit all the commonly cited definitions of a barrier to entry.” These include economies of scale, cost advantages, network effects, regulations, ads, customer loyalty, research, inelastic demand, vertical integration, occupational licensing, mergers, and predatory pricing. Including these factors in models does not typically predict excess concentration.

That wiki page does list some specific factors as fitting “all the common definitions of primary economic barriers to entry.” These include IP, zoning, agreements with distributors and suppliers, customers switching costs, and taxes. But I say that models which include such factors also do not consistently predict excess firm concentration. And I still want to know which of these factors complainers have in mind as the source of the recent increased US concentration problem that they see.

Added 7Sep: Many have in mind the idea that regulations impose fixed costs that are easier on larger firms. But let us always agree that it would be good to lower costs. Fixed costs are real costs, and can’t be just assumed away. If you know a feasible way to actually lower such costs, great let’s do that, but that’s not about excess concentration, that’s about excess costs.

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