Marginal Productivity and the Principle of Variation_JR Hicks

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Marginal Productivity and the Principle of VariationAuthor(s): J. R. HicksSource: Economica, No. 35 (Feb., 1932), pp. 79-88Published by: Wileyon behalf of The London School of Economics and Political Scienceand The

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1932]

Marginal Productivity nd thePrincipleof VariationBy J. R. HICKS

THE various modern versions of the marginal productivitytheory re mainly the resultof a shortperiodof intenseinterestin the subject at the close of the last century. During a fewyears (I889-96), Clark, Marshall, Wicksteed,Wicksell, Walras,Barone and Pareto all wroteabout it, each of thempropoundingoriginal and individuallysignificantviews. It might have beenthoughtthat after all this attention,the status of the theorywould at the end have been firmly stablished. But this wasnot the case; serious differencesremained unsettled. J. B.Clark, for nstance,believed withoutquestion that the marginalproductivity ormulagives a completely atisfactory xplanationof the distributionof the Dividend under conditions of staticequilibrium; and in this he was followedby others, such asWicksteed and Wicksell, whose conceptions of the methodsof economic analysis differedprofoundlyfrom his own. Atthe other extreme stood Pareto, convinced that the marginalproductivityformula is an over-simplification f realitv, anddesirous of replacing it by another,even more complicatedandunwieldy, into which marginal productivitywould fit as aspecial case.' Marshall, it is fairlyclear, stood between theseextremes,though incliningto the same side as Pareto. Whilenever convinced that the marginal productivity formula issatisfactory,he seems to have doubted, at least in later years,whether he groundof his oppositionwas sufficielntlymportantto deserve much insistence.2For a long time the division persistedwithout causing muchtrouble; but ofrecentyears there has been a revival of interest.Partly this has been due to ProfessorCassel's Theory of SocialEconomy, throughwhich the ideas of Pareto and Walras havebecome more accessible to the non-mathematicalreader. Theelaborate but rather nconclusivestudy of Dr. Valk (The Prin-

1 Pareto, Cours, Vol. II, pp. 82 sqq.; Mantel, p. 63I.2 Marshall, Principles, Bk. VI, ch. i. Cf. ist edition, Bk. VII, ch. i.79F

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80 ICONOMICA [FEBRTiARYciples of Wages) is evidently ilnspiredby Cassel; while Dr.Valk in his turn has awakened the interest of Mr. D. H.Robertson.3 On the other hand, Mr. Schultz, of Chicago, hasevidelntly elt the direct thrill of Pareto's mathematicalmagic.The arguments he advances are Pareto's arguments, adoptedwith scarcely any modification.4 None of these discussionsseem to me to be wholly satisfactory; for although I am incompleteagreementwith Mr. Robertson in holding that thereis some sense in which the pure marginal productivity heoryis altogethertrue, I cannot feel altogetherconvincedthat evenhe has finally elucidated precisely what that sense is. Andluntil we have done so, we cannot expect to convince theopposition.A further nquirymay thus perhaps be excused.

IThe particularpointon which the criticsofmarginal produc-tivity have always fastened is the assumed generality of the

Principle of Variation-to use the term employed by Mr.Robertson. How far is it justifiable to assume that a changein economicconditionswill bring about a change in the quan-tities of the factors of productionwhich are used to make aunit of any product? The marginalproductivity heory ssumesthat a change in the relative prices of the factorswill alwaysbe followedbv some change in the quantities of the factorsemploved, that is to say, it assumes that technical methodsare freelyvariable. For if that is not the case, it will beimpossible to reorganise a business effectivelywith one unitless of one factor, but with the same quantity of the others.The removal of a unit of one factorwill not only mean thatthe otherfactorsare used less advantageously-that is grantedin any case-but that a portion of the supply of the otherfactorsbecomes completelyuseless. If the price of a machinefalls, while the price of the labour used to operate the machineremains the same, it will clearly be to the interest of theentrepreneurwho employs both to use more machines andrelatively less labour. It will be to his interest, but it doesnot followthat he can do it. For if the machines are madein such a way that they require one workman, and only one,to run them,no change in relative prices can lead to a change3See his essay " Wage-Grumbles " (published in Economic Fragments)particularly pp. 46-52.4 G. F. Schultz, " Marginal Productivity and the Pricing Process "(Journalf PoliticalEconomy, ecember I928).



