THE ORGANIZATION OF ECONOMIC ACTIVITY: ISSUES

PERTINENT TO THE CHOICE OF MARKET VERSUS

NONMARKET ALLOCATION
BY KENNETH J. ARRow
Kenneth J. Arrow is Professor of Economics at Harvard Univer-
sity and is associated with the Project on Efficiency of Decisionmaking
in Economic Systems at that institution.
Before beginning a discussion of the role of economic analysis in
Government expenditure policy one must determine that set of activities
in which the public sector should properly be engaged. While the price
system of the private sector is an efficient resource allocating mechanism
under many conditions, it fails to function appropriately when certain
conditions prevail. In this paper, Professor Arrow presents the condi-
tions under which the private competitive market system will lead to an
efficient allocation of resources and deals with those conditions in which
nonmarket allocating mechanisms appear superior to the price system.
The concepts of public goods, externalities, increasing returns, and trans-
action costs are presented as pertinent to the market versus nonmarket
allocation debate. A variety of social institutions such as bargaining, the
political process, and prevailing social customs are discussed as non-
market alternatives to the price system.
Introduction
The concept of public goods has been developed through a process
of successive refinement over a long period of time. Yet surprisingly
enough there does not seem to exist anywhere in the literature a clear
general definition of this concept or the more general one of "exter-
nality." The accounts given are usually either very general and dis-
cursive, difficult of interpretation in specific contexts, or else they are
rigorous accounts of very special situations. What exactly is the re-
lation between externalities and such concepts as "appropriability"
or "exclusion" ?*
Also, there is considerable ambiguity in the purpose of the analysis of
externalities. The best developed part of the theory relates to only
a single question: the statement of a set of conditions, as weak as pos-
sible, which insure that a competitive equilibrium exists and is Pareto
efficient.' Then the denial of any of these hypotheses is presumably a
sufficient condition for considering resort to non-market channels of
resource allocation-usually thought of as Government expenditures,
taxes, and subsidies.
At a second level the analysis of externalities should lead to criteria
for nonmarket allocation. We are tempted to set forth these criteria
in terms analogous to the profit-and-loss statements of private busi-
ness; in this form, we are led to benefit-cost analysis. There are, more-
' A competitive equilibrium is defined below. An allocation of resources through the
workings of the economic system is said to be Pareto efficient if there is no other
allocation which would make every individual In the economy better off.
*Further discussion of this issue is found in the paper by Steiner in this volume.
(47)
 48

over, two possible aims for benefit-cost analysis; one, more ambitious
but theoretically simpler, is specification of the nonmarket actions
which will restore Pareto efficiency; the second involves the recognition
that the instruments available to the Government or other nonmarket
forces are scarce resources for one reason or another, so that all that
can be achieved is a "second-best."
Other concepts that seem to cluster closely to the concept of public
goods are those of "increasing returns" and "market failure." These
are related to Pareto inefficiency on the one hand and to the existence
and optimality of competitive equilibrium on the other; sometimes
the discussions in the literature do not adequately distinguish these two
aspects. I contend that market failure is a more general category than
externality; and both differ from increasing returns in a basic sense,
since market failures in general and externalities in particular are rela-
tive to the mode of economic organization, while increasing returns
are essentially a technological phenomenon.
Current writing has helped bring out the point that market failure
is not absolute; it is better to consider a broader category, that of trans-
action costs, which in general impede and in particular cases com-
pletely block the formation of markets. It is usually though not al-
ways emphasized that transaction costs are costs of running the eco-
nomic system. An incentive for vertical integration is replacement of
the costs of buying and selling on the market by the costs of intrafirm
transfers; the existence of vertical integration may suggest that the
costs of operating competitive markets are not zero, as is usually as-
sumed in our theoretical analysis.
Monetary theory, unlike value theory, is heavily dependent on the
assumption of positive transaction costs; the recurrent complaint about
the difficulty of integrating these two branches of theory is certainly
governed by the contradictory assumptions made about transaction
costs. The creation of money is in many respects an example of a pub-
lic good.
The identification of transaction costs in different contexts and under
different systems of resource allocation should be a major item on the
research agenda of the theory of public goods and indeed of the theory
of resource allocation in general. Only the most rudimentary sugges-
tions are made here. The "exclusion principle" is a limiting case of
one kind of transaction cost, but another type, the costliness of the
information needed to enter and participate in any market, has been
little remarked. Information is closely related on the one hand to com-
munication and on the other to uncertainty.
Given the existence of Pareto inefficiency in a free market equilib-
rium, there is a pressure in the market to overcome it by some sort
of departure from the free market; i.e., some form of collective
action. This need not be undertaken by the Government. I suggest
that in fact there is a wide variety of social institutions, in par-
ticular generally accepted social norms of behavior, which serve in
some means as compensation for failure or limitation of the market,
though each in turn involves transaction costs of its own. The ques-
tion also arises how the behavior of individual economic agents in a
social institution (especially in voting) is related to their behavior on
the market. A good deal of theoretical literature has arisen in recent
years which seeks to describe political behavior as analogous to
 49
economic, and we may hope for a general theory of socioeconomic
equilibrium. But it must always be kept in mind that the contexts of
choice are radically different, particularly when the hypotheses of
perfectly costless action and information are relaxed. It is not acci-
dental that economic analysis has been successful only in certain
limited areas.
COMPETITIVE EQUILIBRIUM AND PARETO EFFCiENCY

