Where Do Markets Come From?
Author(s): Harrison C. White
Reviewed work(s):
Source: American Journal of Sociology, Vol. 87, No. 3 (Nov., 1981), pp. 517-547
Published by: The University of Chicago Press
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Where Do Markets Come From?'
Harrison C. White
Harvard University
Production markets have two sides: producers are a fully connected
clique transacting with buyers as a separate but aggregated clique.
Each producer is a distinctive firm with a distinctive product. Each
side continually monitors reactions of the other through the medium
of a joint social construction, the schedule of terms of trade. Each
producer is guided in choice of volume by the tangible outcomes of
other producers-not by speculation on hypothetical reactions of
buyers to its actions. Each producer acts purely on self-interest based
on observed actions of all others, summarized through a feedback
process. The summary is the terms-of-trade schedule, which reduces
to constant price only in limiting cases. The market emerges as a
structure of roles with a differentiated niche for each firm. Explicit
formulae-both for firms and for market aggregates-are obtained
by comparative-statics methods for one family of assumptions about
cost structures and about buyers' evaluations of differentiated prod-
ucts. Not just any set of firms can sustain terms of trade with any set
of buyers. There prove to be three main kinds of markets, and three
sorts of market failure, within a parameter space that is specified in
detail. One sort of market (PARADOX) has a Madison Avenue flavor,
another is more conventional (GRIND), and a third (CROWDED)
is a new form not included in any existing theory of markets. Current
American industrial markets are drawn on for 20 illustrations, of
which three are presented in some detail. Inequality in firms' market
shares (measured by Gini coefficients) is discussed.
Why do so many of our industrial markets have but a dozen or so member
firms, several of which produce substantial shares of the total output
(Scherer 1970; Porter 1980)? It is not enough to cite technological constraints.
Why, when even the largest of firms wants to offer a product new to it
to the public, does it usually do so by acquiring the persona of a firm
I Financial support under grants SOC76-24394, SER76-17502, and SES80-08658 from the
National Science Foundation is gratefully acknowledged, as is technical assistance from
Holly Grano. E. Raymond Corey, Michael E. Porter, and others at the Harvard Business
School generously made available teaching notes and case studies of industries or sets of
firms from industries; they bear no responsibility for the interpretations I propose. In this
development of earlier technical papers, Ronald L. Breiger, Robert G. Eccles, Eric Leifer,
John F. Padgett, Orlando Patterson, and Arthur Stinchcombe contributed ideas and other
aid, as did an anonymous referee. Requests for reprints should be sent to Harrison C.
White, Department of Sociology, William James Hall 470, Harvard University, Cam-
bridge, Massachusetts 02138.
? 1981 by The University of Chicago. All rights reserved
0002-9602/82/8703-0001$01.50
AJS Volume 87 Number 3 517
American Journal of Sociology
belonging to an existing market? This astonishing fact seems to be over-
looked by existing theory; practitioners and consultants take it for granted
(see Salter and Weinhold 1979, pp. 7-16; Steiner 1975, pp. 192, 200).
Why do economists accept a theory of firms in markets which denies in
principle the most commonly observed situation of firms? Most industrial
firms most of the time decide production volume within a range where their
unit costs are constant or decrease as volume increases (see Ijiri and Simon
1977, p. 7).
I developed some tentative answers to such questions in an earlier tech-
nical paper on production markets as induced role structures (White 1981).
Here I wish to flesh out the argument and illustrate it by application to a
number of current U.S. markets.
What I have proposed is embedding economists' neoclassical theory of
the firm within a sociological view of markets. Markets are self-reproducing
social structures among specific cliques of firms and other actors who evolve
roles from observations of each other's behavior. I argue that the key fact
is that producers watch each other within a market. Within weeks after
Roger Bannister broke the four-minute mile, others were doing so because
they defined realities and rewards by watching what other "producers" did,
not by guessing and speculating on what the crowds wanted or the judges
said. Markets are not defined by a set of buyers, as some of our habits of
speech suggest, nor are the producers obsessed with speculations on an
amorphous demand. I insist that what a firm does in a market is to watch
the competition in terms of observables.