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19323 MARGINAL PRODUCTIVITY 8iin the proportions f labour anldmachinerythat are used; forthe proportions re fixed by technique.

If we have to use the margilnalproductivity heory in sucha way that this objection is important,then its consequencesare most serious. If the proportionsare fixed, then an extraunit of one factor,unaccompaniedby an increase in the other,will yield preciselyno addition to the total product. On theother hald, thewithdrawalof one unit will lead to a far areaterdiminutioll in the product than can fairly be attributed tothat unit alone, since its removal would put correspondingunits of the otherfactorsout of action. If all the factorswerepaid according to their marginal products calculated in thissecond manner, their total pay would undoubtedly be far inexcess of the value of the goods they produced. Which isabsurd.In fact, where the proportionsare fixed, the zero differencegot by adding one unit, and the large difference ot by sub-tractingone ullit of the factor,give us upper and lower limitswithinwhichthe returnto the factor must lie. In the extremecase, where the quantities of all the factorsrequired to give aunitoftheproduct-the " coefficientsfproduction as Walrascalled them-are givenby technical facts,marginalproductivitybreaks down completely. For the lower limit to the wageswhich can be paid is zero; and the upper limit is the totalincomingsof the enterprise. And to know that the total wage-bill must lie between these limits we do not need to haverecourseto elaborate analysisBut even in this extreme case, even when no variation ispossible and all the coefficients f productionare constant, itis still nottrue that the returnsto the factors re indeterminate,and that the mechanismof adjustmentbreaks down. For manyofthefactors, articularlycapital, can be used in manydifferentbusinesses and differentndustries, and if its earnings in olleare lower than they are in others, it will move. Even if weare sceptical about the general validity of the Principle ofVariation, we can still fall back on the " net productivityanalysisofMarshall or on the corresponding ormulaofWalras.The wages of labour, according to Marshall, must tend toequal the " net product of a man's labour "- " the value ofthe producewhich he takes part in producing after deductingall the otherexpenses of producing it."' If wages rise abovethis level, costs of productionwill exceed selling prices, or, in

5Principles f Economics, st edition,p. 548.



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8 UECONOMICA L[EBRUARYother words, the return to capital in that industry will becomeless than is offered or it in other industries, so that it willtend to move elsewhere. Siince the proportionof capital tolabour in each industry is fixed, the withdrawal of capitalmust mean unemployment.Mr. Robertson,while recognising that this holds true of aparticular ndustry,seems to findsome difficultyn seeing thatthe same processwill suffice o maintainequilibrium throughoutindustry s a whole. His difficultymuergesmostclearliyn hisdiscussion of Walras, but it is fundamentally responsible forhis criticisms f Marshall as well. Commentingon the Walras-Cassel argument,he says, " The method consists in buildingup a series ofequations in which the total supply of each factor,and the technicalcombinationsof factorsrequiredto make eachproduct, re takenas given. The demandfunction oreach pro-duct beingalso given, t is shownthat thepriceof each factor, ndof each product, s unequivocallydetermined. But how can thefirst wothingsbothbe taken as given? If each of ten industriesrequires the use of ten units of labour to everyunit of capital,and if thereexist ioo ullits of labour and ioo units of capital,what is to happen? " Now, of course, it must be admittedthat in this special case the theory breaks down-or rather,since capital is present in such complete superfluity, t mustbecomea freegood, and its price fall to zero. But in practice,it is surely most unreasonable to assume that the proportionsofcapital to labour are the same in all industries. It is absurdlycontraryto fact, so that it was perfectlyreasonable of Walrasand his followersto take the case of different roportionstobe typical.Once we abandon the assumption of identical proportions,it becomes possible to fit into the system any amounts of thefactorswe please to take. If the supply of one factor ncreases,that will mean a proportionatelygreater developmentof thoseindustrieswhich use relatively large quantities of that factor,and perhaps a contraction f the industrieswhichuse relativelyless.And the possibility of precisely the same adjustment issufficient o maintain an industrial system in determinateequilibrium. Suppose wages rise-say all wages bv the sameproportion-then the returns to the other factors will bediminished. But since some industries use more labour thanothers, the returns to the other factors will not fall in thesame proportion n differentndustries. There will thus be



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1932] MARGINAL PRODUCTIVITY 83an incentive for these other factors to move, capital, forinstance, moving out of the less capitalistic into the morecapitalistic industries. In the less capitalistic industries therewill be unemployment; in the more capitalistic industriesthere will be an expansion of the demand for labour. Butsince in the more capitalistic industries the amount of labourneeded to use a given quantity of capital is less than it is inthe rest, the transferredcapital in its new position absorbsinto employment ess labour than had been thrown out by itswithdrawal. There is net unemployment.