A quick review of the familiar theorems on the role of perfectly

competitive equilibrium in the efficient allocation of resources will be
useful. Perfectly competitive equilibrium has its usual meaning:
households, possessed of initial resources, including possibly claims to
the profits of firms, choose consumption bundles to maximize utility at
a given set of prices; firms choose production bundles so as to maxi-
mize profits at the same set of prices; the chosen production and con-
sumption bundles must be consistent with each other in the sense that
aggregate production plus initial resources must equal aggregate con-
sumption. The key points in the definition are the parametric role 2 of
the prices for each individual and the identity of prices for all indivi-
duals. Implicit are the assumptions that all prices can be known by all
individuals and that the act of charging prices is not itself a consumer
of resources.
A number of additional assumptions are made at different points in
the theory of equilibrium, but most are clearly factually valid in the
usual contexts and need not be mentioned. The two hypotheses fre-
quently not valid are (C), the convexity of household indifference
maps and firm production possibility sets, 3 and (M), the universality
of markets. While the exact meaning of the last assumption will be ex-
plored later at some length, for the present purposes we mean that the
consumption bundle which determines the utility of an individual is
the same as that which he purchases at given prices subject to his bud-
get constraint, and that the set of production bundles among which a
firm chooses is a given range independent of decisions made by other
agents in the economy.
The relations between Pareto efficiency and competitive equilibrium
are set forth in the following two theorems:
1. If (M) holds, a competitive equilibrium is Pareto-effioient. This
theorem is true even if (C) does not hold.
2. If (C) and (M) hold, then any Pareto-egcientallocation can be
achieved as a competitive eguilibriusm by a suitable reallocationof ini-
tial resources.
When the assumptions of proposition 2 are valid, then the case for
the competitive price system is strongest. Any complaints about its op-
eration can be reduced to complaints about the distribution of income,
which should then be rectified by lump-sum transfers. Of course, as
Pareto already emphasized, the proposition provides no basis for ac-
2By "parametric role" Is meant that each household and firm takes the market prices
as given, not alterable by Its consumption or production decisions.
For households, "convexity" means that If we consider two different bundles of
consumption, a third bundle defined by averaging the first two commodity by commodIt'
is not inferior In the household's preferences to both of the first two. For a firm, "convexity'
means that If we consider two different specifications of inputs and outputs, either of
which Is possible to the firm (in that the Inputs suffice to produce the outputs), then a
third specification defined by averaging the Inputs and outputs of the first two Is also
possible for the firm to carry out.
 50
cepting the results of the market in the absence of accepted levels of
income equality.
The central role of competitive equilibrium both as a normative
guide and as at least partially descriptive of the real world raises an
analytically difficult question: does a competitive equilibrium neces-
sarily exist?
3. If (C) holds, then there exists a competitive equilibrium. This
theorem is true even if (M) does not hold.
If both (C) and (M) hold, we have a fairly complete and simple
picture of the achievement of desirable goals, subject always to the
major qualification of the achievement of a desirable income distribu-
tion. The price system itself determines the income distribution only
in the sense of preserving the status quo. Even if costless lump-sum
transfers are possible, there is needed a collective mechanism reallo-
cating income if the status quo is not regarded as satisfactory.
Of course (C) is not a necessary condition for the existence of a
competitive equilibrium, only a sufficient one. From proposition 1, it
is possible to have an equilibrium and therefore efficient allocation
without convexity (when (M) holds). However, in view of the cen-
tral role of (C) in these theorems, the implications of relaxing this
hypothesis have been examined intensively in recent years by Farrell
(1959), Rothenberg (1960), Aumann (1966), and Starr (1969). Their
conclusions may be summarized as follows: Let (C') be the weakened
convexity assumption that there are no indivisibilities large relative
to the economy.
4. Propositions 2 and 3 remain approximately true if (C) is re-
placed by (C').
Thus, the only nonconvexities that are important for the present
purposes are increasing returns over a range large relative to the
economy. In those circumstances, a competitive equilibrium cannot
exist.
The price system, for all its virtues, is only one conceivable form
of arranging trade, even in a system of private property. Bargaining
can assume extremely general forms. Under the assumptions (C') and
(M), we are assured that not everyone can be made better off by a
bargain not derived from the price system; but the question arises
whether some members of the economy will not find it in their inter-
est and within their power to depart from the perfectly competitive
price system. For example, both Knight (1921, pp. 190-194) and
Samuelson (1967, p. 120) have noted that it would pay all the firms
in a given industrv to form a monopoly. But in fact it can be argued
that unrestricted bargaining can only settle down to a resource alloca-
tion which could also be achieved as a perfectly competitive equi-
librium, at least if the bargaining itself is costless and each agent is
small compared to the entire economy. This line of argument origi-
nated with Edgeworth (1881. pp. 20-43) and has been deveeloped re-
cently by Shubik (1959), Debren and Scarf (1963), and Aumanil
(1964).
More precisely, it is easy to show:
5. If (M) holds and a competitive equilibrium prevails. then no set
of economic agents will find any resource a77ocation wvhich they can
accomplish by themse7ve~s (without trade with the other agents) which
they will all prefer to that prevailing under the equilibrium.
 51

