Lecture Note on Double Marginalization
When firms in subsequent stages of a value chain have market power, the total profits
will be lower than what would be jointly optimal for them. The reason is that each firm,
in using its market power, will limit its output in order to increase prices and thus profits.
In doing so, however, it does not take into account the impact these actions have on the
other firms in the value chain. Jointly, these firms will thus exert too much market power
for their own good.
To see this in more practical terms, consider a monopolist newspaper company that sells
newspapers to newsstands. Each newsstand has a monopoly in its own territory. Assume
for simplicity that the marginal costs of producing a newspaper and of selling it are both
zero and that there are no fixed costs.
Consider the relationship between the newspaper company and one of the newsstands.
The final demand for newspapers for that newsstand is Q = 100 - P, with P the price
charged by the newsstand and Q the quantity of newspapers sold. Denote by p the price
charged by the newspaper company to the newsstand.
From the perspective of the newsstand, the effective marginal cost of selling a newspaper
is p, the price charged by the newspaper company. Since its marginal revenue is 100-2Q,
the newsstand will sell Q=50-p/2 newspapers. This is also the demand for the newspaper
company when it sets a price p. The inverse demand curve for the newspaper company is
then p=100-2Q, which gives a marginal revenue of 100-4Q. Since its marginal cost is
zero, it will sell 25 newspapers to this newsstand at a price p=50. The newsstand will
then charge a price P=75 to end consumers. Total profits for newspaper company and
newsstand together are P*Q = 1875 (since costs are zero).
If the newspaper company also operated the newsstand, it would simply face a demand
curve of Q=100-P. Its marginal revenue would thus be 100-2Q. Setting this equal to its
marginal cost of zero, the company should sell Q=50 at a price P=50, for a total profit of
2500. Note that the profit of this merged operation is substantially higher than the joint
profit of the independently operating newspaper company and newsstand.
This shows how the independent exercise of market power in two stages of the value
chain reduces total profits. This phenomenon, known as ‘double marginalization’, has
important implication for firm boundaries and retail contracts. Note, for example, that
both firms could be made better off if the newspaper company charged the newsstand a
concession in exchange for providing the newspapers at marginal cost. (With a
concession of 1850, the profit of the newsstand increases by 25 and of the newspaper
company by 600).
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