Similarlv, a fall in wages will lead to a transference f theother factors n the opposite direction, nd a rise in the demandfor labour.Thus it is not necessary to assume, as Mr. Robertson seemsto imagine, that a declilne n the reward of capital will leadto a diminution of its supply, irLorder for the " net produc-tivity analysis to be perfectlyvalid. A rise in wages abovethe equilibrium level will lead to unemployment, hrough thetransference f other resources betweell industries, even if nootherroute is open.The " net productivity analysis remainsvalid, on the otherhand, even if we do admit the principle of Variation. It isstill true that a system will not be in equilibrium, if anyadvantage is to be gained by transferringresources betweenindustries; so that wages must equal the net productof labour.But in this case they must also equal the marginal product;the net product and the marginal product must be equal ina state of equilibrium.

IIHaving, we may hope, established that the methodby whichPareto and Marshall sought to " eke out " marginal produc-tivity s a perfectly alid one, it now remains for us to examinedirectly their criticisms of the Clarkian form of that doctrine.In the case of Marshall, we are dealing with one of the vaguerand more slippery parts of his work, so that it is not easy tobe quite certain what his difficultieswere. But Pareto wasnever vague; we have to face up to Pareto.The mathematicalmethod, of which Pareto was so great amaster, is an almost perfect safeguard against mistakeninference; if a conclusionis wrong,the fault is likely to lie inthe premises. And the thingwhich, I wish to suggest, Paretohad overlooked,does lie deep in his premises; it is a funda-



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84 tCONOMICA [FEBRUARYmentalweakness of that great analytical tool which he wieldedso skilfully. With the arrogancewhich (now that he is safelydead) is one of his more pleasing characteristics, Paretobelieved that he had found in his equations the one perfectmethod of ecolnomicanalysis, besides whose results all thedoctrines of " literary economists were mere fragmentsofknowledge. It was a great claim; and on many counts it isjustified. But to hope that from any single line of approach,all the facets of economiclife would be equally illumined,wasprobablyto indulge a vain illusion.

It is one of the great advalntagesof the Lausanne analysis,that in it the " individualistic9 method, which has beendescribedbv Dr. Hayek as olle of the greatest assets of neo-classical economics,6 s carried to its most completefulfilment.It is the object of Walras' and Pareto's equations, to determinethat svstem of prices which can exist in an economic system(with given population, given tastes, given abilities, givenknowledge and given stocks of capital and land), without anysingle inidividual, s consumeror laboureror capitalist or entre-preneur, havilng any incentive whatever to do anything elsethan go on doillg what he has done in the past. And the wayby whichthese conditionsare reduced to a systemof equations,is by taking each individual, one by one, and findilngwhat hewill preferto do at any given set of prices. Alndif a systemof prices can be found at which the preferencesof all theindividuals in the communityare contsistent, he communitvis in equilibriumat those prices. If anyone had an incentiveto change his conduct, that change would chalnge prices andso upset the whole equilibrium. But at the equilibriumsystemof prices, no one has any incentive to chalnge, and so theequilibriumcan go on. It is proved that such alnequilibriumcan be found.The particular conditions which interest us at present arethose which concern the entrepreneurs. Each entrepreneurhas a choice of differentmethodsby whichto make his produLct,each methodusing different uantities of the factorsof produc-tion. In orderto be in equilibrium,he must choose thatmethodwhich makes his unit cost of productiona minimum. For ifhe does not do so, he can move to a preferredposition bychanginghis methods,and so increasing his proi'ts.Now if the Principle of Variation is accepted, this conditionof minimum ost ofproductionresults in margilnal roductivity.

