Bator, 1958

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THE ANATOMY OF MARKET FAILURE

By FRANCIS M. BATOB*

Introduction, 851. I. The conditions of market efficiency, 868. II.

Neoclasdcal external economies: a digression, 866. III. Statical externalities:

an ordering, 868. IV. Comments, 871. V. Efficiency, marketa and choice

of institutions, 877.

What is it we mean by market failure ? TypicaUy, at least in

allocation theoiy, we mean the failure of a more or less idealized

system of price-market institutions to sustain desirable activities

or to estop imdesirable activities.* The desirability of an activity,

in turn, is evaluated relative to the solution values of some expiidt

or implied maximum-welfare problem.

It is the central theorem of modem welfare economics that under

certain strong assumptions about technology, tastes, and producers'

motivations the equUibrium conditions which characterize a system

of competitive markets will exactiy correspond to the requirements of

Paretian efficiency.* Further, if competitivdy imputed incomes are

continuoudy redistributed in costiess lump-sum fashion so as to

achieve the income-distribution implied by a sodal welfare function,

then the competitive market solution will correspond to the one

electronically calculated Pareto-efficient solution which maximizes,

subject only to tastes, technology and initial endowments, that par-

ticular welfare function.*

* Center for International Studies and Department of Economics, Masssr

chusetts Instituto of Technology.

I am mudi indebted to R. S. Eckaus and R. M. Solow for detailed conunent

anddis

1 Activities broadly defined, to cover consumption as well as production.

2

I.e., to the conditions which define the attainable frontier of maximal

utility combinations with given preference functions, resource endowments and

technology. A community is on its Faretian frontier if it is imposmble to make

anyone better off (in terms of his own ordinal preference function) without mak-

ing someone else worse off. Associated with the utility possibility frontier, in

tum, is a production possibility frontier denoting maxinial alternative output

combinations. (Cf. my Simple Analytics of Welfare Maximisation, American

Economie

Reeiew XLVII (Mar. 1957), 22-50, and references therdn.)

8. In other

warda

given the right lump-sum taxes, markets will mateh

the aUocation called for by the point of tangenqr of the rdevant TT-function with

the utiliiy-possibiUly frontier, i.e., by the bliss point. The TT-function need

not, of course, be explicit it could be implicit in the political powei configuiHr

tkm which characterises a community. On the other hand, it cannot be just any

land of function. It has to have some special characteristics which refiect a

number of ethic-loaded restrictions, e.g., that individuals' preference functions

are to count, and to count positively (cf.,

HM.

and Section V bdow).

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3 5 2 QUARTERLY JOURNAL OF ECONOMICS

Many things in the real world violate such coiiespondence:

imperfect information, inertia and resistance to change, the infeasi-

bility of costless lum p^u m ta xes, businessmen's desire for a quiet

life,

uncertainty an d inconsistent expectation s, the vagariesd aggre-

gate demand, etc. W ith mo st of these I am not here concem ed: they

ha ve to do w ith the efficiency of real life ma rket institu tions

operated by real life people in a nonstationary world of unc ertainty,

iT'scalculation, etc.

What foUows is an attempt, rather, to explore and order those

pheno men a w hich cause eve n errorless profit- and preference-maxim iz-

ing calculation in a stationary context of perfect (though limited)

information an d foresight to fail to sustain Pareto-efficient aUocation.

I am concemed, in other words, with the decentralizing efficiency of

that regime of signals, rules and built-'in sanctions which defines a

price-market system.*

SpecificaUy, Section I sets out the necessary conditions for effi-

ciency of decentralized price-profit calculations both in a laissez-

faire and in a socialist setting of Lange-Lem er d v il servants.

Section II is a brief digression on an often discussed mode of faUure

in these cond itions: neoclassical external econom ies. It is concluded

tha t the m od em formulation of the doctrine, in terms of direct inter-

action , begs more questions than it answers; further, tha t the usual

em phasis on divorce of scarcity from effective ownership is m is-

placed. Section III , then , suggests a comprehensive ordering of type s

of market failure, with generalized indivisibility, pubUc goods, and,

last and least, nonapprop iiabiUty as the villains of the piece. Sectio n

IV con sists of some comm ents on the M eade and Scitov sky daasifiea-

tions of external economies; on tKe analytical link between indivisi-

bility and pubUc good s; on the significance of exclusion ; on oigan -

izational arrangements designed to c set extemaUty; and on blends

of the various typ es of market failure. Section V con du des w ith

som e cautionary no tes on the relevance of market-efficiency for choice

of institutions.

4.

In most of what follows, I shall assume that individual preferences,

though not necessarily sensitive cmly to own-consumption, are representable by

strictiy convex indifference surfaces (i.e., by an ordering (one for eaeh individual)

such that all points on a sttaight line connecting two equivalent pdnts x and

y

are preferred to

x

(hence to

y .

Bu t convexity is too restrictive. It exdud es

not only such duu acteristics of man's psyche as violato the usual regularities

these I do want to exclude but also such physical and topographical facts

as lumpy consumption-goods. Rather than attemp t a specification of preferences

with convex-like properties w h n e ch dc e must b e made among disorato bundles,

I dodge the problem by attributing lumpiness only to inputs (including, however,

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THE ANATOMY O F MARKET FAILURE

353

I . T H E CONDITIONS OF M AR K ET EITPTCIENCT

The central theorem of modem welfare economics, the so-caUed

duality theorem,asserts a correspondence betw een P are to efficiency

and market performance. It s ana lytical essence lies in the remark-

able fact that with all-round convexity, independence of tastes, etc.,

the technocratically formulated, institutionally neutral, Paretian

maximum-of-welfare problem has embedded within it a set of con-

stan ts: duals, Lagnm gean multipliers, shadow-prices, which hav e

all the analytical characteristics of prices, wages, rents, interest

rates.* Correspondence betwee n Pareto-efficiency and ma rket per-

formance implies, at th e least, th at decentralized decisions in response

to these prices by atom istic profit- and satisfaction-maximizers

sustain just that constellation of inputs, outputs and commodity-

distribution, that the maximum of the specified social welfare func-

tion calls for. It imp lies, in other words, th at decentralized m arket

calculations correctiy accoun t for aU economic costs and benefits

to which the rdevant W-function is sensitive.'

D u ali ty can fail in m any w ay s. SpecificaUy, and in a statical and

laissez-faire contex t:^

(1) D ua lity wiU fail unless the Pareto-efficient (a) in pu t-outp ut

points (production) and (b) associated commodity distribution points

(exchange) which associate with the maxim um of the welfare fun ction

in hand are characterized by a com plete set of marginal-rate-of-

substitution

MRS)

equalities (or limiting inequa lities) which, in

5. Th e theorem holds for the statical steady-statofiow mo dd of the W alrasian

sort where the solution values are station aiy time-rates; it holds, also, for dynam i-

cal system s involving cap ital formation Upven, still, convexity throuBluMit). For

these last, the solution values are time paths of inputs, outputo, prices, eto. (A

set of pointo is convex if, and only if, the strsight lines connecting all posdUe

pairs do not anywhere pass outside the set. Th e set of feadble outp ut points

bounded by a production posdbility curve is convex, for instance, if the curve

itself is concave-to-the-origin or a straight line. On all this, see Section V of

ffimple Analytics,

Und.)

6.

Given, again, optimal himp-sum redistribution of as-imputed incomes.

While I make use of the luinp-sum transfer device throui^iout this paper to

abstnwt from the income distribution problem and permit exdudve attention to

Fareto efficiency, it is w dl to noto that this involves a measure of deight-of-hand.

N o decentralised price-market typ e game can reveal the pa ttem of taxes and

transfers tha t would nuudmise a particular welfare function. Central calcula-

tion im plid t if not escplidt is unavoidable. Moreover, since_ distribution

(hence correct redistribution) of numersire^comes interdepends witii allocation

in production and exchange, the supposedly automatic, nonpolitical character of

market mediation is a myth on the strictest neoda sdcal assumptions. Th is is

not to say, even on our stratospheric levds of abstntction, that markets are

useless. Where i h ^ do computo well we are saved aa awful lot of calculation.

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QUARTERLY JOURNAL OF ECONOM ICS

tu m , yield a set of price-like constants. Where no such constan ts

exist, reference wiU be tofailure of existence.

(2) Should such an associated set of Lagrangean parameters

exist, duaUty would neverthdess faU, specifically in production, unless

the bliss configuration of inputs and outputs, evaluated in terms of

these price parameters, wiU y id d : (a) a local profit-maximum position

for each producer, rather than , as po ssible, a profitTniniTnnm;(b) no n-

negative profits for all producers from whom production is required;

(c) m aximu m profits-in-the-large for each producer. Failure on

counts (a) and (c) wiU be labeled failure bysignal that on count (b)

failure by incentive.^

(3) }ven if aU efficient production configurations, or the one

which maximizes a particular welfare-function, coincide with points

of maximum and non-negative producers' profits, market mediation

m ay fail in produ ction. If prices are determ ined by m arket forces,

they will not correspond to a Paretian maximum unless self-policing

perfect com petition obtains in aU mark ets. Self-policing com petition

requires very m an y producers in every m arke t.' If, the n, for

whatever reason, some markets are saturated by a few firms of

effident scale, the fuU welfare-maximum so lution of inpu ts, outpu ts

and prices wiU no t be sustained. There wiU be faUure by structure.