In my proposal, markets are social structures in which producers repro-
duce their own set of actions; the set confirms as correct each firm's expec-
tations of what it hoped was an optimal volume. This view is a special case
of "rational expectations" (Muth 1961; for a recent survey, see Kantor
[1979]). In this feedback model there is also a self-selection aspect derived
from the "signaling theory" of Akerlof (1976), Spence (1974), and others
intrigued by notions of "imperfect information."
A modest generalization of the notion of price is required: generalized to
a market schedule of observed outcomes. These observed outcomes are a
set of pairs, one pair for each firm: revenue received for volume shipped.
Look at the hypothetical outcome sets in the panels of figure 1. Figure 1A
outcomes cannot sustain a market, figure 1B outcomes can. Figure 1C, in
which a curve is interpolated through the points of figure 1B, is one way a
firm may visualize those outcomes, revenue (W) as a function of volume
(y). This schedule must not be confounded with the demand function, a
hypothetical construct of economists. This schedule may be perceived in
terms of price (revenue/unit), buit it is a volume-dependent price. As will
be seen below, this generalization of the conventional notion of price is
crucial for my approach.
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Where Do Markets Come From?
wI
Revenue Revenue Revenue
W(y)
Volume Volume y, Volume
A. B C
FIG. 1.-Outcomes for each firm in a clique. A, Outcomes do not sustain a market.
B, Outcomes do sustain a market. C, Market schedule inferred from B; decisions using it
sustain it.
Because it frames the only hard, tangible evidence available, each firm
treats W(y) as its own opportunity set. Obtaining even that mulch informa-
tion requires alert inquiry-over luncheons with others in the trade, from
trade associations, from one's own customers, and so on. Each firm knows
that its product is distinctive, but it also knows the difficulty and risk of
assessing one's own distinctiveness (see Corey 1978; Porter 1976). In par-
ticular, when the total volume one offers in the market changes, its attrac-
tiveness to buyers changes, in ways hard to estimate. No firm can reliably
assess relative qualities of other firms, and every firm knows that its position
could be affected by choices made by any one or more of its competitors.
The market schedule W(y) is a shared social construction incorporating
all the interaction effects.
Such mutually interlocking confirmations of a unique choice by each
producer (fig. 1B) are not possible for any arbitrary collection of producers
and any population of buyers. A variety of attributes may distinguish indi-
vidual producer firms (product quality, location, plant investment). On the
one hand, some of these attributes affect cost structures (e.g., figs. 4 and 7
below) and thus the production level which looks optimum to that firm.
On the other hand, some of these attributes influence attractiveness to
buyers. A self-confirming market schedule, W(y), is induced here for a
clique of products whose cost structures and taste structures can each be
ranked by quality.
A market is an "act" which can be "got together" only by a set of pro-
ducers compatibly arrayed on the qualities which consumers see in them.
Quality arrays have recently figured in microeconomics under the rubrics of
"hedonic prices" (Terleckyj 1976) and "consumer as producer" (Lancaster
1966, 1979). Nearly 20 years ago Alonso (1964) proposed an array for loca-
tions in a city, where distance from the center provides a natural metric
519
American Journal of Sociology
for equality but also geometric constraints on areas, his analogue of volumes;
more recently Rosen (1974) has generalized this schematization to imperfect
competition.
Building a market is a conflict-ridden and erratic process with quite a
range of outcomes possible in the form of market schedules. The various
firms' products will presumably be akin within a market, but we do not as
observers impose any a priori cultural or linguistic criterion of similarity.
Markets are defined by self-reproducing cliques of firms, and not the other
way around.
The body of this paper is divided into a section on the general model and
a section on applications and results.