Proposition ,5 holds for any number of agents. A deeper proposition

is the following converse:
6. If (C') and (M) hold, and if the resources of any economic agent
are small compared with the total of the economy, then, given any allo-
cationnot approximatelyachievable as a competitive equilibrium,there
will be some set of agents and some resource allocation they can achieve
without any tradewith others which each one will prefer to the given
allocation.
These two propositions, taken together, strongly suggest that when
all the relevant hypotheses hold, (a) a competitive equilibrium, if
achieved, will not be upset by bargaining even if permitted, and (b)
for any bargain not achievable by a competitive equilibrium there is a
set of agents who would benefit by change to another bargain which
they have the full power to enforce.
The argument that a set of firms can form a monopoly overlooks the
possibility that the consumers can also form a coalition, threaten not
to buy, and seek mutually advantageous deals with a subset of the
firms; such deals are possible since the monopoly allocation violates
some marginal equivalences.
In real life, monopolizing cartels are possible for a reason not so far
introduced into the analysis: bargaining costs between producers and
consumers are high, those among producers low-a point made most
emphatically by Adam Smith (1937, p. 128) ; "People of the same trade
seldom meet together, even for merriment or diversion, but the conver-
sation ends in a conspiracy against the public, or in some contrivance
to raise prices." It is not the presence of bargainingcosts per se but
their bias that is relevant. If all bargaining costs are high, but competi-
tive pricing and the markets are cheap, then we expect the perfectly
competitive equilibrium to obtain, yielding an allocation identical with
that under costless bargaining. But if bargaining costs are biased, then
some bargains other than the competitive equilibrium can be arrived at
which will not be upset by still other bargains if the latter but not the
former are costly.
Finally, in this review of the elements of competitive equilibrium
theory, let me repeat the obvious and well-known fact that in a world
where time is relevant, the commodities which enter into the equilib-
rium system include those with future dates. In fact, the bulk of mean-
ingful future transactions cannot be carried out on any existing present
market, so that assumption (M), the universality of markets, is not
valid.
IMPERFEcrLy CoMPETiEIn EQULIBRIUM

There is no accepted and well-worked out theory corresponding to

the title of this section. From the previous section it is clear that such
a theory is forcibly needed in the presence of increasing returns on a
scale large relative to the economy (hereafter, the phrase "increasing
returns" will always be understood to include the prepositional phrasi.
just employed), and is superfluous in its absence.
There are two approaches to a theory of general equilibrium in
an imperfectly competitive environment; most writers who touch on
public policy questions implicitly accept one or the other of these
prototheories without always recognizing that they have made a
choice. One assumes all transactions are made according to the price
 52
system, i.e., the same price is charged for all units of the same com-
modity; this is the monopolistic competition approach. The alterna-
tive approach assumes unrestricted bargaining; this is the game
theory approach. The first might be deemed appropriate if the costs
of bargaining are high relative to the costs of ordinary pricing, while
the second assumes costless bargaining.4
It cannot be too strongly emphasized that neither approach is, at
the present stage, a fully developed theory, and it is misleading to
state any implications about the working of these systems. Chamber-
lain's (1933), purpose was certainly the incorporation of monopoly
into a general equilibrium system, together with a view that the com-
modity space should be viewed as infinite-dimensional, with the pos-
sibility of arbitrarily close substitutes in consumption; Triffin (1941)
emphasized this aspect, but the only completely worked-out model of
general monopolistic equilibrium is that of Negishi, (1960-61), and
he made the problem manageable by regarding the demand functions
facing the monopolists as those preceived by them, with only loose
relations to reality. Such a theory would have little in the way of
deducible implications (unless there were a supplementary psycho-
logical theory to explain the perceptions of demand functions) and
certainly no clear welfare implications.
Of course, whatever a monopolistic competitive equilibrium means,
it must imply inefficiency in the Pareto sense if there are substantial
increasing returns. For a firm can always make zero profits by not
existing; hence, if it operates, price must at least equal average cost
which is greater than marginal cost. Kaldor (1935) and Demsetz
(1964), however, have argued that in the "large numbers" case, the
welfare loss may be supposed very small. I would conjecture that this
conclusion is true, but it is not rigorously established, and indeed
the model has never been formulated in adequate detail to discuss
it properly.'
With unrestricted bargaining it is usual to conclude that the equi-
librium, whatever it may be, must be Pareto-efficient for, by definition,
it is in the interest of all economic agents to switch from a Pareto-
inefficient allocation to a suitably chosen Pareto-efficient one. This
argument seems plausible, but is not easy to evaluate in the absence of
a generally accepted concept of solution for game theory. Edgeworth
(1881) held the outcome of bargaining to be indeterminate within
limits, and von Neumann and Morgenstern (1944) have generalized
this conclusion. But when there is indeterminacy, there is no natural
or compelling point on the Pareto frontier at which to arrive. It is
certainly a matter of common observation, perhaps most especially in
the field of international relations, that mutually advantageous agree-
ments are not arrived at because each party is seeking to engross as
much as possible of the common gain for itself. In economic affairs
4 Within the framework of each prototheory, attempts have been made to modify it
in the direction of the other. Thus, price discrimination Is a modification of the price
system In the pure theory of monopoly, though I am aware of no attempt to study
price discrimination in a competitive or otherwise general equilibrium context. Some
game theorists (Luce (1954, 1955 a, b), Aumann and Maschler (1964)) have attempted to
Introduce bargaining costs in some way by simply limiting the range of possilbe coalitions
capable
5 of making bargains.
.Suppose that the degree of increasing returns is sufficient to prevent there being more
than one producer of a given commodity narrowly defined, but not to prevent production
of a close substitute. Is this degree of returns sufficiently substantial to upset the achieve-
ment of an approximately perfect competitive equilibrium, as discussed In the last section?
 53