(4) F inally , even if aU ab ov e is satisfied, ma rket performance

could still faU, and fail in a statical sense, due to arbitrary legal and

organizational imp erfections, or feasib ility lim itation s on keeping

book, su di as leave some inputs or outpu ts hidden, or predu de

their expUcit allocation or capture by market processes (e.g., the

restriction, unless I go into basebaU, on the sale of the capitalized

valu e of m y lifetime service s). FaUure isb y enforcem ent.

8. We could consider, instead, the configuration which associates with the

initial pattern of ownership of endowm ent. Or we could play it safe and extend

the conditions to cover each and eve iy Fareto effident configuration. Bu t this

would be overly strict, since many efficient dtuations bave no rdevance dther to

any interesting IT-functions or in terms of the initial distribution of scardties.

It may bie worth noting, incidentally, tha t enstence, as used above^ is

not the same as existence in the sense of, e.g., An ow and Debreu (in Existence

ofanEquilibrium for a Competitive Economy, Econometrica,Vol. 22 (July 1054),

pp.

266-00). They use the term to denoto the completo set of conditions which

defines competitive equilibrium, and this indudes, in addition to all that is

implied by (1) above, conditions akin to my conditions (2), and some analogous

conditions co consumers.

0. Th is is slightly midesd ing: a s we shall see, failureoncount c)leads both

to MgnuWngand to incentive troubles. Anyway, the lahd s are only for expodtoty

convenience.

1.

Or at least the potentiality of veiy many producers, ready and able to

enter the fray instantaneously. Th is may be sufficient in the constant-cost

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THE ANATOMY

O

MARKET FAILURE

355

All the above are germane to duality in its usual sense, to tbe

statical Ptueto-efficiency of laissez-faire markets witb genuine pixxfit-

and satisfaction-seekers.* Con ditions (1), (2) and (4) are relevant,

also,

to th e decentralizing efficiency of a L ange-Lem er ty pe organiza-

tional schem e. In its capitalist version, w ith profit-motivated

operation of privately-owned means of production where it is simply

an anti-monopoly device to assure parametric take-prices-as-given

behavior, conditions (1), (2) and (4) are all necessaiy for efficiency.

Of course condition (3): self-policing competition, no longer matters.

In its tm e socialist version, a Lange-Lemer f ^ t e m can afford to

fail also by incen tive, (2b ). Socialist civU servan ts, under injunc-

tion to maximize profit (in the small) in terms of fixed centrally-

quoted prices, care or should care not at aU about absolute profit-

ability. B y assum ption the scheme can dispense wit h the built-in

incentive of po sitive profit: the lure of bureaucratic adva ncem ent, the

image of Siberia, or the old school tie presumably substitute for the

urge to get rich. B ut if prices and the injunction to maximize profit

are to be used to decentralize, condition (1): existence, and (2a) and

(2c):

correct and unam biguou s signals, remain crucial.* S o do es

condition (4): the solution of quantities and prices need not be

profitable and sdf-enforcing, b ut it does hav e to be enforceable. If

the nectar in apple blossoms is scarce and carries a podtive shadow

price, it must be possible to make eveiy beekeeper pay for his

It warrants repetition that this has to do with whether a decen-

tralized price-market game wiU or will not

sustain

a Pareto-efficient

configuration. Th e word sustain is critical. There exists a ho st of

further considerationis which bear on dynamical questions of adjust-

m ent , of how the system get s there. (E.g ., wiU some natural

price-market type computational routine of price-quantity responses

with a meaningful institutional counterpart tend to track the sdu-

tion?) Th ese are no t here at issue. W e shaU be conc em ed only wit h

the prior problem of wh ether a price-market sy stem which finds itself

2. Th e mathematically minded will object tha t \3 and (4), at least, do not

rea l^ violato duality in its strict mathematical sense; the dual minimum prob-

lem still yields Lagrangean constants. True, yet I think it suggestive to use

dualily mther more loosely as a labd for the general wdfare theorem, particu-

larly as this does not lead, in this context, to any ambiguity.

8. It is tempting, bu t wrong, to suggest that in a true Lange-Lemer world

totals do not m atter and only margins count. It is true that the non-negativeness

of profits is immaterial. Where there is any sharing of diadow-price sets by tw o

or more production points, however, totals necessarily become a part of the

signaling system and if 2(c) does not hd d t h ^ may lead down the garden path.

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QUARTERLY JOURNAL OF ECONOMICS

a t the m aximum -welfare poin t wUl or wUl no t tend to remain there.*

Th e rd ev an t literature is rich but confusing. It abounds in

mutually reinforcing and overlapping descriptions and explanations

of market faUure: external economies, indivisibUity, nonappropri-

ability, direct interaction, public goods, atmosphere, etc. In a sense,

our problem is simply to sort ou t the relations amo ng these. In doing

so, it is appropriate and useful to begin with a brief review of the

neoclassical doctrine of external economies and of its modem formula-

tion in terms of direct intera ction .

II . NEOCLASSICAL EXT ERN AL ECONO MIES: A DIOBEBSION

By Way cf Some H istory

Mardiall, as has

dtea

been pointed out,

jarapaaed

the external

economy argument to explain, without resort to dynamics, the phe-

nomenon of a nega tively sloped ( forward falling ) long -mn indu stry

supply curve in terms consistent with a horizontal or rising marginal

cost curve

M C)

in the representative firm. Th e device perm its

in logic, if not in fact long-run competitive equilibrium of many

firms within an in du stiy, each producing at its profit-maximum price-

equal-to-a-rising-ilf C position, without foredosing the possibility of a

falling supply price with rising industry output.*

Th e mechanism is simple. It is postulated tha t an expansion in

the output of the industry as a whole brings into play econcmiies

which cause a dow nward shift of the cos t curves of aU the comp

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THE ANATOMY OF MARKET FAILURE 357

firms. Th ese econom ies, how ever, are no t subject to exploitation b y

any one of the myriad of tiny atomized firms. Their own M C curves,

at p =

M C,

rise both before and after the shift, due, presumably, to

intemal diseconomies associated with the entrepreneurial function

which defines the firm. Even the modem formulation is not entirdy

witho ut am biguity institutional amb iguity is intrinsic to th e device

of parametrization: how many firms does it take for the demand

curve of each to b e perfectiy horizontal? bu t it does provide a

means for saving the comp etitive m od d, of ducking the mon opoly

problem.

M arshaU, and also Professor Pig ou , preferred, as it were, th e

other ho m of wh at they perhaps saw as a dilemma. Th e external

economy device, whUe saving competition, implies a flaw in the effi-

cacy of the invisible han d in guiding production.* Price equal to

M C is saved, but wrong. Market forces, they aigued, wiU not give

enough output by industries enjoying external economies and wiU

cause industries with rising supp ly curves to overexpand. H ence th e

MarshaU-Pigou prescription: to harmonize private production deci-

sions with pubUc welfare, tax t he latter se t of industries and subsidize

the fonner.

It took th e better part of thirty years, and the cumu lative powers

of AUyn Young, and Messrs. Robertson, Knight, Sraffa, and Viner,

to unravd the threads of truth and error which mn through the

M arshall-Pigou argum ent.' Th e cmcial distinction, which provides

the k ey to it aU,.is between w hat Viner labd ed tec hnd ogical external

economies, on the one hand, and pecuniary external economies on the

other. Th e latter, if dominan t, cause the long-run supp ly curve of

an industry, say A, to decline because the price of an input, B, falls

in response to an increase in A 's dema nd for it. Th e tech nd ogica l

variety , on th e other hand, thou gh also a reversible function of indus-

try output, consists in organizational or other improvements in effi-

ciency which do not show up in input prices.*

6. Tha t there are difficulties also with income distribution was by tha t time

generally recognised.

7. The stntegic articles, with the exception of Young's ( Figou's WtaUh

and W Ojate,

this /ourno /, X X V II (1018), 672-86 ), as wdl as Ellis and FeUner's

1048 treatment, have all been reprinted in American Economic Association,

RmUrn^tn Price Theory,ed. Stigler&Boulding. For an excdlent modem dis-

cussion, see R. L. Bidiop, conomic Theory(to appear).

8. Note, however, that there need be nothing about an organisational

improvement to make it obvious in advance whether it will tum ou t to be techno-

logical or, thro ui^ intconalisation, pecuniaiy. Many trade assoda tion typ e

services which are justified by the scale of an industiy could as wdl be provided

commercially, and vice versa.

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3 5 8


As regards pecuniaiy external economies, Robertson and Sraffa

made it clear that in a sense both the MarshaU-Pigou condusions

were wrong. For one thing , no subsid y is caUed for. Th e implied

gains in efficiency are adequately signaled by the input price, and

profit-maximizing output levds by the A-firms are sociaUy efficient.