THE GENERAL MODEL
Firms in the market differ from one another, not only in cost structure but
also in appreciation of their products by the buyers. These dispersions
occupy center stage in my analysis. In this respect I follow the long-standing
tradition of economic studies of "imperfect competition" initiated by
Chamberlain (see Dixit and Stiglitz 1977; Spence 1976). But that tradition
has firms using conjectures on buyer taste to decide their market offers.
In contrast, my view, presented above, is that firms decide on the basis of
observed positions of all other producers.
In my view, firms seek niches in a market in much the same way as
organisms seek niches in an ecology. Because each firm is distinctive, they
are engaged not in pure competition but in finding and sustaining roles with
respect to one another given an environment of discerning buyers. But there
is no auctioneer to shape the market; instead, its structure depends on the
interlocking of local orders. This leads to the postulate that firms with
neighboring cost schedules (amount of variable cost to produce various
volumes) must also have, in the eyes of buyers, neighboring schedules of
valuation with respect to volume. If the postulate is not satisfied, the
nascent market situation, a set of producers with an attendant population
of buyers attracted by them, cannot sustain itself: W(y) will not be repro-
duced through the self-interested actions of firms, checked by buyers.
In an observed market, the producing firms are dispersed in quality of
product perceived by buyers as well as in volume produced. By the pos-
tulate of the preceding paragraph, neighboring qualities must lead to
neighboring volumes of production. In the model each firm is assigned a
value on an index of quality, denoted by n; the value assigned is charac-
teristic: an attribute which cannot be changed quickly as can the volume
of production. The volume of production is denoted by y.
The key feature of my approach is this: Firms can observe only volumes
and payments, not qualities or their valuations, and they act on the basis of
520
Where Do Markets Come From?
these observations, thereby reproducing the observations. My model, however,
can predict all these volume choices by different firms because it assumes
knowledge of quality, n, for each firm, as well as valuations. (Higher values
on this index are defined as higher quality-always as judged by buyers'
evaluations.)
First I develop the cost and valuation schedules, and then I derive the
range of market schedules that may resuilt from a given set of facts. A
topology of markets-a two-dimensional array with each point a particular
shape of payment schedule-follows as a by-product. The varieties and
implications of market failures are then discussed before the second part
of this paper: applications and predictions for industrial markets.
The central theme proves to be a trade-off between dispersions, an affair
of variances rather than the matter of means one might expect from the
cliche' of supply equaling demand.
The Facts of Cost and Value across Volume and Quality
The primitives of my description are two schedules (of cost and of valuation),
each given in terms of two dimensions (volume y and quality n). If the facts
about a set of firms and buyers cannot be approximated in terms of nested
schedules,2 those producers and customers will not be able to sustain a
market which reproduces itself as in figure 1. In order to achieve a compre-
hensiv~e yet clear inventory, I shall specialize to particular families of power
functions to describe possible schedules.
The schedule of the firm characterized by n for variable costs of produc-
tion is
C(y; n) = qyc/nd, with q and c positive . (1)
The firm's contribution to buyer valuation is defined as
S(y; n) = ryanb, with r, a, and b positive . (2)
Intuitively it is clear that a balance must be struck by the market between
the trade-off taking place between contribution and cost, with respect to
more volume or less volume, on the one hand, and the trade-off between
desirability and expense with respect to quality, on the other. Equations
2 Nested means simply that the function describing a schedule defined by one value of the
parameter (e.g., n) never crosses the function for another value of the parameter. (The
concept, though slippery, is familiar and important in other areas, such as Lorenz distribu-
tions; see Schwartz and Winship [1980].) This assumption, as well as the more basic
assumption that each empirical schedule can be represented by a perfectly sharp function
(see n. 10 below), clearly is more stringent than necessary to obtain the main findings.
But to simplify explanation of the theory in these first papers, I make not only these
assumptions but also the further assumption that particular Cobb-Douglas (power-law)
forms are appropriate for the schedule. Elsewhere I have explored alternative functional
forms.
