The Few

in print · The Power · plate iv

A few sellers must reckon with one another’s responses as well as their own costs and customers. Quantity competition, price competition and repeated restraint can produce different prices with the same number of firms. Original examples make the temptation to depart from joint restraint explicit, then show why observation, credible responses and entry govern what can last.

A common interest does not choose a common course.The argument of this plate

Between the single seller and the anonymous crowd stand the firms that know one another by name. A new factory, a discount, a larger shipment enters their calculations twice: first as something that changes the firm’s own earnings, then as something to which its rivals may respond. A seller in this position cannot settle his choice by looking only at his customers and his costs. He must also form a view of other sellers who are forming a view of him. This is oligopoly’s peculiar difficulty. A few firms can have a common interest in restraint while each has an individual interest in being the one firm that does not restrain itself.

Cournot made the dependence precise by giving the producers a quantity to choose. Each chooses its output against the output supplied by the other, and the market price clears their combined production. The equilibrium occurs where neither can improve its return by changing its own quantity alone. It is a position of mutual best responses, which need not be the position that maximizes their combined profit. Cournot’s two springs could earn more together by behaving as one proprietor. Their separate ownership mattered because an output that served their joint interest left each owner a profitable way to depart from it.

Consider two invented firms selling the same good, each able to produce another unit at a cost of twenty. Let the market price be one hundred minus their combined output. If the other firm supplies twenty, the best quantity to produce is thirty. If the other supplies thirty, the best quantity is twenty-five. The two best-response schedules meet when each supplies twenty-six and two-thirds, making total output fifty-three and one-third and the price forty-six and two-thirds. Each then earns about seven hundred and eleven. The price remains above the cost of an extra unit, although the firms have made no agreement to keep it there. Independent quantity competition itself produces that gap.

Joint restraint is more profitable and less secure. The same firms could maximize their combined earnings by supplying forty units at a price of sixty. An equal division gives each twenty units and a profit of eight hundred. But if one keeps to twenty, the other can increase to thirty, lower the market price to fifty, and raise its own profit to nine hundred. The gain from breaking ranks is private; part of its cost falls upon the rival. Once both adjust independently, the result is the quantity equilibrium just calculated. The breakdown of restraint does not carry this particular market all the way to price equal to marginal cost. It carries it to the outcome of the particular contest the firms are playing.

The variable a firm can change is part of the explanation, not a detail to be added after counting the firms. Suppose the same two firms instead post prices for an identical product, have enough capacity to meet the entire market, and face buyers who all choose the cheaper seller, dividing evenly at a tie. A shared price above twenty that attracts buyers can be profitably undercut by a small amount, winning the market. At twenty, an undercut loses money and an increase loses sales. Two sellers suffice for a price equal to marginal cost under these assumptions. Capacity limits, differentiated products, search costs or restrictions on changing prices can undo the conclusion. The number two is unchanged; the mechanism of competition has changed.

Repeated encounters can make present restraint depend on future earnings. Return to the quantity example and imagine that each firm supplies twenty so long as neither has departed, but both switch permanently to the quantity equilibrium after a departure. The punishment is credible in the limited sense that, once it begins, neither firm wants to change its quantity alone. A firm must weigh the immediate extra hundred from cheating against the repeated loss of about eighty-nine in every later period. If future profits are discounted by a factor of at least nine-seventeenths per period, the stipulated strategy can sustain restraint. A sufficiently long shadow of future business can therefore support a high price without erasing the temptation to cut it.

An enduring relationship alone does not tell firms what their rivals have done. A seller may lose orders because another has secretly cut its effective price, because a customer has closed a factory, or because its own delivery has disappointed. A nominal price can stay fixed while credit, quality, service or rebates change. Stigler treated the policing of collusion as a problem of information: participants need enough evidence to distinguish an ordinary fluctuation from a profitable departure. His analysis also makes the buyers matter. Large transactions, shifting customers and differences in the terms offered create opportunities that a common posted price may conceal. The path from a few sellers to effective restraint runs through observability as well as incentives.

Quiet coordination is thus possible, but its possibility is not proof that it explains a particular quiet market. The same price movement may follow a common increase in fuel costs or a common change in demand. A price that remains high may reflect unilateral pricing of differentiated products. Conversely, a sequence of discounting and retaliation may sustain a pattern no single firm could enforce alone. The investigator needs evidence about costs, alternatives, the visibility of decisions and the responses those decisions induce. Similar outcomes can emerge from different strategies, and the strategy cannot be read from the similarity alone. Whether the observed conduct satisfies a legal standard is a further inquiry, with its own evidence and rules.

Each firm would like the others to restrain themselves.

Entry changes the value of the future on which restraint depends. A newcomer may prefer the immediate gain from expansion to the preservation of a price whose benefits have accrued to established firms. An incumbent with unused capacity may be able to answer that expansion; another with different costs may prefer to accommodate it. Differences among firms also make agreement over shares difficult: a low-cost producer gives up more by accepting the same quantity as a high-cost rival. These are reasons to examine a market’s history and technology. They are also reasons not to treat every concentrated market as one representative firm multiplied a few times.

The few remain together only while the gains from a shared course exceed the gains from departure, given what each can observe and credibly do afterward. They remain apart when expansion, undercutting, innovation or entry promises more. Neither tendency abolishes the other. The price records the temporary settlement between them, and it may record that settlement without revealing how it was reached. Product differentiation adds a further twist: a rival can be close enough to constrain a seller and different enough to leave him some customers at a higher price. The next plate follows that small distance between alternatives, where competition and pricing discretion meet.