Second, monopoly troubles may be with us, via, as it were, the back

door. For wh at causes the price of to drop in response to increased

demand? W e are back where we started : a declining long-run supply

curve.

In the end, then, if

intemal

technological economies of scale are

ruled out, we are left with only

tedaiological

external econom ies. AU

pecuniaiy external economies must be due to technological economies

somewhere in the system .' It is tm e and this is wh at remains of

the original MarshaU-Pigou proposition th at tech nological exter-

naUties are not correctly accounted for by prices, that they violate

the effidency of decentralized market calculation.

The Modem Formulation^

In its m odern version, the n otion of external economies exter-

nal econ(Hnies proper that i s: Viner's techn do gical variety bd on gs

to a more general doctrine of direct intera ction. Suc h interaction ,

wh ether it involv es producer-producer, consumer-consum er, producer-

consumer, or emplQyermployee relations, consists in interdepend-

ences tha t are external t o the price system, h ence unaccounted for by

market valuation s. AnalyticaUy, it implies the nonindependence of

various preference and production function s. It s effect is to cause

divergence between private and social cost-benefit calculation.

That this is so, is easUy demonstrated by means of a simplified

variant of a production m od d suggested by J. E. Meade.* Assum e

a world of all-round perfect competition where a single purchasable

and indastically supplied input, labor

L),

is used to produce tw o

homogeneous and divisible goods, apples A) and honey H), a t

nonincreasing retums to scale. B ut while the outp ut of A is depend-

ent only

aa Lji :A = A LA),

hon ey production is sensitive also to

the level of apple output:

H = H LH,A LA)).

(Professor M ead e

0. Fecun iaiy diseconomies, in contrast, need have no technological coun ter-

part. Finite-elastic supplies of unproduced inpu ts are a sufficient cause. Recall,

indd enta lly, th at only narrowly statical reverdble phenomenaare adm isdble here.

1. While this section makes some dight use of elementary calculus, the

reader uninterested in technicalities may avnd, without loss of continuity, all

but some dmple notation.

2 .

conomic

Journal,LX II (Mar. 1052 ). Meade uses a two factor modd

and, while he does not explidtiy solve the Faretian maximum problem, shows

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makes pleasurable the thought of apple blossoms making for honey

abundance.)*

By solving the usual constrained maximum problem for the

production-possibility curve, it can be shown that Paretian produc-

tion efficiency implies

dA , dH dA

,

...

where

PH, PA,

and

w

represent the prices, respectively, of honey,

app les and labor.* Eq uation (1) is famUiar enough and c onsistent

with profit max imizing. Ea ch com petitive honey producer wUl do

for profit what he must for efficiency: hire labor until the value of its

social as weU as priva te mftrgini^l produc t equ als the wage rate. N o t

3H

so the apple producers; unless

T = 0

unless the cross effect of

oA

apples on hon ey is zero their profit-maximizing production deci-

sions wUl be nonefficient. SpecificaUy, if app les ha ve a po sitive exter -

nal effect on honey output, market-determined L^ wiU be less than

is soc ially desirable.*

A different w ay to see this is to exam ine the relations of private to

social marginal cost. Th e marginal m oney cost of apples to the com -

8. Both functions reassumed homogeneous of d ep ee one. Moreover, apple

blossoms (or the nectar therein) are exhaustible, nti on ab le privato good s:

more nectar to one bee means less to anotber. On the need for tiiis assumption,

sse Section I I M bdow.

4. Assuming intemal tangend es ndall-rouud convexity (the last is im plid t

in constant retums to L: the A-effect on

H

reinforces convexity), as well as non-

satiation and nonredundam ^(L ^ L^ + Lg), the maximisation ofp^A + PgH,

subject to the production functions and the supply of labor, is equivalent

to finding a critical vulue for the Lagrangean expresdon,

F

p^A (Ii^) +

PgHlLg A(Lj)] + v(L - LA - Lg). To do so, differentiato Fwith respect

to

L

an d

L y,

treating

p^, Pg

and w as arbitrary constants and set the resulting

first order partial derivative s equal to sero. This will giv e exactiy (1) and (2).

(Needless to say, the value weights can be varied at will, or taken as given.)

5. To see this, lewrito (2) to read

:;=-

,. ^ and match it against

aii on

theprofitrmaximidngrule,

^ -

Clearly, 3 - : ^ 0

at p OA >

/ d A \ < : /_ d A\

V V dL ^/S od

odal

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360

QUARTERLY JOURNAL

OF

ECONOMICS

p e t i t i v e a p p l e p r o d u c e r i s . . . . ,; t h a t 0,the tme

margiTial

social

cost

ofan

extra

oA

apple,intermsof honey foregone,isless than

the

m arket-indicated

private cost.

It is

less precisely

bythe

amount

of

positive feed-

back

on

honey output

due the

extra apple.

By combining

1) and 2),

diminatingw

and

dividing through

dA

by PB

and T T - we get the

cond ition

for

Pareto efficiency in terms of

dL

private JlfC's:

dH dLg

_ PA dH

dA dLA

PH dA

Clearly, price equaltoprivate marginal cost wiUnotdo. Further,if

prices are market-determined, the y wiU diverge from tm e,

social

mar-

ginal cost.

Any number

of

variations

on the

m od d suggest themselves.

As

Meade pointed out, interactions can

be

mu tual and need

not be

asso-

ciated with

the

outputs. Even

in the

above case,

it

is perhaps more

suggestive

to

think

of

L^

as

producing some social value-product both

in

the

industiy and

the

H industry.

In the

most general formula-

tion, one

can

simply think

of

each p roduction function

as

containing

aU liie other variables

of the

system, some perhaps with zero weight.

Moreover,

by

introducing

two or

more nonproduced inputs

one can,

as M eade d oes, work ou t the consequences for income d istribution and

input proportions.*

6.

The

question

of

whether technological external economies involve shifts

of eadi other's production functions, or mutually induced movements along such

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361

Some Queries

The modem formulation of the doctrine of external economies,

in terms of direct interaction, is not only intemaUy consistent: it also

yields insight. Y et one m ay weU retain abou t it som e dissatisfaction.

Th ere is no dou bt th at th e Robertson-SraffarViner distinction betw een

the technological and the pecuniary sort gets to the nub of what is

the matter wit h th e original M arshallian analysis. It cuts right

through the confusion which led MarshaU and Pigou to conclude

that the price mechanism is faulty in situations where in tmth it is

at its best: in aUocating inputs in less than infinitdy elastic supply

betw een altem lttive produ ctive uses. It also facOitates unam biguous

formu lation of the more difficult faUing sup ply price case. B u t in

a sense it only begs the fundamental question: what is it that gives

rise to direct inter actio n, to short circuit, as it wer e, of th e signaUng

system?

M ost m od em writers have le t ma tters rest with the EUis-FeUner

ty pe explanation : the divorce of scarcity from effective own ership.'

D oe s nonapp ropriability then explain all direct interaction? In a

sense it does, yet by directing attention to institutional and feasibility

considerations wh ich ma ke it impracticable for real life m arket-

institutio ns to mim ic a price-profit-preference com puta tion, it d iverts

atte ntio n from some deeper issues. Surely the word ownership

serves to iUuminate but poorly the phenomenon of a temperance

leaguer's reaction to a hard-drinking neighbor's (sound insulated and

solitary) Satu rday n ight, or the reason wh y a price system , if efficient,

wUl no t permit fuU comp ensation, in an age of dec tron ic scramblers,

for an advertisemen t-less radio program, or for the services of a

bridge.*

function as to give a xes only to inputs and outp uts tha t are purchased and sold,

or a t least controlled, and the effects of everything else impinging on production

(e.g., of humidity, apple blossoms, eto.) are built into the curvature cf the func-

tion,

then it follows that externalities will condst in shifts of some functions in

response to movem ents along others. On the other hand, if, a s in our apple-

hon ey case, it seems useful to think of the production function for 0 as having

an A-aida then, dearly, induced movement along the function is a signal of

extemality.

7.

Op. cU.

8. Moreover, in th e one sense in which nonappropriability fits all cases of

direct interaction, it explains none. If

a

it denotes is the failure of a price-market

game properly to account for (to appropriato) all rdevant costs and benefits,

tben it is simply a qrnonym for market failure (for generalised extemality)i uid

cannot be used to explain what causes any particular instance of such fsilure. I

use i t in a much narrower sense, to mean the inability of a producer of_ a good or

service phydcally to exclude users, or to control the rationing of bis produce

among them. In my sense not only bridges but also, say, tolevidon programs are

fully appropriable: it is always posdble to use scramblere.

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It m ay b e argued, of course, tha t at least the tw o latter examples

are out of order, that radio programs and bridges do not involve

d irect, i.e., non-price, interaction. B ut is this really so? D oes no t

the introduction of a new program directly affect my and your con-

sumption possibilities, in ways other than by a change in relative

prices? D oe s not a bridge, or a road, hav e a direct effect on the pro-

duction possibilities of neighboring producers, in precisely the sen se in

which apples affect the possibilities of beekeepers?'