a frequently cited illustration is the assembly of land parcels for large

industrial or residential enterprises whose value (net of complemen-
tary costs) exceeds the total value of the land in its present uses. Then
each owner of a small parcel whose acquisition is essential to the
execution of the enterprise can demand the entire net benefit. An
agreement may never be reached or may be long delayed; at positive
discount rates even the latter outcome is not Pareto-efficient. It is to
avoid such losses that the coercive powers of the state are invoked
by condemnation proceedings.
There is, however, another tradition within game theory which
argues for the determinacy of the outcome of bargaining. Zeuthen
(1930, ch. IV) had early propounded one such solution. After von
Neumann and Morgenstern, Nash (1950, 1953) offered a solution,
which Harsanyi (1956) later showed to be identical with that of
Zeuthen. Nash's analysis of bargaining has been extended by Harsanyi
(1959, 1963, 1966); variant but related approaches have been studied
by Shapley (1953) and Selten (1964). The analysis has proceeded at
a very general level, and its specific application to resource allocation
has yet to be spelled out. In the simplest situation, bargaining between
two individuals who can cooperate but cannot injure each other except
by withholding cooperation and who can freely transfer benefits be-
tween them, the conclusion of the theories is the achievement of a
joint optimum followed by equal splitting of the benefits of coopera-
tion net of the amounts each bargainer could obtain without coopera-
tion. Thus, in a land assembly, if the participation of all parcels is
essential, each owner receives the value of his parcel in its present (or
best alternative) use plus an equal share of the net benefits of the
project. Without further analytic and empirical work it is not easy
to judge the acceptability of this conclusion.
An elementary example may bring out the ambiguities of allocation
with unrestricted bargaining. Since the perfectly competitive equilib-
rium theory is satisfactory (in the absence of marketing failures
and costs) when increasing returns on a substantial scale are absent,
the problem of imperfectly competitive equilibrium arises only when
substantial increasing returns are present. In effect, then, there are
small numbers of effective participants. Suppose there are only three
agents. Production is assumed to take place in coalitions; the output
of each coalition depends only on the number of members in it. If
the average output of the members of a coalition does not increase
with the number of members, then the equilibrium outcome is the
perfectly competitive one, where each agent produces by himself and
consumes his own product. If the average output of a coalition in-
creases with the number of members, then clearly production will
take place in the three-member coalition; but the allocation is not
determined by the threats of individuals to leave the coalition and
go on their own, nor by threats of pairs to form coalitions (for any
one member can claim more than one-third of the total output and still
leave the other two more than they could produce without him). But
perhaps the most interesting case is that where the average output
is higher for two individuals than for either one or three; i.e., increas-
ing returns followed by diminishing returns. For definiteness, sup-
pose that one agent can produce one unit, two agents can produce
four units, and all three agents together can produce five units.
 54
Clearly, Pareto efficiency requires the joint productive activity of all
three. Since each pair can receive four units by leaving the third
agent out, it would appear that each pair must receive at least four
units. But this implies that the total allocated to keep the three-man
coalition together must be at least six, more than is available for
distributions
(Theories of the Nash-Harsanyi type arrive at solutions in cases
like this by assuming that the economic agents foresee these possible
instabilities and recognize that any attempt by any pair to break away
from the total coalition can itself be overturned. If each is rational
and assumes the others are equally rational, then they recognize, in the
completely symmetric situation of the example, that only a symmetric
allocation is possible.)
The point of this lengthy discussion of possible game theory con-
cepts of equilibrium is to suggest caution in accepting the proposition
that bargaining costs alone prevent the achievement of Pareto effi-
ciency in the presence of increasing returns, as Buchanan and Tullock
(1962, p. 88) and Demsetz (1968, p. 61) assert.
RISK AND INFORMATION*
The possible types of equilibria discussed in the previous two sec-
tions are not, in principle, altered in nature by the presence of risk. If
an economic agent is uncertain as to which of several different states
of the world will obtain, he can make contracts contingent on the oc-
currence of possible states. The real-world counterparts of these theo-
retical contingent contracts include insurance policies and common
stocks. With these markets for contingent contracts, a competitive
equilibrium will arise under the same general hypotheses as in the
absence of uncertainty. It is not even necessary that the economic
agents agree on the probability distribution for the unknown state of
the world; each may have his own subjective probabilities. Further,
the resulting allocation is Pareto-efficient if the utility of each indi-
vidual is identified as his expected utility according to his own sub-
jective probability distribution.
But, as Radner (1968) has pointed out, there is more to the story.
Whenever we have uncertainty we have the possibility of informa-
tion and, of course, also the possibility of its absence. No contingent
contract can be made if, at the time of execution, either of the con-
tracting parties does not know whether the specified contingency has
occurred or not. This principle eliminates a much larger number of
opportunities for mutually favorable exchanges than might perhaps
be supposed at first glance. A simple case is that known in insurance