521
American Journal of Sociology
(1) and (2) yield the simplest family of schedules that allow these four
independent variations of schedule as measured in total dollars and with
respect either to physical volume y of production or to its quality n.
Figure 2 schematizes the phenomenology underlying these schedules. It
explicates equation (1) as the variable cost of producing the volume y
chosen by a firm being the product of the volume-sensitive cost and the
quality-sensitive expense. Cost must increase with volume so that the
exponent c is positive; this exponent gives the proportionate logarithmic
rate of increase with volume. Quality, unlike volume, is in the eye of the
beholder, here the buyers, and therefore is an exogenous "social fact"
confronting the producers; so the exponent d can be either positive or nega-
tive. When positive, d describes what I denote below as a PARADOX
market in which a producer whose product is liked better finds it less costly
to make! There is in figure 2 a parallel rationale for equation (2). By defini-
tion, the exponent b for desirability is positive; one could even insist that it
be set equal to unity, but I prefer not to constrain the scaling of quality
values n for different firms' products in that way (see disctssion of tables
1 and 2 below).
On the buyer side there is an asymmetry which is not captured in figure 2.
Firms are the active decision makers; each has an independent cost schedule
i) Phenomenology of Market Context
Dispersions
across Firms
on Volume (y) of Firms Production on Quality Index (n)
S
c Contribution of the product Desirability of the product
h Valuation increases with volume, as increases with quality as
e perceived by the buyers judged by the buyers
u Cost of production increases Expense of building in the I Costs as volume increases quality changes(+or-)
e with increased quality
s
Increases With Volume Changes With Quality
ii) Parameters--Proportionate (log) Rates
a b
r c | d
iii) The Basic Tradeoffs
--Over variation, in product volume Contributin= a/c Cost - c
--Over variation in producers' quality Desirability = b/d Expense
FIG. 2
522
Where Do Markets Come From?
known to itself (at least). Buyers, on the other hand, are lumped together
as an aggregate, in a passive role. The aggregate buyer may say "no" to
the market entry (volume and price pair) offered by a firm, but it has only
this binary choice. This binary decision depends on how the buyers in
aggregate evaluate more of one firm's product against less of another's. To
simplify the model further, I assume that buyers do not see particular pairs
of products in interaction, but only the set of products. In formal terms,
the buyers in aggregate value their total array of purchases as
V(#) = [2 S(y; n)]" . (3)
The symbol V for this valuation is in boldface type to signal that it is an
aggregate quantity over the whole market: I adhere to this convention
throughout. The symbol # gives the number of firms in the market and
hence the number of terms in the summation. Observe that the contribu-
tion of one firm's product volume to the total valuation can replace the con-
tribution of any other firm. In the special case in which the exponent a is
unity, further volume increments from a given firm are neither more highly
valued (as they would be with a > 1) nor less highly valued than a begin-
ning volume. More decisive is the overall exponent y (gamma) which is
usually less than unity; this corresponds to a saturation of taste, for the
sum of purchases from all firms in the market, by the given aggregation of
buyers as the aggregate volume purchased increases.3
The scale factors q for cost schedules (eq. [1]) and ry for valuation sched-
ules (eqq. [2] and [3]) are worth keeping distinct. In the section on applica-
tions, changes in these will be interpreted as exogenous shifts in cost and
demand imposed on the market. I do not define a distribution of firms over
the quality index n, only their number. In this view of markets there are
relatively few member firms as producers, as few as a half dozen, and there
is no reason to suppose any particular spacing on the quality index among
those few: These are best treated as a set of constants to be fitted to the
observed producers (as is done in several empirical examples later).
Certain special cases bear considerable weight in the past development of
theories of markets, a point I develop at length elsewhere (White 1980).
Setting the exponent b to zero reduces the market to pure competition:
products of different firms are indistinguishable. Perfect competition models
assume in addition that there is no taste for sheer diversity on the part of
I In this simplified representation (eq. [3]) of aggregate buyer evaluations across products,
I follow recent innovations of mic