True, perhaps bridges and roads are unfair: they violate the neo-

classical assumption of perfect divisibility and nonincreasing retums

to scale. B ut they surely do involve non-price interaction. In fact,

lumpiness and increasing retums are perhaps the most important

causes of such interaction. Are they t o be denied statu s as external-

ities? M ore generaUy, ure we to exclude from the class of exte m alitie s

any direct interaction not due to difficulties w ith effective owner-

ship, an y faUures other than by enforcement ?

It w ould be, of course, perfectly legitimate to d o so tastes are

various. B ut I think it more natural and useful to broaden rather

than restrict, to let externality denote any situation where some

Paretian costs and benefits remain

external to

decentralized cost-

revenue calculations in terms of prices.' If, ho weve r, we do so, then

clearly non approp riability' wiU no t do au a com plete explana tion. It s

concem with the inability of decentralized markets to sustain the

sdution-prices and quantities called for by

a

price-profit-preference

type calculation, as computed by a team of mathematicians working

with IBM machines, tends to mask the possibUity that such machine-

0. l t is posdble, of courae, to intorpret these examples sinvolving very large

changes in price: from infinity to zero. Bu t it does not help to do so. The shared

characteristic of bridges and programs is tha t therei no price which will efficiently

mediato both supply and demand.

I have pussled over ways of limiting the notion of direct intoraction to

something lesa than all inatanceg where tbere ia wme intoraction not adtiquatoly

signaled by price. Robert Solow has suggested to me tha t tbis might be done by

distinguishing situationH where something ia not subject to a market tost at all

from instanceiji where no single price constitutes

H

correct teat for both ddea of a

transaction (e.g., where the correct ration price for the aervicea of an expensive

facility ia sero). I am inclined, rather, to drop the attom pt to uae direct intor-

action as an explanation of market failure; it ia beat uaed, if a t all, yet another

aynonym for such failure.

1.

Recall that it ia the exiatence of such extornality, of reddue, at the

blias-point, of Pigouvian unoompenaated aervicea and inddental uncharged

disservices tha t definea market failure. It may be objected that to generalize

the extemality notion in thia way is to rob it of all but deacriptive aignificance.

Bu t surely tbere ia not much to rob ; even in ita atrictost neodasd cal formulation

it begs more than it anawera. In its generalised aenae it at leoat has the virtue

of suggesting the right questions.

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THE ANATOM Y OF MARKET FAILURE

363

calculated solution

Q'S

m ay weU be nonefficient.* I t explains failure

by enforcement, bu t leave s hidden the empirically more impo rtant

phenom ena wh ich cause failure by nonexistence, signal, and

incentive. S ection III is designed to bring these deeper causes of

generalized extemaUty into the foreground.

III . STATICAL EXTER NALITIES : A N OBDEBINO

If nonappropriability is, by

itself

too fiimsy a b ase for a doctrine

of generalized (statical) externality, what broader foundation is there?

Section I's hierarchy of possible modes of market failure suggests a

fivefold classification. If, how ever, one looks for an organizing prin-

ciple not to modes of failure but to causes, there appear to be three

polar types: (1) Ownership Extemalities, (2) Technical Extemalities,*

and (3) Public Good Extem alities. These are not mu tually exclusive:

most extem ality phenomena are in fact blends. Y et there emerges a

sufficient three-comered clustering to warrant consolidation.*

Type 1): Own ership Extemalities

Imagine a world which exhibits generalized technological and

taste convexity, where the electronically calculated solution of a

Paretian maximum-of-welfare problem yields not only a unique set

of inputs, outputs and commodity-distribution, but where initial

endo wm ents plus lump-sum transfers render income distribution o pti-

mal in terms of the comm unity' s social welfare function. Assum e,

further, that everything that matters is divisible, conventionally

rationab le, and either av ailable in inelastic tota l supply,* or producible

at constant retums to scale; also that tastes are sensitive only to

own-consumption. W e know, then, from the duality theorem, t ha t

8. Or that tbe algorism may break down for lack of a condstent set of p's.

4.

I should much prefer technological, but rince tbia would necessarily

confuse

my Typa

(2) with Frofeaaor Viner'a technolcicical Ifixedon technical. .

5. In effect, we end up with a five-by-th ree ordering of types of failure :

five modes vs . three cauaea. Its relation to Meade's catogoriea (op.cit.)

and to Tibor Sdtovsky's claadfication (in 'Two Concepts of Extomal Econ-

omies, Journa l ttf Political Econom y,LXII, April 1054) is discussed in Section IV

bd ow . I have had tbe benefit of reading, alao, William FeUner's Individual

Investment Frojects in Growing Economies,

nvestment Criteria and Economic

Growth

(Froceedinga of a Conference, C entor for International S tudies, Massa-

chusetts Inatituto of Technology, 1955) and an unpublinhed paper by Svend

Laursen, Extemal E^ionomiea and Econonuc Growth.

6. The supply of such nonproduced acard ties need not, of courae, rem ain

constant. On the other band, thdr ownership distribution m ust not be ao con-

centrated aa to preclude com petitive rationing. There muat exist no indivis-

ible lake full of fish, etc., such aa might lie subject to monopolisation, but tbou-

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3 6 4


the bliss point implies a unique' set of prices, wages and rents, such

as would cause atomistic profit- and preference-maximizers to do

exa ctiy w hat is necessary for bliss. In particular, aU required produc-

tion points give maximum and non-negative producer's profits.

Th is is an Adam Sm ith dream world. Y et it is possible that due

to more or less arbitrary and accidental circumstances of institutions,

laws, customs, or feasibility, competitive markets would not be

Pareto-efficient. Ta ke, for instance, the Mead e exam ple of app les

and honey. Apple blossoms are produced at constant retums tu

scale and are (we assumed) an ordinary, private, exhaustible good:

the m ore nectar for one bee, the less for another. It is easy to show

that if apple blossoms have a positive effect on honey production (and

abstracting from possible satiation and redundancy) a maximum-of-

welfare solution, or any Pareto-efficient solution, wiU associate with

apple blossom s a po sitive Lagrangean shadow-price. If, then , apple

producers are unable to protect their equity in apple-nectar and

markets do not impute to apple blossoms tJieir correct shadow value,

profit-maximizing decisions wiU fail correctly to allocate resources

(e.g.,

L)

at the margin. The re will be failure by enforcement.

This is what I would call an ownershipextern ality. It is esseii-

tiaUy M eade's unpaid factor case. Non appropriation, divorce of

scarcity from effective ownership, is

the

binding consideration. Cer-

tain goods (or bads ) with determ inate non-zero shado w-values

are simply not attributed . It is irrelevant here whether this is

because the lake where people fish happens to be in the public dom ain,

or because keeping book on who produces, and who gets wh at,

may be impossible, clumsy, or costly in terms of resources.* For

whatever legal or feasibility reasons, certain variables which have

positive or negative shadow value are not assigned axes. Th e

beekeeper thinks only in terms of labor, the orchard-owner only in

terms of apples.

The important point is that the difficulties reside in institutional

arrangem ents, the feasibUity of keeping tab , etc. Th e scarcities at

issue are rationable and finely divisible and there are no difficulties

with total conditions : at the bliss-configuration every ac tiv ity

would pay foritself Apple nectar has a positive shadow price, which

7. Or, where there are cornera, only inesaentially indeterminato.

8. Set up a variant of tbe A pple-Honey model of Fart II, introducing apple

blossoms, B, explicitly. Add a production function, B

i?(&^), and aubatituto

B Lji) for A L^) as the second input in honey production. The solution will

give out a positive Lagrangean shadow price for

B,

and profit-maximising pro-

A

and

B,

will puah L^ to the so dally dedrabiemargin.

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THE ANATOM Y OF MARKET FAILURE

365

would, if only payment were enforceable, cause nectar production in

precisely the right amount and even distribution would be correctly

rationed. T he difficulty is due exc lusive ly to the difficulty of keep ing

accounts on the nectar-take of Capulet bees as against Montague

bees.'

Many of the few examples of interproducer extemal economies

of the reversible technological var iety are of this typ e: shared

dep osits of fish, water, etc.* M uch more important, so are certain

irreversible dynam ical exam ples associated with investm ent. For

instance, many of Pigou's first category of extemalities: those that

arise in connection with owner-tenant relationships where durable

investments are involved, have a primarily organizational quality.*

Perhaps the most important instance is the training of nonslave labor

to skills as distinct from education in a broader sense (which par-

take s more of T yp e ( 3)) . In the end, however, and in particular if

restricted to reversible statical cases, it is not easy to think of many

significant ownership exte m alities pure and simple. Y et it turn s

out that only this type of extemaUty is really due to nonappro-

priabUity.

Type 9): Tedm ical Extem alities

Assume, aga in, tha t all goods and services are rationable, exhaust-

ible, scarcities, that individual ordinal indifference maps are convex

and sensitive only to own-consumption and that there exist no

ownership defects of Ty pe (1). If, then , th e technology exhib its

indivisibility or smooth increasing retums to scale in the rdevant

range of output, these give rise to a second and much more important

typ e of market failure: technical extemaUty. *

1.