literature as "adverse selection." Suppose, for example, there are two
types of individuals, A and B, with different life expectancies, but
the insurance company has no way to distinguish the two; it cannot
in fact identify the present state of the world in all its relevant as-
pects. The optimal allocation of resources under uncertainty would
require separate insurance policies for the two types, but these are
clearly impossible. Suppose further that each individual knows which
e The general principle illustrated by this example has been briefly alluded to by
Shapley and Shubik (1967, footnote 5, p. 98).
* Further discussion of this issue is found in the papers by Zeckhauser and
Davis &Kamien in this volume.
 55
type he belongs to. The company might charge a rate based on the
probability of death in the two types together, but the insurance
buyers in the two types will respond differently; those in the type with
the more favorable experience, say A, will buy less insurance than
those in type B, other things (income and risk aversion) being equal.
The insurance company's experience will be less favorable than it
intended, and it will have to raise its rates. An equilibrium rate will
be reached which is, in genera], between those corresponding to types
A and B separately but closer to the latter. Such an insurance arrange-
ment is, of course, not Pareto-efficient. It is not a priori obvious in gen-
eral that this free market arrangement is superior to compulsory in-
surance even though the latter is also not Pareto-efficient because it
typically disregards individual differences in risk aversion.
As the above example shows, the critical impact of information on
the optimal allocation of risk bearing is not merely its presence or
absence but its inequality among economic agents. If neither side
knew -which type the insured belonged to, then the final allocation
would be Pareto-efficient if it were considered that the two types were
indistinguishable; but in the above example the market allocation is
Pareto-efficient neither with the types regarded as indistinguishable
nor with them regarded as distinguishable.
There is one particular case of the effect of differential information
on the workings of the market economy (or indeed any complex econ-
omy) which is so important as to deserve special comment: one agent
can observe the joint effects of the unknown state of the world and
of decisions by another economic agent, but not the state or the deci-
sion separately. This case is known in the insurance literature as
"moral hazard," but because the insurance examples are only a small
fraction of all the illustrations of this case and because, as Pauly
(1968) has argued, the adjective "moral" is not always appropriate,
the case will be referred to here as the "confounding of risks and
decisions." An insurance company may easily observe that a fire has
occurred but cannot, without special investigation, know whether
the fire was due to causes exogenous to the insured or to decisions of
his (arson, or at least carelessness). In general, any system which,
in effect, insures against adverse final outcomes automatically reduces
the incentives to good decisionmaking.
In these circumstances there are two extreme possibilities (with all
intermediate possibilities being present): full protection against un-
certainty of final outcome (e.g., cost-plus contracts for production or
research) or absence of protection against uncertainty of final outcome
(the one-person firm; the admiral shot for cowardice "pour encour-
ager les autres"). Both policies produce inefficiency, though for dif-
ferent reasons. In the first, the incentive to good decisionmaking is
dulled for obvious reasons; in the second, the functions of control and
risk bearing must be united, whereas specialization in these functions
may be more efficient for the workings of the system.
The relations between principals and agents (e.g., patients and phy-
sicians, owners and managers) further illustrate the confounding of
risks and decisions. In the professions in particular they also illustrate
the point to be emphasized later: that ethical standards may to a cer-
tain extent overcome the possible Pareto inefficiencies.
 56
So far we have taken the information structure as given. But the
fact that particular information structures give rise to Pareto inef-
ficiency means that there is an economic value in transmitting informa-
tion from one agent to another, as well as in the creation of new in-
formation. J. Marschak (1968), Hirshleifer (unpublished), and others
have begun the study of the economics of information, but the whole
subject is in its infancy. Only a few remarks relevant to our present
purpose will be made here.
(1) As both communications engineering and psychology suggest,
the transmission of information is not costless. Any professor who has
tried to transmit some will be painfully aware of the resources he has
expended and, perhaps more poignantly, of the difficulties students
have in understanding. The physical costs of transmission may be low,
though probably not negligible, as any book buyer knows; but the
"coding" of the information for transmission and the limited channel
capacity of the recipients are major costs.
(2) The costs of transmitting information vary with both the type
of information transmitted and the recipient and sender. The first
point implies a preference for inexpensive information, a point stressed
in oligopolistic contexts by Kaysen (1949, pp. 294-295) and in other
bargaining contexts by Schelling (1957). The second point is relevant
to the value of education and to difficulties of transmission across cul-
tural boundaries (so that production functions can differ so much
across countries).
(3) Because the costs of transmission are nonnegligible, even situa-
tions which are basically certain become uncertain for the individual;
the typical economic agent simply cannot acquire in a meaningful
sense the knowledge of all possible prices, even where they are each
somewhere available. Markets are thus costly to use, and therefore
the multiplication of markets, as for contingent claims as suggested
above, becomes inhibited.
EXTERNALITIES ILLUSTRATED*

