Monopolistic Competition and Optimum
Product Diversity
By AVINASH K. DIXIT AND JOSEPH E. STIGLITZ*
The basic issue concerning production in
welfare economics is whether a market solution
will yield the socially optimum kinds
and quantities of commodities. It is well
known that problems can arise for three
broad reasons: distributive justice; external
effects; and scale economies. This paper is
concerned with the last of these.
The basic principle is easily stated.' A
commodity should be produced if the costs
can be covered by the sum of revenues and
a properly defined measure of consumer's
surplus. The optimum amount is then
found by equating the demand price and the
marginal cost. Such an optimum can be
realized in a market if perfectly discriminatory
pricing is possible. Otherwise we
face conflicting problems. A competitive
market fulfilling the marginal condition
would be unsustainable because total profits
would be negative. An element of monopoly
would allow positive profits, but would
violate the marginal condition.2 Thus we
expect a market solution to be suboptimal.
However, a much more precise structure
must be put on the problem if we are to
understand the nature of the bias involved.
It is useful to think of the question as one
of quantity versus diversity. With scale
economies, resources can be saved by producing
fewer goods and larger quantities of
each. However, this leaves less variety,
which entails some welfare loss. It is easy
and probably not too unrealistic to model
scale economies by supposing that each
potential commodity involves some fixed
set-up cost and has a constant marginal
cost. Modeling the desirability of variety
has been thought to be difficult, and several
indirect approaches have been adopted.
The Hotelling spatial model, Lancaster's
product characteristics approach, and the
mean-variance portfolio selection model
have all been put to use.3 These lead to results
involving transport costs or correlations
among commodities or securities, and
are hard to interpret in general terms. We
therefore take a direct route, noting that the
convexity of indifference surfaces of a conventional
utility function defined over the
quantities of all potential commodities already
embodies the desirability of variety.
Thus, a consumer who is indifferent between
the quantities (1,0) and (0,1) of two
commodities prefers the mix (1/2,1/2) to
either extreme. The advantage of this view
is that the results involve the familiar ownand
cross-elasticities of demand functions,
and are therefore easier to comprehend.
There is one case of particular interest on
which we concentrate. This is where potential
commodities in a group or sector or industry
are good substitutes among themselves,
but poor substitutes for the other
commodities in the economy. Then we are
led to examining the market solution in relation
to an optimum, both as regards
biases within the group, and between the
group and the rest of the economy. We expect
the answer to depend on the intra- and
intersector elasticities of substitution. To
demonstrate the point as simply as possible,
we shall aggregate the rest of the economy
into one good labeled 0, chosen as the
numeraire. The economy's endowment of it
is normalized at unity; it can be thought of
as the time at the disposal of the consumers.
*Professors of economics, University of Warwick
and Stanford University, respectively. Stiglitz's research
was supported in part by NSF Grant SOC74-
22182 at the Institute for Mathematical Studies in the
Social Sciences, Stanford. We are indebted to Michael
Spence, to a referee, and the managing editor for comments
and suggestions on earlier drafts.
I See also the exposition by Michael Spence.
2A simple exposition is given by Peter Diamond and
Daniel McFadden.
3See the articles by Harold Hotelling, Nicholas
Stern, Kelvin Lancaster, and Stiglitz.