More generally, it could as wdl be due to difficulty in knowing who

produced the benefit oil wd la drawing on the same pool are an example.

Th e owner cannot protect his own; in fact it is difficult to know wh at one m eans

by his own . Moreover, in the case of diseconomies, at least, it ma y be tha t

both the source and the redpien t of the bad are identified: one factory pro-

dudng soot and notbing but one laundiy in tbe neigbborbood, yet it is difficult

to see how a price can be brought to bear on the dtu ation. Fresumably t he

laundry can pay for negative un its of smoke.

2.

Though individb ility elements entor into some of these. W hy can't

somebody own p u t of a lakeful of fish?

8. When not dmply due, in a world of uncertainty, to incondstent expec-

tations.

4 .

Again, this snot the same as Viner'a technological. No to, indde ntally,

that the above formulation unabashedly begs tbe question of wbether smooth

increadng returns to scale could or could not azise without individbility some-

where. Th e issue is entirely definitional: it is conceptually impo sdble to dis-

prove dt her view by reference to empirical evidence. (Cf. Simple An alytics,

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3 6 6

QUARTERLY JOURNAL OFECONOMICS

The essential analytical consequence of indivisibiUty,* whether

in inputs, outputs or processes, as wdl as of smooth increasing retums

to scale, is to render the set of feasible points in production (input-

output space) nonconvex. A connecting straight line between some

pairs of feasible points will pass outside the feasible set. Non-

convexity, in tum, has a devastating effect on duaUty.*

In situations of pure technical extemality there does, of course,

stiU exist a maximal production possibility frontier FF); and with

a Samuelson-type social indifference map SS) i.e., a map cor^

rected for income distribution which provides a ranking for the

community as a whde of aU conceivable output combinations' it

is possible, in concept, to define a bliss point(s).* Also, where indi-

visibility is exhibited by outputs, and only outputs, or, stronger,

where smoothly increasing retums to scale is the only variety of

nonconvexity isoquants for one, are properly convex the locus

of efficient output combinations can be defined in terms of conditions

on marginal-rates-of-input-substitution.* Moreover, bliss could pos-

sibly occur at a point where

SS

is intemaUy tangent to

FF,

perhaps

to a convexFF. But even in the least pathological, most neodassi-

Tbe pioneer work on decreasing cost dtuations is Jules Dupuit's remarkable

1844 essay,

On the

Measurement

of

Utility

of

Fublic Works, trandated

in

International Economic

Papers

No . 2, ed. A. T. Feacock,etal. Harold H otdling 's

The General WdfareinRelationtoFroblemsofTasiation andofRailway and

Utility Rates, inthe Ju ly 1088 issueof

E conometriea

istbe originating mod em

formulation.

Cf.,

also, references

to

work by

R.

Frisch, J. E . M eade, W. A. Lewis

and othersin Nancy Ruggles' excdlent survqr artidesonnuuginal cost pricing

Reviewef

Ecmumic

Studies XVII (10^^50), 20-46,and 107-20).

5. Individbilitymeanslumpiness inscale andnot tbekindof individbility-

in-timewe call durability. (Durability, as such, doesnot violato conveidty.)

Lumpinesshas

t

do with th e imp osdbilitytovaiy continuoudy, e.g., the capadty

service-yidd per unit timeofsuch thinggasbridges.

6. The best knownand perhaps most important variety of nonconvexity

occurs where isoquants are properly convex,butretumstosode are increasing,

bence the fullset offeadble input^output pointsisnonconvex. (Inatwainput,

one-output dtuation, dices

by

(vertical) planes through the origin perpendicuUr

to

the input phme will cut the production surface in such

a

way as

to

give

a

non-

convex boundaiy.) A production punt lyingin an increadng retu ms region

ofaproduction function implies that(1)the associated average cost curve AC)

is downward slopingat that levd of output; (2) theassociated marginal cost

curve MO, whLe

it may be

rising, could

as wdl be

falling and wiU certainly

lie bdo w AC;and(8)the production posdbility curveoftbe community maybe

nonconvex. Onallthis,see FartV of Simple An alytics, loc.

cU .

7. Cf. F. A.Sam udson, ScKdal Indifference Cu rves, tiiis Journal LXX

(Feb. 1056), 1-22. Sucha function presumes that numeratra-incomesare con-

tinuoudy redistributedso as tomaximiseinutility space overthecom munity's

operative aodal welfare function.

8. Thisissaying very Iittie,ofcourse, excepton thelevelofmet^>hydcs.

0. Inequalities duetokinks and comers areasgoodasequalities w h eall

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caUy weU-behaved case, where there exists a mean ingfully defined set

of shadow prices associated with the bUss point, genuindy profit-

seeking com petitive producers, responding to t ha t set of prices, wou ld

fail to sustain optima l production. A t best, eve n if at the bliss-

configuration allM CB are rising, some producers would ha ve t o m ake

continuing losses, hence wou ld go out of business; mark et calculations

would necessarily faU by incen tive. If, in tu m , prices are no t

centrally quoted but permitted to set themsdves, monopoly behavior

wiU result. Th ere will be faUure by stm ctu re .

Further, bliss may require production at levels of output where

losses are no t only positive, b ut a t a constrained maximum;*p = MC

m ay be correct, though M C at tha t point

s

falling . Ifso,the embedded

Lflgrangean constants may stiU retain meaning as marginal rates of

transformation, bu t th ey wiU faU to sustain efficient production eve n

by Lange-Lemer civil servants who care only about m argins and n ot

abo ut absolute tota ls. There wiU be failure by signal : producers

under injunction to maximize profit (in the small) will not remain

where they ought to be.

If, moreover, we drop the assumption of smooth increasing

retums to scale and permit indivisibilities such as ^ve scaUop-like

effects and kinks in cost curves and in the production-possibiUty

curve, things ge t even more compUcated. Bliss could require produc-

tion at points of positive but locaUy minimum profit, where

M C

exceeds

AC

bu t is faUing. W orse, eve n if bliss should occur at p oints

where production functions are locaUy convex and M C (greater than

AC is rising, prequoted prices may still not sustain the solution

unless production functions are in fact convex throughout. T h o u ^

positive and at a local maximum , profits m ay not be a tth dr m ax im um -

nuudmorum: other hills w ith higher peaks ma y indu ce producers with

vision at a distance to rush aw ay from bliss. Altern atively, if prices

are not administered, competition may not be self-policing and

mark ets could fail by stmcture. *

1. Subject to the requirement that total cost for that levd of output be a

minimum, i.e., that each producer be on his least-cost expansion path.

2 .

Where du up individb ility gives a nonconvex production posdbility curve

witb comere and kinks, duality may fail even if there exists a price vector in

terms of wbich decentralised producer-calculations would sustain the bliss-point

outpu t mix. Th e existence of such a vector does not assure tha t it will coindd e

with tb e price-vector wbicb would effidentiy ration tba t bill of goods among

consumers. Th e point is tha t there may not exist a

single

set of prices whidi

will at th e same tim e keep both consumers and producers from rushing aw ay from

where they ought to be. Th e pricea which will effectively mediato production

may cause consumers' calculations to go wrong and vice versa.

It should be noted, indden tally, th at none of the above takes space anddis-

tance condderations into accoun t. For aome interesting effects of plant-ind ivid-

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3 6 8


On the other hand, given our assum ptions, the Paretian contract

locus of maximal (ordinal) utility combinations which is associated

with any one particular output point is defined, as in the trouble-

free neoclassical modd, by the usual subjective, taste-determined,

marginal-rate-of-substitution equalities (or, at comers, inequalities).

These

M RS

equaUties, in tu m , im ply a set of shadow -prices which,

if centraUy quoted, would efficientiy ration among consumers the

associated (fixed) totals of goo ds. In the sphere of excha nge, then,

a decentralized price system works without fiaw.

In what sense do these Ty pe (2) situations exhibit extemaUty ?

In the (generalized) sense that some social costs and benefits remain

extem al to decentralized profitability calculations. W ith T y p e ( l )

extem aU ties, tho ugh it is no t feasible t o poUce the b liss valu es of aU

quantities and prices, there exists embedded in the solution a set of

prices whose use for purposes of decentraUzed signaUng would su stain,

if only appropriation or exdusion were feasible, both itsdf and the

maximum welfare configuration of inputs, outputs, and distribution.

Th is is not the case here. In Ty pe (1) situations, at the bliss point

there is complete correspondence between social and private pay-off

both at the margin and in totals.* Profits are at their ma xima and

non-n egative throughout. Here there is no such correspondence;

there may weU be divergence, either at the margin: bliss-profitB may

be at a minimum , or in

toteUs.

Th e private totals in terms of wh ich

producers in an (idealized) ma rket calculate total revenue minus

tota l c ost will no t reliably signal th e social co sts and benefits

implied by the relevant social indifference curves.* Hence at th e

set of prices which would correctly ration the bliss point bUl of goods,

that biU of goods may not be prodilced by profit seekers, or even by

Lange-Lemer civil servants.*

bility where tliere are interplant fiows and transport takes resources, aee T. C.