After this long excursus into the present state of the theory of equi-
librium and optimality it is time to discuss some of the standard con-
cepts of externality, market failure, and public goods generally. The
clarification of these concepts is a long historical process, not yet con-
cluded, in which the classic contributions of Knight (1924), Young
(1913 pp. 676-684), and Robertson (1924) have in more recent times
been enriched by those of Meade (1952), Scitovsky (1954), Coase
(1960), Buchanan and Stubblebine (1962), and Demsetz (1966). The
concept of externality and the extent to which it causes nonoptimal
market behavior will be discussed here in terms of a simple model.
Consider a pure exchange economy. Let xk be the amount of the kVh
commodity consumed by the i'h individual (i=l, ... , n; k=l, .
(m) and x, be the amount of the PIh commodity available. Suppose in
general that the utility of the i'h individual is a function of the con-
sumption of all individuals (not all types of consumption for all
individuals need actually enter into any given individual's utility
*Further discussion of this issue is found in the papers by Davis &Kamien, and
Kneese &d'Arge in this volume.
 57
function); the utility of the ith individual is Ui(x,,, X.,J). We
have the obvious constraints:
(1) E~_O

Introduce the following definitions:

(2) x 1f= Xfk-

With this notation a Pareto-efficient allocation is a vector maximum

of the utility functions U (xi 1 1, . . ., xim,,), subject to the constraints
(1) and (2). Because of the notation used, the variables appearing in
the utility function relating to the j"h individual are proper to him
alone an appear in no one else's utility function. If we understand
now that there are n2m commodities, indexed by the triple subscript
jik, then the Pareto-efficiency problem has a thoroughly classical form.
There are n2m prices, Pjik, attached to the constraints (2), plus m
prices, qk, corresponding to constraints (1). Following the maximiza-
tion procedure formally, we see, much as in Samue son [19541, that
Pareto efficiency is characterized by the conditions:
(3) )1i(builabf=Pi.k1

and
(4) ZPJfk=qk,

where x, is the reciprocal of the marginal utility of income for indi-

vidual j. (These statements ignore corner conditions, which can easily
be supplied.)
Condition (4) can be given the following economic interpretation:
Imagine each individual i to be a producer with m production proc-
esses, indexed by the pair (i,k). Process (i,k). has one input, namely
commodity k, and n outputs, indexed by the triple (j,i,k). In other
words, what we ordinarily call individual i's consumption is regarded
as the production of joint outputs, one for each individual whose
utility is affected by individual i's consumption.
The point of this exercise is to show that by suitable and indeed
not unnatural reinterpretation of the commodity space, externalities
can be regarded as ordinary commodities, and all the formal theory of
competitive equilibrium is valid, including its optimality.
It is not the mere fact that one man's consumption enters into an-
other man's utility that causes the failure of the market to achieve
efficiency. There are two relevant factors which cannot be discovered
by inspection of the utility structures of the individual. One, much ex-
plored in the literature, is the appropriability of the commodities
which represent the external repercussions; the other, less stressed, is
the fact that markets for externalities usually involve small numbers
of buyers and sellers.
The first point, Musgrave's "exclusion principle," (1959, p. 86) is
so well known as to need little elaboration. Pricing demands the possi-
bility of excluding nonbuyers from the use of the product, and this
 58
exclusion may be technically impossible or may require the use of con-
siderable resources. Pollution is the key example; the supply of clean
air or water to each individual would have to be treated as a separate
commodity, and it would have to be possible in principle to supply to
one and not the other (though the final equilibrium would involve
equal supply to all). But this is technically impossible.
The second point comes out clearly in our case. Each commodity
(jik) has precisely one buyer and one seller. Even if a competitive
equilibrium could be defined, there would be no force driving the sys-
tem to it; we are in the realm of imperfectly competitive equilibrium.
In my view, the standard lighthouse example is best analyzed as
a problem of small numbers rather than of the difficulty of exclusion,
though both elements are present. To simplify matters, I will abstract
from uncertainty so that the lighthouse keeper knows exactly when
each ship will need its services, and also abstract from indivisibility
(since the light is either on or off). Assume further that only one ship
will be within range of the lighthouse at any moment. Then exclusion
is perfectly possible; the lighthouse need only shut off its light when
a nonpaying ship is coming into range. But there would be only one
buyer and one seller and no competitive forces to drive the two into
a competitive equilibrium. If in addition the costs of bargaining are
hi h, then it may be most efficient to offer the service free.
If, as is typical, markets for the externalities do not exist, then the
allocation from the point of view of the "buyer" is determined by a
rationing process. We can determine a shadow price for the buyer;
this will differ from the price, zero, received by the seller. Hence, for-
mally, the failure of markets for externalities to exist can also be
described as a difference of prices between buyer and seller.
In the example analyzed, the externalities related to particular
named individuals; individual i's utility function depended on what a
particular individual, j, possessed. The case where it is only the total
amount of some commodity (e.g., handsome houses) in other people's
hands that matters is a special case, which yields rather simpler re-
sults. In this case, aUJ/jxk is independent of i for i dj, and hence, by
(3), pjtk is independent of i for i5xj. Let,

pifk=pik, Pjik=Pjk for iFij.

