1954 - MIT Press - PA Samuelson - The Pure Theory of Public Expenditure.pdf

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The Pure Theory of Public Expenditure

Paul A. Samuelson

The Review of Economics and Statistics, Vol. 36, No. 4. (Nov., 1954), pp. 387-389.

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388 T H E R E V I E W O F E C ON O M I CS A N D S T A T I S T IC S

Equat ions ( I ) and (3 ) a re essent ially those

given in the chapter on welfare economics in

m y Foundations of Economic Analysis . Th ey

co nsti tute my version of th e "new we lfare eco-nomics." Alone ( I ) represents tha t subs et of

relations which defines the Pareto-optimalutility frontier and which by itself representswhat I regard as the unnecessarily narrow ver-sion of what once was called the "new welfareeconomics."

The new element added here is the set ( 2 ) ,

which constitutes a pure theory of governmentexpenditure on collective consumption goods.By themselves ( I ) and (2 ) define the ( s - I ) -fold infinity of utility frontier points; only

when a set of interpersonal normative condi-

tions equivalent to (3) is supplied are weable to define an unambiguously "best" state.

Since formulating the conditions (2 ) someyears ago, I have learned from the publishedand unpublished writings of Richard Musgrave

that their essential logic is contained in the"voluntary-exchange" theories of public finance

of the Sax-Wicksell-Lindahl-Musgrave type,and I have also noted H oward Bowen7s inde-

pendent discovery of them in Bowen's writingsof a decade ago. A graphical interpretation ofthese conditions in terms of vertical rather thanhorizontal addition of different individuals7marginal-rate-of-substitution schedules can begiven; but what I must emphasize is that thereis a different such schedule for each individuala t each of the ( s - 1) fol d infinity of differentdistribution s of relative welfare along the util-ity frontier.

3. Impossibi l i ty of decentral ized sponta-

neous solut ion. So much for the involved op-timizing equations that an omniscient cal-

culating machine could theoretically solve iffed the postulated functions. No such machinenow exists. But it is well known th at a n

"analogue calculating machine" can be pro-vided by competitive market pricing, (a) so

long as the production functions satisfy theneoclassical assumptions of constant returns

to scale and generalized diminishing returnsand (b ) so long as th e individuals7 ndifference

contours have regular convexity and, we may

add , (c ) so long as al l goods are private. W e

can then insert between the right- and left-

han d sides of ( I ) the equali ty with uniformmarket prices p j / p , and adjoin the budget

equations for each individual

where Li is a lump-sum tax fo r each individual

so selected in algebraic value as to lead to the"best" sta te of the world. Now note, if the rewere no collective consumption goods, then ( I )and ( I) ' can have their solution enormouslysimplified. W hy ? Because on the one hand

perfect competition among productive enter-prises would ensure that goods are produced at

minimum costs and are sold at proper m arginalcosts, with all factors receiving their proper

marginal productivi ties; and on the other han d,each individual, in seeking as a competitive

buye r to get to the highest level of indifferencesubject to given prices and tax, would be led asif b y an Invisible Ha nd to the gran d solutionof th e social maxim um position. Of cou rse theinstitutional framework of competition wouldhave to be maintained, and political decision-

ma king would still be necess ary, but of acom putationally minimum type! nam ely, alge-

braic taxes and transfers (L1, . . . L" would

have to be varied until society is swung to theethical observer 's optimum . T he servant ofthe ethical observer would not have to make

explicit decisions about each person's detailedconsumption and work; he need only decide

about generalized purchasing power, knowingthat each person can be counted on to allocate

it optimally. In terms of com munication theoryand game terminology, each person is moti-va ted to do the signalling of h is taste s neededto define and reach th e attainable-bliss point.

No w all of the abo ve remains valid even if

collective consumption is not zero but is insteadexplicitly set at i ts optimum values as de-t e rmined by ( I ) , ( 2 ) , an d ( 3 ) . However no

decentral ized pricing sys tem c an serve to de-

term ine opt im ally these levels of col lect ive con-

sumpt ion. Other kinds of "voting" or "signal-ling" would have to be t r ied . But , and t W i s

the point sensed by Wicksell but perhaps notfully appreciated by Lindahl, now it is in the

selfish inte res t of each perso n to give false

signals, to pretend to have less interest in a

given collective consumption activity than he



T H E P U R E T H EO R Y O F

really has, etc. I must emp hasize this: taxingaccording to a benefit theory of taxation cannot at all solve the computational problem inthe decentralized manner possible for the first

categ ory of " private " goods to which the

ordinary market pricing applies and which donot have the "external effects" basic to the

very notion of collective consumption goods.Of course, utopian voting and signallingschemes can be imagined. ("Scandinavian con-sensus," Kant's "categorical imperative," andother devices meaningful only under conditions

of "symmetry," etc.) T h e failure of ma rke tcatallactics in no way denies the followingtru th: given sufficient knowledge the optimaldecisions can always be found b y scanning over

all the attain able states of the world an d select-ing the one which according to the postulatedethica l welfare function is best. T h e solution"exists"; the problem is how to "find" it.

One could imagine every person in the com-munity being indoctrinated to behave like a

"parame tric decentralized bureaucrat" whoreveals his preferences by signalling in response

to price parameters or Lagrangean multipliers,to questionnaires, or to other devices. Bu t

PUBL I C E X P E N D I T U R E

there is still this fundamental technical differ-

ence going to the he ar t of the whole problem ofsocial economy: by departing from his indoc-trinated rules, any one person can hope to

sna tch some selfish benefit in a w ay no t possible

under the self-policing competitive pricing ofprivate goods; and the "external economies"or "jointness of demand" intrinsic to the very

concept of co llective goods an d gove rnm entalactivities makes it impossible for the grandensem ble of optim izing equations to have tha t

special pattern of zeros which makes laissez-

faire competition even theoret ical ly possible asan analogue computer.

4. Conclusion. T o explore further the prob-

lem raised by public expenditure would ta ke usinto the ma them atical doma in of "sociology"or "welfare politics," which Arrow, DuncanBlack, and others have just begun to investi-

gate. Political economy can be regarded a s onespecial sector of this general dom ain, and itmay turn out to be pure luck that within thegeneral domain there happened to be a sub-sector with the "simple" properties of tra-

ditional economics.

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1954 - MIT Press - PA Samuelson - The Pure Theory of Public Expenditure.pdf