Koopmans and M. Beckmann, Asdgnment Froblems and the Location of

Economic A ctivities, Econometrica, Vol. 25 (Jan. 1057).

3.

More correctly, there would be such correspondence, if only the

p s

could

be po liced.

4. This is particularly awkward since the very nonconvexities which cause

a diveigence between privato and aodal total conditions render outputrmix cal-

culations based on margins alone wholly inadequato. Eiven if bliss gives all local

profit maxima, there may be several such open to any one

producer,

hence he muat

make total calculations in order to choose.

5. There is one qualification to be mAde to tbe above. It may be tba t the

bliss configuration gives unique and podtive profit maxima throughout, though

some production functions exhibit nonconvexities at a distance. It was to ex dud e

this case that we assumed that increadng retunis or individbility obtun in the

relevant ranges. Should this happen, no externality dive igsnc e of sod al

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A poin t to not e, in all this, is th at in relation to technical

naUties th e nonappropriabiUty notion, as generaUy co nc dv ed , tends

to miss the point. Strictiy speaking, it is, of course, true th at price

me diation, if effident, cann ot be counted on to appropriate th e

fuU social benefits of activities showing increasing retums to scale

or othc typ es of indivisibUity to those engaged in them . B ut the

existence of such uncom pensated services has in this case noth ing

wh atever to do with divorce of scarcity from own ership, w ith

feasibility limitations on exclusion. It is en tir dy feasible to own

a bridge and profitably ration crossings; indeed, a private owner

would do so. Th e point is, rather, th at such profitable rationing,

such com pensation for services rendered, would ineffidently mis-

aUocate th e ou tpu t of bridge crossings. If in term s of scarce

resouree inputs the marginal cost of an additional crossing is zero,

any podtive toU wiU, in general, have the usual monopoUstic effect:

the resulting output configuration wUl not be effident.*

This, incidentally, is where most pecuniary extemal economies

lead: a supplier is required to produce in a range of declining AC due

to intemal technological economies of scale and hence cannot make

ends m eet at the socially correct price. Th e cm cial associated

difficulty at the levd of social organization is monopoly.

Can we leave matters at that? N o t quite. There is a third kind

of extemality, recently emphadzed by I^essor Samuelson, caused

by so-caUed pubUc go od s.

Type S): Pub lic Good E xtemalities

In som e recent writings on public expenditure theory, S am uelson

ha s rdntro duced th e notion of the coUective or pubUc good . Th e

defining quality of a pure public good is tha t each individual's con-

sumption of such a good leads to no subtractions from any other

indiv idual's consump tion of th at good . . . ,' hen ce, it differs from

a private consumption good in that each man's consumption of it,

Xl

and Xf respectivdy , is related to the total

Xt

by a condition of

is convex throughout, the existence of such a locally stable tangenqy cannot be

taken as evidence that the point is in fact the bliss-pcnnt a difficulty of con-

siderable significance for dynamical effidenqy.

6. Of course, if at bliss the bridge were to be used to capad ty, it is pos-

dble that the iAgrangean ration price (now podtive) would make commercial

operation profitable. If so, an administered price setup would effidentiy mediato

the demand and supply of crossings. Bu t while a Lange-Lemer qrstom would

work fine, laisses-faire marketa would fail by stmc ture.

7. F. A. Samudson,

Review cf conomics and Statistics,

XXXVI (Nov.

1054), 887.

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equalityrather than of summ ation. Th us, b y definition, Xi = Xt and

XI =

Xt.'

As Samuelson has shown, the form of the marginal rate of sub-

stitu tion c ond itions wh ich define the Pareto-efficient utU ity possibUity

frontier in a world where such public goods exist, or at least where

there are outp uts with imp ortant pubUc qualities, renders any

kind of price-market routine virtuaUy useless for the computation of

output-mix and of distributirai, hence, also, for organizational decen-

tralization. W here some restraints in the maximum problem take

the form: total production of

X equals

consumption by Crusoe of

X equals

consum ption of X by Friday , Pare to efficiency requires tha t

the marginal rate of transformation in production between X and Y

equal not the (equalized) MRS d each separate consumer, but rather

the algebraic

sum d

such

MRS'a.

Th is holds, of course, in wh at in

other respects is a conventionaUy neoclassical world: preference and

production functions are of wdl-behaved curvature, all is convex.

If, then , at th e bliss point, w ith Yas numeraire,Px is equated to

the marginalY eaBt

ai X in

production (as is required to g et optimal

produ ction), and

X

is offered for sale at th at

p ^

preference-maximizing

consumers adjusting their purchases so as to equate their individual

MRS'B to

pt

wiU necessarily under-use

X.

M oreover, a pricing gam e

wUI no t induce consumers tmth fuU y to reveal their preferences. It

pays each consumer to understate his desire for X relative to Y,

since his enjoyment of X is a function only of total X, rather than,

as is tm e of a pure private good, just of th at fraction of ic he pays for.

The two Samuelson artides* explore both the analytics and the

general implications of public goo ds. Here the notion is of rd e-

vanc e because much extem ality is due precisely to the pubUc

quaUties of a great ma ny activities. For example, the extem ality

associated with the generation of ideas, knowledge, etc., is due in

good part to the pubUc character of these comm odities. M any

interconsumer extem alities are of this sort: m y par ty is m y neighbor's

disturbance, your nice garden is any passerby's nice view, my chU-

dren's education is your chUdien's good company, my Strategic Air

Comm and is your Strategic Air Com mand, etc. Tlie same con sump -

tion item enters, positivdy or n^ativdy, both our preference func-

8. F. A. Samudson, Review of

conomics

and Statistics, XXXVII (Nov.

1055), 850.

0. And a third unpublished paper, which was read at tbe 1055 American

Economic Assodation meetings and to a copy of which I came to bave access

while this piqier wa s being written. For earlier writings on public goods, by

W icksdl, Iind ahl, Musgrave, B owen and others see references in the above dte d

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THE ANATOMY O F MARKET FAILURE 371

tions. Th e consum ptions involv ed are intrinsicaUy and essentially

joint.

This kind of extemaUty is distinct from dther of the other two

pure typ es. Here technological non convex ities need in no w ay be

involved. In fact the MRT = XMRS condition is certain to hold

true precisely where production takes place at constant or non-

increasing retums, and hence where the production possibility set

is necessarily con vex. Further, there are no decentra lized organiza-

tional rearrangements, no private bookkeeping devices, which would,

if only feadbiUty w ere no t at issue, eliminate the difficulty. It is the

central implication of the Samuelson model that where public good

phenom ena are present, there does n ot exist a set of prices associated

w ith the (perfectiy definable) bliss poin t, which would sustain th e bliss

configuration. T he set of prices wh ich wou ld induce profit-seeking

com petitors to produce th e optimal biU of goods, would be necessarily

ineffident in aUocating that bUl of good s. M oreover, even abstracting

from production, no single set of relative prices wiU efficientiy ration

an y fixed biU of goods so as to place the system o n its contract

locus, except in the singular case where at that output and income-

distribution MRS B d every individual are identically the same

(or zero for all bu t on e). There is failure by existence.

IV. COHHENTB

Type (1). In a sense. Ty pe (1) is not symm etrical with the other

tw o categories. One can think of some nontrivial instances where the

institutional dem en t does appear to be binding : skill-training of

people, for exam ple. Bu t even there, it could be argued th at the

cmcial elements are durability, uncertainty, and the fact that slavery

as a mod e of organization is itself in th e nature of a pubUc good w hich

enters people's preference functions, or the implicit social welfare

function, inseparably from the narrowly economic variables. In

those instances, in turn, where bookkeeping feasibUity appears to be

the cause of the trouble, the question arises why bookkeeping is less

feasible than where it is in fact being done. In the end, it m ay b e

that much of what appears to partake of Type (1) is really a com-

pound of Types (2) and (3), with dynamical durability and uncer-

tain ty elements tiirown in. A t an y rate, a deeper analysis of this

category may cause it substantially to shrink.

Nonproduced scarcities.

One particular instance where wh at

appears Uke Type (1) is really Type (2) warrants special mention.

Public own ership of nonproduced resources, e.g., t he lakes and m oun -

tains of national parks, may make it appear that extemality is due

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to statutory barriers to private ownership and commereial rental.

B ut this is missing the point. Tak e, for instance, a com mu nity wh ich

ha s availab le a single source of fresh water of fixed capacity . Assum e

that the bliss solution gives out a positive ration-price per gaUon

such as would make sale of the water comm ercially profitable. Y et

a laissez-faire syst em wou ld faU, by stm ctu re, to sustain bliss. A

private owner of the single indivisible well, if given his head, would

take advantage of the tilt in the demand curve. The real cause of

externality is not the arbitrary rapaciousness of public authority but

the indivisibility of the source of supply. Th is case, by the way , is

akin to where indivisibility or increasing returns to scale within a

range allow profitable scope for one or a few effident producers, but

for no more. At the bliss price all wUl do the right thing, but if

prices are no t adm inistered, oligopoly or mo nopo ly wUl result. A

capitalist Lange-Lemer system with private ownership but adminis-

tered prices would work fine, but laissez-faire markets would fail.