Then (4) becomes,

Pik+ E pik=qk,
jFi
or,
(Pikt Oik) + ZPjk=qk,
j
from which it follows that the difference, Pik-Yik, is independent of i.
There are two kinds of shadow prices, a price Pik, the price that indi-
vidual i is willing to pay for an increase in the stock of commodity k in
any other individual's hands, and the premium, Pfk-pfk, he is willing
to pay to have the commodity in his possession rather than someone
else's. At the optimum, this premium for private possession must be
the same for all individuals.
 59

Other types of externalities are associated with several commodities

simultaneously and do not involve named individuals, as in the case
of neighborhood effects, where an individual's utility depends both on
others' behavior (e.g., esthetic, criminal) and on their location.
There is one deep problem in the intepretation of externalities
which can only be signaled here. What aspects of others' behavior do
we consider as affecting a utility function? If we take a hard-boiled
revealed preference attitude, then if an individual expands resources
in supporting legislation regulating another's behavior, it must be
assumed that that behavior affects his utility. Yet in the cases that
students of criminal law call "crimes without victims," such as homo-
sexuality or drug-taking, there is no direct relation between the
parties. Do we have to extend the concept of externality to all matters
that an individual cares about? Or, in the spirit of John Stuart Mill,
is there a second-order value judgement which excludes some of these
preferences from the formation of social policy as being illegitimate
infringements of individual freedom?
MARKET FAILURE
The problem of externalities is thus a special case of a more general
phenomenon. the failure of markets to exist. Not all examples of
market failure can fruitfully be described as externalities. Two very
important examples have already been alluded to; markets for many
forms of risk-bearing and for most future transactions do not exist
and their absence is surely suggestive of inefficiency.
Previous discussion has suggested two possible causes for market
failure: (1) inability to exclude; (2) lack of necessary information to
permit market transactions to be concluded.
The failure of futures markets cannot be directly explained in
these terms. Exclusion is no more a problem in the future than in the
present. Any contract to be executed in the future is necessarily con-
tingent on some events (for example, that the two agents are still
both in business), but there must be many cases where no informa-
tional difficulty is presented. The absence of futures markets may be
ascribed to a third possibility: (3) supply and demand are equated
at zero; the highest price at which anyone would buy is below the
lowest price at which anyone would sell.
This third case of market failure, unlike the first two, is by itself
in no way presumptive of inefficiency. However, it may usually be
assumed that its occurrence is the result of failures of the first two
types on complementary markets. Specifically, the demand for future
steel may be low because of uncertainties of all types; sales and tech-
nological uncertainty for the buyer's firm, prices and existence of com-
peting goods, and the quality specification of the steel. If, however,
adequate markets for risk-bearing existed, the uncertainties could be
removed, and the demand for future steel would rise.
TRANSACTION COSTS*

Market failure has been presented as absolute, but in fact the situa-
tion is more complex than this. A more general formulation is that
* Further discussion of this issue is found in the paper by Demsetz in this
volume.
27-877-69-vol. 1-6
 ,60
of transaction costs, which are attached to any market and indeed
to any mode of resource allocation. Market failure is the particular
case where transaction costs are so high that the existence of the
market is no longer worthwhile. The distinction between transaction
costs and production costs is that the former can be varied by a change
in the mode of resource allocation, while the latter depend only on the
technology and tastes, and would be the same in all economic systems.
The discussions in the preceding sections suggest two sources of
transaction costs. (1) exclusion costs; (2) costs of communication and
information, including both the supplying and the learning of the
terms on which transactions can be carried out. An additional source
is (3) the costs of disequilibrium; in any complex system, the market
or authoritative allocation, even under perfect information, it takes
time to compute the optimal allocation, and either transactions take
place which are inconsistent with the final equilibrium or they are de-
layed until the computation are completed (see T. Marchak, 1959).
These costs vary from system to system; thus, one of the advantages
of a price system over either bargaining or some form of authoritative
allocation is usually stated to be the economy in costs of information
and communication. But the costs of transmitting and especially of
receiving a large number of price signals may be high; thus, there is a
tendency not to differentiate prices as much as would be desirable from
the efficiency viewpoint; for example, the same price is charged for
peak and offpeak usage of transportation or electricity.
In a price system, transaction costs drive a wedge between buyer's
and seller's prices and thereby give rise to welfare losses as in the
usual analysis. Removal of these welfare losses by changing to another
system (for example, governmental allocation on benefit-cost criteria)
must be weighed against any possible increase in transaction costs (for
example, the need for elaborate and perhaps impossible studies to
determine demand functions without the benefit of observing a
market) .
The welfare implications of transaction costs would exist even if
they were proportional to the size of the transaction, but in fact they
typically exhibit increasing returns. The cost of acquiring a piece of
information, for example, a price, is independent of the scale of use
to which it will be put.
CoLETVEcnv ACTION: THE POLITICAL PROCESS