6 Prices and Production, p. .4.



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1932] MARGINAL PRODUCtIVITY 85For if the price of any factorexceeds the value of its marginalproduct,unit costs of production an be decreased by using lessof it; in the reverse case, unit costs of production can bedecreased by using more. But we are now in a positionto seewhy Pareto had difficultyn accepting the Principle of Varia-tion. In hardly any modern industry does an entrepreneurbuy only the factorsof production,land, labour and capital;in nearly everyindustrya considerableportionof his expendi-ture goes on "intermediate products," raw materials andplant, the products of other industries. Now so long as wefix our eyes on one entrepreneuronly-and that is all, that,according to the strictness of the Lausanne method, we areallowed to do-the only possible changewhichthat entrepreneurcan make, is to buy more or less of the particular kinds ofplant, machines and raw materials, which are for sale on themarket. He is definitelyimitedto these kinds of goods, thosewhich are already being produced, and these goods, undermodernconditions,are likely to consist, to a large extent, ofspecialised articles made for a specialised use, which requirea given amount of other factorsto be used with them. If theamounts of co-operatingfactors can be changed at all, it isonly within narrow limits. An entrepreneur,working underPareto's limitations, is faced to a considerable extent withfixed proportions,and thereforehe cannot alter his methodsto such a point as would achieve that ideal of minimumcost,where the prices of the factorsequal their marginal products.

But these limitations are set, not by the circumstancesofreality,nor by the fundamental conomicadvantages of Pareto'ssystem,but by mere assumptionthat the onlygoods withwhichthemarketneed be concerned re those goods whichare actuallybeing produced, and which have definiteknown prices. Thisassumption is introduced for mathematical convenience, andon it, indeed, the whole mathematicaledificerests, but it hasabsolutely no economic significance. Once it is dropped,Pareto's objectionto marginal productivityfalls flat.It is perfectlypossible to conceive of a community n whichall Pareto's equations are satisfied, but which is not inequilibrium. For so long as the n commoditieswhich are beingproduced are arbitrarilychosen commodities,each individualmay have reached his preferredposition within that charmedcircle, but he may still have an inicentive o move outside it.And in the case we have just been considering, where eachentrepreneurhas reached his position of minimumcost within



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86 ECONOMICA [FEBRUARYthe limits set by an arbitrarilyrestricted ist of possible com-modities, but where the prices of the factorsof production arenot given by their marginal products, there would be anincentive to change. It would be possible for the machine-makers (say), or generally the entrepreneurs in earlier(" higher ") stages of production, to modify slightly thecharacter of the goods they produce, so as to meet the needsof their customersmore exactly. By so doing, it would bepossible for them to sell their new goods at a price which wouldyield thema greater profit han they had earned before; whileon the other hand their customers would be better satisfied,for they in their turn would also earn larger profits.To look at the matter anotherway. Pareto's arguments donot suggest7 that he would have denied that the pure marginalproductivitydoctrine holds good in one particular case-whenall the industries are perfectly integrated," so that there areno intermediateproducts, but each entrepreneurhires only theservices of the true factors of production, land, labour andmoney capital. In this case the only technical limitations onthe change of methods would arise from sheer ignorance ofdifferentmethods to pursue; and in these days, at least, wesurely need not have so low an opinion of man's devisingability as to deny that, sooner or later, he would find meansof reducing his costs to the lowest possible level. And thatis all that the equilibrium doctrine assumes.If the marginal productivity doctrine would work withintegrated ndustries, s thereany reason, other than the formalconvenienceof a particularmethod of analysis, to deny that itwould work where the industriesare differentiatednto stages?Surely not.

IIII believe the foregoing o be an answer to Pareto's objectionsagainst marginal productivity,but it has evidently ittle to do

with Marshall's difficulties. The indications seem to be thatMarshall was chiefly troubled by the durability of materialequipment,and its consequence, that the variation in methodsbroughtabout by a change in factor-prices,may be a very long-run affair. In the first edition of the Principles, the only7 Apart froman odd passage in the Cours (p. 85) when he suggests that asilk factory requires a fixed amount of land, and would get no advantagefrom an increased supply, unaccompanied by an increase in the other

factors. This is merely silly. There is nothing corresponding to it in theMcanuel,