Meade's atmosphere. The relation of my tri-comered ordering

to M eade 's polar categories is of interest.' H is first category , unpaid

factors, is identical to m y Ty pe (1). B ut his second, labd ed atmo s-

phere, is a rather curious comp osite. M eade's qua litative charac-

terization of atm osphere : e.g., of afforestation-induced rainfaU,

comes very close to the pubUc good notio n.' H e Unks this, however,

as necessarily bound up with increasing retums to scale in production

to society at large, hence a J. B. Clark-like overexhaustion, adding-up

problem.*

If, following Meade, one abstracts from shared water-table phe-

nomena (let rain-caused water input be rigidly proportional to area)

then Farmer Jones' rain is Farmer Smith's rain and we have my

Ty pe (3 ). B ut nothing in this situation requires th at dth er farmer's

fuU production function (with an axis for rain) need show increasing

returns to scale. It m ay be tha t retums to additional bund les of

non-rain inputs, with given constant rainfall, diminish sharply, and

that it takes proportional increases of land, labor

and rain

to get a

proportional effect on outpu t. If so, M eade's overexh austion problem

1.

Op.dt. (Thia and tbe next aection can be omitted w ithout loss of con-

tinuity.)

2.

See esp. bottom of p. 61 and top of p. 62,

op. dt.

8. Since bis argument ia restricted to compietitive dtuations, hence neces-

sarily exdudes increadng-retum-to-paid-factors such as would reqiure produc-

tion at a loss, Meade spedfies constant retums to proportional variation of labor

and land in wheat farming, though the full production function for wheat, indud-

ing the atmosphere input (rain), exhibits increasing retums to scale. But the

individual fanner does not pay for rain, bence bis factor paym ents just matob bia

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373

wiU no t arise. B ut aU would no t be weU: the p ublic good quaUty of

rainfall would cause an independent difficulty, one that Meade, if I

understand him correctiy, does not take into account, i.e., that rain

oug ht to be produced by timber growers until its

M C

is equal to

the sum of all the affected farmers MRS'B for rain as an inpu t, wh at-

ever may be the curvature of the latter's production functions.*

On the other hand, Meade's formal mathematical treatment of

atmo sphere, as distinc t from his verbal characterization and his

example, suggests that it is a nonappropriable, and therefore unpaid,

factor which gives rise to increasing retums t o scale to soc iety thou gh

no t to the individual producer. A t least this is aU he needs for the

effect he is looking for: a self-policing thou gh n onoptimal com petitive

situation, where, because the full production functions (i.e., with an

axis for rain) are of greater than first degree, the correction of exte>

naUty via subsidies to promote the creation of favorable atmosphere

requires ne t add itions to society's fiscal burden. If this is the c m cial

consequence of atmosphere, then it need ha ve no pubUc quaUty.

AU this would happen even though Smith and Jones were compet-

ing for the water from the shared wateivtable under their subsoU,

just like bees competing for nectar.

Sdtovskj^s two concepts. ^

Professor Scitovsky, in tum, in his

sugg estive 1954 article, distinguishes betw een th e statical direct inter-

actions of equilibrium theory and the kinds of pecuniary extemal

econom ies emph asized in the economic develop men t literature. H e

classifies the former as consumer-consumer, producer-consumer, and

producer-producer interactions, labels the last as extemal economies

and asserts that they are rare and, on the whole, unimportant.

WhUe Sd to vsk y does not raise the q uestion of what give s rise to

such producer-producer interactions, both his examples, and his con-

clusion that they are of Iittie significance, suggest that he is thinking

4. Formally, Meade denotes atmospbere as a dtua tion where the pro-

duction function, e.g., of farmen takes the form

Xi = Hi(Li,Ci)Ai(X,),

with

L

as labw, as capital and A the atmosphere effect on X , of

X t.

The full function

exhibits increasing retum s to scale but theHfunction sJone, with A constant, is

homogeneous oi first degree. Bu t why can't this be put in terms of Meade's un-

paid factor type function where

Xi

-

Hi(Li,Ci,X,)1

Example:

X,

- L^

C\-' Xt.

All this has nothing to do with whether

A - Ai + A,m

rather A - A . - At.

Unfortunately, the example itsd f tends to midead . Th e fact that exdusion of

ram-users (farmers) by producers (timbergrowers) is hardly feadble, i.e., tbat

rain is like Type (1), distracts attention from the important pdnt that

if

rain is,

as Meacle tdls us, a public good, then rationing it by price would be inefficient

even if it were feadble. (It should be said tbat Meade concludes his artid e:

But, in fact, of coura^ extemal economies or diseconomies may not fall into

dth er of these precise divido ns and may contain features of both of them . )

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3 7 4


primarily of Ty pe (1 ): nonappropriability. Bu t this is to ignore

public goods sur dy a more importan t cause of interaction. M ore-

over, by taking full account of these, Sd to vs ky 's fifth and important

case, which, however, does not quite fit into . . . (his) . . . classifica-

tion . . . , where society provides social services through communal

action and makes these available free of charge to aU persons and

firms, can be m ade nicely to faU in to place.*

Samuelson on Types i) and S). WhUe the pubUc good model

h d p s to sort out the plienoiiiena M eade lumped under atmosphere,

Samuelson himself emphasizes the analytical bond between Indivisi-

biUty and public good situations. In both an expUcit summing in

is required of aU direct and ind irect utiUties and co sts in all social

de cision s. ' In Tjrpe (2) situa tion s it is the intramarginal consumer's

and producer's siupluses associated with various all or nothing deci-

sions in-the-lump tha t hav e to be properly (interpersonally)

weighted and summed, while in Type (3) it is only utiUties and costs

at the margin th at require adding. Bu t, and this is the cmc ial shared

quaUty of the two categories, both make it necessary to sum utiUties

over many people.*

Exdusion.

One more comm ent m ay be warranted on th e signifi-

cance, in a pubUc good ty pe situa tion , of nonappropriabiUty. Exc lu-

sion is alm ost never impo ssible. A recluse can build a waU around

his garden, Jones can keep his educated children away from those of

6. Ibid. fn. 8 , p. 144. Sd tov sky , following Meade, restricts his first con-

cept of extemal economies to phenomena consistent with competitive equilib-

rium. He treats individbilities and increasing retum s to scale as bdon ging to

bis second concept which has to do with disequilibrium, investm ent ded dona,

and growth. It is, of course, entird y legitimato to restrictaaalym to competitive

dtua tions. Bu t the Sd tov sky treatment must not be taken to imply that lumpi-

ness is irrelevant to statical analysis of stationary solution points. If m e is inter-

ested in the statical effidency of decentralised price calculations, thqr are crucial.

Bu t this is caiping. Sd tovs ky's important contribution lies in em pba ddn g and

clarifying the pcdnt first hinted a t b y F . N . Rosenstdn-R odan that in a worid of

disequilibrium djmamics pecuniary extemal economies may play an indqiendent

role one distinct, that is, from simply being an unreliable signal of monopoly

troubles EconomicJournal,LIII, 1048, 202 -11).

7.

Ibid.

p. 0.

8. There is one qualification to be made: if all public good and increasing

retums to scale industries produce only intennediato products, all estemalities

may cancel out in intrspbudness-sector transactions. If so, only total revenues

and total costs have to be summed. Incidentally, the expodtion m ay nusiead-

ingly suggest another symmetry between Typ es (2) and (8 ). In a pure IV pe (8)

dtuation, if tbere are no public producera' goods, tben wbile prices cannot^ be

used to ration the bliss point output-mix, t h ^ can be used efficiently to mediato

production. In Ty pe (2), on tbe other hand,i fall final consumables are dividble,

price calculations, while failing in production, will work in exchange. Th is

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Sm ith, etc. B u t if thereby some people (e.g., the reduse ) are ma de

happier and some (e.g., the passers-by) less hap py, an y decision ab ou t

whether to exclude or not implies an algebraic summ ing of the

somehow -weighted utilities of the people involved . An d if the waU

requires scarce resources, the final utility sum must be matched

against the cost of the waU. W hen Ty pe (3) blends with indiviabiUty

in production, as it does in the case of the waU, or in the case of a

li^thouse, the comparison has to be made between intramarginal

totals. W here no lumpiness is involv ed (e.g., the decibels at w hich

I play my radio) only M RS and perhaps M C calculations are called

for. B ut the really cm cial decision ma y weU be abo ut how m uch

perfectiy feasible appropriation and exclusion is desirable.

Arrangements tooffset It is of interest to speculate what, if any,

organizational rearrangements could offset the three categories of

extemaUty and avoid the need for centrally calculated tax-subsidy

schemes.* In concept. Ty pe (1) can be offset by rearrangements of

ownership and by proper bookkeeping, such as need not vi d a te

the stm ctura l requirements of decentralized com petition. Further,

no resort to nonmarket tests would be required.'