The State may frequently have a special role to play in resource

allocation because, by its nature, it has a monopoly of coercive power,
and coercive power can be used to economize on transaction costs. The
most important use of coercion in the economic context is the collec-
tion of taxes; others are regulatory legislation and eminent domain
proceedings.
The State is not an entity but rather a system of individual agents,
a widely extensive system in the case of a democracy. It is appealing
and fruitful to analyze its behavior in resource allocation in a manner
analogous to that of the price system. Since the same agents appear in
the two systems, it becomes equally natural to assume they have the
same motives. Hotelling (1929, pp. 54-55) and Schumpeter (1942,
ch. XXII) had sketched such politicoeconomic models, and von Neu-
 61i

mann and Morgenstern's monumental work is certainly based on the

idea that all social phenomena are governed to essentially the same
motives as economics. The elaboration of more or less complete models
of the political process along the lines of economic theory is more re-
cent, the most prominent contributors being Black (1958), Downs
(1957), Buchanan and Tullock (1962), and Rothenberg (1965).
I confine myself here to a few critical remarks on the possibilities
of such theories. These are not intended to be negative but to suggest
problems that have to be faced and are raised by some points in the
preceding discussion.
1. If we take the allocative process to be governed by majority vot-
ing, then, as we will know, there are considerable possibilities of
paradox. The possible intransitivity of majority voting was already
pointed out by Condorcet (1785). If, instead of assuming that each
individual votes according to his preferences it is assumed that they
bargain freely before voting (vote-selling), the paradox appears in
another form, a variant of the bargaining problems already noted in
section 2. If a majority could do what it wanted, then it would be op-
timal to win with a bare majority and take everything; but any such
bargain can always be broken up by another proposed majority.
Tullock (1967) has recently argued convincingly that if the dis-
tribution of opinions on social issues is fairly uniform and if the
dimensionality of the space of social issues is much less than the num-
ber of individuals, then majority voting on a sincere basis will be
transitive. The argument is not, however applicable to income dis-
tribution, for such a policy has as many dimensions as there are in-
dividuals, so that the dimensionality of the issue space is equal to the
number of individuals.
This last observation raises an interesting question. Why, in fact,
in democratic systems has there been so little demand for income re-
distribution? The current discussion of a negative income tax is the
first serious attempt at a purely redistributive policy. Hagstr6m
(1938) presented a mathematical model predicting on the basis of a
self-interest model for voters that democracy would inevitably lead
to radical egalitarianism.
2. Political policy is not made by voters, not even in the sense that
they choose the vector of political actions which best suits them. It is
in fact made by representatives in one form or another. Political rep-
resentation is an outstanding example of the principal-agent relation.
This means that the link between individual utility functions and
social action is tenuous, though by no means completely absent. Rep-
resentatives are no more a random sample of their constituents than
physicians are of their patients.
Indeed, the question can be raised: to what extent is the voter, when
acting in that capacity, a principal or an agent? To some extent, cer-
tainly, the voter is cast in a role in which he feels some obligation to
consider the social good, not just his own. It is in fact somewhat hard
to explain otherwise why an individual votes at all in a large election,
since the probability that his vote will be decisive is so negligible.
COLLECTIVE ACTION: SOCIAL NORmIS
It is a mistake to limit collective action to State action; many other
departures from the anonymous atomism of the price system are
 62
observed regularly. Indeed, firms of any complexity are illustrations
of collective action, the internal allocation of their resources being
directed by authoritative and hierarchical controls.
I want, however, to conclude by calling attention to a less visible
form of social action: norms of social behavior, including ethical and
moral codes. I suggest as one possible interpretation that they are re-
actions of society to compensate for market failures. It is useful for
individuals to have some trust in each other's word. In the absence
of trust, it would become very costly to arrange for alternative sanc-
tions and guarantees, and many opportunities for mutually beneficial
cooperation would have to be foregone. Banfield (1958) has argued
that lack of trust is indeed one of the causes of economic under-
development.
It is difficult to conceive of buying trust in any direct way (though
it can happen indirectly, for example, a trusted employee will be paid
more as being more valuable) ; indeed, there seems to be some inconsist-
ency in the very concept. Nonmarket action might take the form of a
mutual agreement. But the arrangement of these agreements and es-
pecially their continued extension to new individuals entering the
social fabric can be costly. As an alternative, society may proceed by
internalization of these norms to the achievement of the desired agree-
ment on an unconscious level.
There is a whole set of customs and norms which might be similarly
interpreted as agreements to improve the efficiency of the economic
system (in the broad sense of satisfaction of individual values) by
providing commodities to which the price system is inapplicable.
These social conventions may be adaptive in their origins, but they
can become retrogressive. An agreement is costly to reach and there-
fore costly to modify; and the costs of modification may be especially
large for unconscious agreements. Thus, codes of professional ethics,
which arise out of the principal-agent relation and afford protection
to the principals, can serve also as a cloak for monopoly by the agents.
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