The theory of double marginalization, also known as the problem of successive
monopoly, was independently developed by Cournot (1838) and Ellet (1839). Spengler
(1950) is the classic reference for double marginalization in the vertical integration
context (i.e., where the two monopolists and a final good producer and its supplier).
Since Spengler was published in English before Cournot and Ellet, sometimes he is cited
as originating the idea.
The problem of double marginalization occurs when two firms independently set prices
for complementary goods. This framework can be used in both the case of traditional
complements (e.g., tea and sugar) and in the case of a vertical relationship (e.g., where
the complementary goods are a manufactured good and the retail service whereby the
good is sold).
Consider two monopolists who produce complementary products. If they independently
set prices (or quantities), then the prices chosen would be higher then those chosen by a
merged firm, since each firm ignores the negative externality of its price on the profits of
the other firm. If this effect is particularly strong, it can lead the merged firm to set price
below marginal cost for one of the two products.
Note that this effect does not require perfect monopoly. Both firms must have some
market power (more specifically, they must have the ability to price above marginal cost
and earn positive profits). If one of the two firms lacked any market power, then they
would not be earning any profits, and the pricing of the other firm would have no
negative externality on that firm (at least in the long run). Thus, double marginalization
requires some market power by both firms, but not necessarily a full monopoly.
Nor does the double marginalization effect require perfect complementarity between the
two goods. As long as prices of each firm exert a negative externality on the profits of
the other firm, this effect will hold.
The double marginalization effect is closely related to the normal effect whereby
horizontal mergers raise prices. In the case of horizontal mergers, the goods are
substitutes. This means that the price of one firm exerts a positive externality on the
other firms (a higher price for my competitor’s product means more profits for me).
Thus, when horizontal competitors set prices independently, they price too low, relative
to the prices that would maximize their total profits. When these firms merge, collude, or
otherwise find a way to internalize this externality, they raise prices.
The exact opposite happens in the case when the goods are complements. The externality
is negative (a higher price for a complement means less profit for me), which means that
independent pricing results in prices that are too low relative to the prices that maximize
collective profits. Thus, when producers of complements merge, collude, or otherwise
find a way to internalize this externality, they lower prices, resulting in a Pareto
improvement (since consumers also prefer lower prices).
The double marginalization problem can be solved in a number of different ways. I have
already mentioned collusion (which could be implemented by a contract specifying a
maximum resale price, which may or may not be legal under U.S. antitrust laws) and
vertical mergers as two possibilities. A third possibility involves the use of franchise
fees. This is easiest to see in the case where the two firms are monopolies in a vertical
relationship (an upstream monopoly and a downstream monopoly). The upstream firm
could charge its marginal cost to the downstream firm, and allow the downstream firm to
extract the full monopoly profit. In return, the downstream firm would pay the upstream
firm a lump sum franchise fee. This allows the upstream firm to capture a share of the
monopoly profit, while effectively eliminating the double marginalization problem
(since, conditional on one firm charging marginal cost, the other firm maximizes joint
profits when it prices independently).
Which solution is best will depend on industry details that go beyond the basic concern of
double marginalization. In more general models, there may be asymmetric information,
incomplete contracts, antitrust laws, and other externalities, and all of these issues will be
affected by the regime chosen for jointly determining prices. Thus, the optimal choice of
a strategy for dealing with double marginalization will have to consider the effect
alleviating or aggravating other problems.
References
Cournot, A. (ed.) (1838 originally, 1971 English translation), Mathematical Principals of
the Theory of Wealth. August M. Kelly, New York, Chapter IX.
Ellet (1839 originally, 1966 English translation), An Essay on the Laws of Trade.
Augustus M. Kelly, New York, pp. 77-80.
Spengler, J.J. (1950), “Vertical Integration and Antitrust Policy,” Journal of Political
Economy, pp. 347-352.