Types (2) and (3) are not so amenable to correction consistent

with decentralized institution s. Th e easiest pos db le case occurs

where increasing returns obtain on the level of single producers'-good

plants, much of whose production can be absorbed by a single user

firm. Here vertical integration tak es care of the problem. N o t every

process inside a weU-mn firm is expected to cover its cost in teims

of the correct set of inte m al accoun ting (shadow ) prices. To tal

profits are the on ly criterion, and it m ay pay a firm to b uild a pr ivate

bridge between its two installations on opposite sides of a river yet

charge a zero accoun ting price for its use by the va rious d ecentralized

manufacturing and administrative divisions; the bridge would make

accoun ting losses, ye t total company profits wiU hav e increased. A s

long, then, as sudi integration is consistent with the many-firms

requirement for com petition, no extrarmarket t est s are required.*

Th e private total conditions:

TR

less

TC,

correctiy account for social

gain.

0. For illustntive derivation of the formulas for corrective taxes and sub-

ddies in l^pe (1) dtuations, see Meade

op.

ed.).

1. Tb e E ma ndpation Frodam ation could co nstitute, of course, a substantial

barrier.

2. If, however, tbe break even scale of operation of the integrated firm

(i.e., where

MC

cuts

AC

from bdow) is much greater than if the river had not

been tbere to span, or could be spanned b y some means of a lower fixed-cost-to-

variable-cost latio , tbe monopoly problem may dmp ly be pusbed forward to

consumer markets.

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Where a producers'-good firm, required to produce at a stage of

faUingAC, sd ls to m any customer firms and industries, an adding up

(tf aU the associated

TR a

and TC's at the precalculated as if com -

petitiv e prices associated with th e bliss point w ould again effectively

mopup all social costs and benefits.* B ut the institutio nal reorgan-

ization required to get correct decentraUzed calculation involves hori-

zontal and vertical integration, and the monopoly or oligopoly

problem looms large indeed . T he T yp e (.3) case of a pure producers

public good belongs here: only input MRS a along production func-

tions require summ ing.

In the general case of a mixed producer-consumer good (or of a

pure consumer good) which is pubUc or is produced under cond i-

tions of increasing retums to scale, it is impossible to avo id com parison

of multiperson utilit y tota ls. ExpUcit adm inistrative consideration

must be given, if you like, to consumer's and producer's surpluses for

which no market-institution tests exist short of that provided by a

perfectly discriminating m ono polist. Bu t to invoke perfect discrim-

ination is to beg the question. It imp lies know ledge of aU preference

functions, while as Samuelson has emphasized,* the cmcial game-

theoretical quality of the situation is that consumers will not cor-

rectly reveal their preferences: it wiU pa y them to chea t.

Blends. Exam ination is needed of various blends of Ty pe s (2)

and (3), such as Sidgwick's lighthouse;' or, for that matter, and as

suggested by Samudson, of blends of pubUc and private goods even

where all production functions are fully convex. There are ma ny

puzzling cases. D o bridge crossings differ in kind from radio programs?

Both involve indivisibility and, where variable cost is zero for the

bridge, zero

M C s.

The correct price for an extra stroUer, as for an

extra listener, is clearly zero. Ye t bridge crossings ha ve a distinctiy

private quality: bridges get congested, physical capacity is finite.

Th is is not true of a broadca st. There is no finite limit to th e number

8. Aaauming tbat all conaumer gooda are finely dividble and require no

lumpy dedsions by consumers.

4. Cf. any of the three Fublic Expenditure artidea (supra).

5. Sidgwick, by the way, aa also Figou, thought of a lighthouse aa of Type

(1).

It is, of courae, inconvenient to levy tolls on ships, but it is hanily impos-

sible to exdude, for instance by means of scrambling devices (thou t^ poor

Sidgwick could hardly have known about such things) . Th e point is, rather,

that it would be ineffident to doao:the marginal coat to sodety of an additional

ship taking directional guidance from the beacon atop tbe Statue of Liberty ia

sero,

ipso price diould be cero. In the case of a lighthouse tbis is twice true:

because tbe beacon is in the nature of a public good: more for the Queen Maiy

means no leaa for the Ubertd; and becauae a lij^thouse ia virtually an all-fixed-

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THE ANATOM Y OF MARKE T FAILURE 2 11

d sets th at can costiessly tun e in.* Ra dio programs, then , hav e a

pubUc dimension. Y et, in a sense, so do bridges. W hift your bridge

crossing is not my bridge crosdng, in fact could limit my crossings,

you r bridge is m y bridge. W hat is involved here is tha t m ost thing s

are multidimensional and more than one dimension may matter.

V. EFF ICIEN CT, M AB KE TS AND CHO ICE OF INSTTFITTIONB

AU the above has to do with the statical efficiency of price-

directed allocation in more or less idealized market situation s. Re le-

vance to choice of institutions depends, of course, on the prevalence

of the phenomena which cause externality and on the importance to

be attach ed to statical efficiency. Space precludes extensive discus-

sion of these important issues, but a few casual comments, in the

fonn of

dicta

are perhaps warranted.

How important are nonappropriability, nonconvexity and pubUc

goods? I would be inclined to argue tha t while nonappropriabiUty

is of smaU imp ort,' the same cannot be said of the other two . T m e

enough , it is difficult to think of man y exam ples of pure public goods.

Most things even battieships, and certainly open air concerts and

schools (thou gh n ot know ledge) ha ve an "if more for you then

less for m e" quaUty. B ut this is of little comfort. A s long as activ-

ities hav e even a trace of pubUcness, price calculations are ineffident.*

And it is surdy hard to gainsay that some degree of public quaUty

pervades much of even narrowly "economic" activity.

Lumpiness, in tum, and nonUnearity of the increasing retums

sort, while in m ost instan ces a ma tter of degree, and, within lim its, of

choice, are also in the nature of thin gs. Th e universe is fuU of singu -

larities, thresholds and nonproportionalities: speed of light, gravita-

tional constant, the relation of circumference to area, etc. A s econo-

mists we can cajole or bully engineers into designing processes and

installations that save on congealed inputs and give smaUer maximal

service yid d s, especiaUy when d esigning for low-income co mm unities.

But the economicaUy perhaps arbitrary, not completdy physics-

imposed quality of indivisibilities associated with standsurd designs

6. Richard Eckaus bas suggested to me that it is posdble to exbaust the

space to which the broadcast is limited and tbat this makes the dtuation a Iittie

more Hke tha t of a bridge. N dtb er of us is entird y satisfied, however.

7. Excep t for labor skills and these would tak e us beyond the bounds

of reverdble statics.

8. Th is is not to say that there exist otber feadble modes of soda calculation

and organisation which are more effident.

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3 7 8 QU RTERLY JOURN L OF ECONOMICS

and ways

d

doing things should not blind. NonU nearity and lumpi-

ness are evident facts of nature.*

M ore imp ortant, at th is le vd of discourse' though perhaps i t

hardly need be said is th at statical m arket efficiency is n dt he r

suffident nor necessary for market institutions to be the prefen ed

mod e of social organization. Qu ite apar t from institution al considera^

tions, Pare to efficiency a s such ma y not be ne cess aiy for bliss.* If,

e.g., people are sensitive not only to their own jobs but to other

people's as weU, or more generaUy, if such things as relative status,

power, and the like, matter, the injunction to maximize ouQiut, to

hug the production-possibUity frontier, can hardly be assum ed neu-

tral, and points on the utility frontier m ay associate with p oints

inside the production frontier.* Furthermore, there is no thin g pre-

ordained about welfare functions which are sensitive only to indi-

vidual consumer's preferences. As a m atter of fact, few people wo uld

take such preferences seriously enough to argue against any and all

protection of individuals against their own mistakes (though no

extemal effects be involved).

AU this is tm e even w hen maxim ization is subject only t o techno-

logical and resource limitatio ns. Once we adm it other side relations,

which link input-ou tput variables with noneconomic poUtical and

organizationiJ value s, m atter s becom e mu ch more compU cated. If

markets be ends as weU as means, thdr nonefficiency is hardly suffi-

cient ground for rejection.'* On the other hand, efficient markets may

9. Thdr quantitative aignificance is, of course, veiy sendtive to scale, to

dse

of markets. Th is explains tbe particular emphasis on the role of aodal

overheads in low income countriea.

1.

Where recourse to atrategic condderations of feadbility, cnidal though

t h ^ be, is quito out of order.

2. Th at it ia never auffident ia, of courae, w dl known. Of the infinito

Fareto-effident configurationa at best only one: th st which gives the ri|^ t

distribution of income in terma of the TT-function tiiat is to count, has normative,

prescriptive dgnificance. Moreover, most interesting IF-functions are likely to

be sen dtiv e to noneconomic factors, such as are, if not incon dsten t, at least

extraneous to Faretian condderations. Where such additional values of a political

or social nature are separable from input-output value

Bator, 1958

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