COMMODITY BUNDLING BY
SINGLE-PRODUCT MONOPOLIES*
RICHARD SCHMALENSEE
Massachusetts
Institute of Technology
Alfred P.
Sloan School of Management
CONSIDER two products that have independent demands in the sense that
all individual buyers consider them neither substitutes nor complements. Then,
if the two products are priced separately, the demand for either is independent
of the price of the other. In his classic analysis of block booking of feature
films, George Stigler shows that it may be profitable for a monopoly seller of
two such products to bundle them by requiring a buyer to take both in order to
get either.[1] His
work provides a rationale for tying arrangements that does not depend on
technological or other dependencies among the products involved.[2]
Adams and Yellen extend the analysis of multiproduct monopoly with
independent demands.[3]
They discuss two different bundling strategies: pure bundling, in which the seller only offers the products in
fixed proportions; and mixed bundling, in
which buyers may either buy the products separately or purchase a bundle with
fixed proportions of each.
In this note, I consider a single-product
monopoly and investigate the profit and welfare implications of bundling
its product for some other
* This paper was written while
I was a Visiting Scholar at the Harvard Department of Economics, to which I am
indebted for its hospitality. I am also indebted to the Ford Motor Company for
research support through a grant to MIT and to Dennis Carlton and a referee for
helpful comments.
68 THE JOURNAL OF LAW AND
ECONOMICS
product produced competitively. For
simplicity, and to permit comparisons with the earlier bundling literature, I
stick with the case of independent demands. Section 1 sets up the model and
shows that pure bundling, as defined above, is never better for such a monopoly
than simply selling its product separately. Section II shows that mixed
bundling, on the other hand, may enhance profits under these assumptions. If
there is a negative correlation (speaking
loosely) among buyers’ reservation prices for the two products considered, the
monopolist may be able to use buyers’ revealed valuations, of the competitive
product to sort them into groups between which he can profitably discriminate.
I. PURE BUNDLING
The formal setup here basically follows the
notation and assumptions of Adams and Yellen.[4]
Two goods, labeled I and 2, are produced at constant unit costs of C1 and C2, respectively. Potential buyers are
interested in at most one unit of each good. Every potential buyer is
completely described by a pair of reservation prices (R1,R2). If the goods are priced separately, a buyer will purchase
good I if and only if its price, P1, does
not exceed his or her reservation price for that good, R1. The values of the market price, P2, and reservation price, R2, for the second good are irrelevant for that decision because
demands are independent. Similarly, the decision to purchase the second good
depends only on a comparison of P2 and R2. In general, buyers’ reservation price pairs differ; these
differences may permit profitable price discrimination.
Good 1 is assumed in all that follows to be
produced by a competitive industry and thus to be available at price P1 C1. Good 2 is produced by
a monopoly. If the monopoly sets a price of P2 per unit for its output, it
sells to all buyers with R2 > P2, while all buyers with R1 > C1 buy good 1 from the
competitive industry.
Now suppose that, for some reason, the
monopoly elects to engage in pure bundling. It offers for sale only bundles
consisting of one unit of good 1 and one unit of good 2, and it charges a price
PB for these bundles.[5]
The sales pattern under pure bundling is depicted in Figure 1.[6] Good 1 is sold by the
competitive industry to all buyers located to the right of the R1 = P1 line and below the R2 = — C1 line. The monopolist sells the bundle to
all buyers located above the R1 + R2 = PB line and above the R2 =PB — C1 line.
We can now prove that unbundled selling must be at least as profitable as pure bundling in
this model. Suppose the contrary, and let PB be the optimal price of the bundle. The monopolist
then makes a profit of (PB —C1 — -C2) on
every bundle sold. Suppose the firm shifts to unbundled selling with a price P2 = PB — C1 for
its output. By construction, the profit per unit of sales is the same. But the
monopolist now sells to all buyers
located above the R2 = PB - — C1 line in Figure 1, so that, if there are any buyers in the shaded
triangular area there, sales are increased. Since profit per unit sales is the
same under unbundled selling, and unit sales are at least as large, unbundled
selling must be at least as profitable as pure bundling.
The demand pattern under mixed bundling is
depicted in Figure 2.[7]
Good 2 is sold separately by the monopolist to all buyers located to the
northwest of point A, the competitive
industry sells good 1 to all buyers southeast of point B, and all
buyers located to the northeast of line
segment AR elect to purchase the bundle.
Note that any buyers located strictly above
line AR have R1 <C1, yet
they consume good 1 as
part of the bundle. Mixed bundling thus
generally leads to an inefficient oversupply of good 1, the competitively
produced product.[8] If
the monopoly produces all the units of good 1 it sells, however, the total
output of the competitive industry falls under
mixed bundling. Members of that industry might well complain that the monopoly
is using “leverage” to monopolize the production of good 1 as well as good 2.
They can be expected to notice that pricing satisfying (I) implies PB — P2 <C1 and, perhaps, to argue that
the monopolist is thus selling good I below cost in order to drive them from
the market. Since the monopoly is here indifferent between making good I and
buying it at cost from the competitive industry, such charges would not be
valid under our assumption.
The markup on sales of the bundle is PB- — C1 — -C2, which
is less than P2 -C2, the
markup on separate sales of good 2, by conditions (1). If Figure 2 is
considered, it follows that buyers with large values of R1 make smaller
contributions to the monopoly’s profits than those who value the competitive
good less. If large values of R1 are
generally associated with large values of R2 in the population of potential
buyers, this sort of separation cannot enhance profits. But if there is a
general negative relation between
COMMODITY BUNDLING 71
the
reservation prices for the two goods, of the sort that drives the examples
considered by Stigler and by Adams and Yellen,[9]
mixed bundling may he more profitable
than unbundled sales.
In both
cases, a switch from unbundled sales to mixed bundling increases profit,
despite the social loss of three units caused by Beta’s consumption of good 1
in the bundle. If (2) holds, mixed bundling increases profits and net
(consumers’ plus producer’s) surplus by two units; neither consumer’s surplus
is affected. If (3) holds, however, mixed bundling increases profits by less
than it reduces Alpha’s surplus, and net surplus is reduced by three units.
Thus a profitable switch from an bundled
sales to mixed bundling may increase or decrease net surplus; it all
depends on the details of the distribution of reservation prices.
In the
analysis of tying contracts as metering devices, it is usually assumed that the
two products involved are complements and that buyers with higher reservation
prices for the tying product demand more units of the tied product at any
price.[10]
This positive association between demands is exploited by selling the tied
product. above cost, thus capturing more surplus from those who value the tying
product more. Here, in contrast, a negative
relation between reservation prices in the population is exploited, and
good 1 is accordingly sold below cost
(in the sense that PB-— P2 < C1). This permits extraction of
more surplus from those who value it less and value good 2 more.