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I932] MARGINAL PRODUCTIVITY 87paragraph in which he discusses true marginal productivityposes the case of an employerwho is " in doubt whetherhehas enough labour to turnhis stock,machineryand othertradeappliances to good account"; and although in later editions,the extraordinary confusion between net productivity andmarginal productivity quite clearly distinguished in the firstedition) makes it extremely difficult o see what is meant bywords which are evidently the fruits of separate and un-co-ordinated ayers of Marshall's development,the probabilityseems to be that he had not profoundlymodifiedhis attitudeto the problem. If we do not allow the entrepreneur ime toreplace his equipment, the old difficulty f fixed proportionsis absolutely unescapable. Marginal productivitydoes leavea considerable range of indeterminateness,and is thereforewhollyunsatisfactory s the main part of a theoryof distribu-tion.Marshall's refusal to look ahead to thereplacement f materialequipment,sprang no doubt partlyfromhis well-knowndislikeof the rigours of static analysis, but partly, one cannot doubt,because he was tryingto impose upon the theorymoreweightthan it will carry. For Marshall, it is true, marginal produc-tivity and net productivity, orthatmatter) s a case of normalvalue; but in the case of a price which is notoriouslysticky,the difference etweenmarketand normal value did not appearsignificant. It is hard to resist the conclusion that Marshallwas seeking a formula which would, generally at any rate,express the level of the wages whichare reallypaid to particularmen at particular times; and his obscurity arises from thefact thatno amountof juggling with marginal productivity ndnet productivitywould give him such a formula. But is notthe reason for this that he was going too fast.? To havedallied a little longer in the realm of abstractionsmight havemeant greatersureness and greaterconcreteness n the end.If we accept the view,which it has been the business of thesepages to justify, that the marginal productivitypropositionisa necessary conditionof static equilibrium, then that in itselfonly gets us a little way towards a theoryof wages. But itis a necessary prolegomenonto such a theory. It does sum-marise in a silngleconvenientexpression the complex causeswhich slowlymould the level ofwages, and the prices of otherfactorsof production. It is not true that a man's wage mustalways equal his marginal product, but if it does not, thereis a danger of certainthings happening. If his wage is below



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88 ECONOMICA [FEBRUARYhis marginal product, other employerswill have an incentiveto attract him away by offeringhim higher pay. They maydesire to take him on so as to put him in the place of anotherman who was costing more; or because they are reorganisingtheir businesses, and can thus put him in the place of someother more expensive factor; or because they are expandingtheir businesses. The statement that his wage is less thanlhis marginal product means simply that these things can bedone profitably. Similarly, if his wage is more than hismarginalproduct,his own employerhas an incentive to dismisshim. This may take place because it is cheaper to use someother methodof production,which dispenses with his services;or because thewhole business in which he works ceases to pay.8But dismissal may not be feasible at once; it may have to waituntil machinery comes to be replaced; yet an incentive todismissal exists, and again that is what is meant by themarginal productivityproposition. Stated in these terms, thetheory seems both simple and impossible to controvert. It isan absolutelynecessary foundation for sound economicreason-ing aboutwages.

8 The contractionof the demiiand or labour because of substitutionand thecontraction which arises from the contraction of businesses are mostproperlydistinguished bv Mr. Robertson; but one must question the neces-sity of the extraordiniary erminologywhich he uses. " An artificialraisingof the rate of wages " produces " two analytically separable reactions. Thefirst s a movement along the existing curve-a reduction in the numbersemployed up to a point at which the product of the marginal man equals theartificial wage. The second is a cunmulativeowering of the curve, causedby the decline in profitsand the consequent check to the supply of capitaland enterprise" (Op. Cit., p. 49). It must certainly be granted that thesecond tendency will take time to work out its full effect although surelvso will the first). But why describe a price-movementas shiftingthe curve,which is surelv a simple expression of the relation between the price andthe amount bought? After all, just the same thing takes place with com-nmodityemand. I buy less foreignvegetables if a tariff s imposed, partlybecause the English variety is now relatively more advantageous, and partlvbecause I cannot affordthe higher price demanded. If we are to say thatthe raising of a price shifts the demand curve, we had better abandon allhope of teaching elementary economics. What do they mean by curvesat Cambridge?

Marginal Productivity and the Principle of Variation_JR Hicks

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