mumy (1990) - a microeconomic reconstruction of marx's labour market theory

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A Microeconomic Reconstruction of Marx's Labour Market TheoryAuthor(s): Gene E. MumySource: Economica, New Series, Vol. 57, No. 225 (Feb., 1990), pp. 91-105Published by: Blackwell Publishingon behalf of The London School of Economics and Political Scienceand The Suntory and Toyota International Centres for Economics and Related Disciplines

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Economica, 57, 91-105

A Microeconomic Reconstruction of Marx's LabourMarket TheoryBy GENE E. MUMY

Ohio State UniversityFinal version received 11 April 1989. Accepted 25 April 1989.

The purpose of this paper is to show that there is a more consistent implied microeconomicmodel of wage and hours determination in Marx's Capital than is usually recognized. Theargument is that, rather than merely assuming wages equal to an exogenously given value oflabour-power, Marx's labour market model actually describes how the market evolves to alower-bound frontier of wages as a function of hours worked. This frontier is the real-wageequivalent of the value of labour-power, and is generated from average-cost-minimizingconsiderations by business firms. Likewise, the same market process also determines hours,rather than having them depend on some primitive level of class struggle. Labour marketoutcomes depend on worker preferences over wages and hours, thus giving rise to politicalclass struggle over hours when labour market outcomes evolve in utility-reducing ways.

INTRODUCTIONKarl Marx's Capital is a structurally complex work. Even though wages andhours are crucial Marxian magnitudes, a piecemeal reading of various chapters,particularlyin Volume I, has tended to forestall the emergence of a consistentmicroeconomic foundation for an interpretation of the role played by thelabour marketin determination of these magnitudes. For instance, the relativelyearly chapter on 'The Buying and Selling of Labour-Power'(I: chap. 6)1, seemsto license the view that Marx has the real wage determined outside of thelabour market, basically by the complex social determination of the requiredrealwage for the reproduction of the workerand workers.Likewise, the chapteron 'The Working Day' (I: ch. 10) seems to leave the determination of hoursin the arena of class struggle pure and simple. On the other hand, the muchlater chapter on 'The General Law of Capitalist Accumulation' (I: ch. 25),with its emphasis on the industrial reserve army, seems more in tune with asupply and demand determination of wages and employment, and not verymuch encumbered by the pronouncements in earlier chapters. Is there, then,a coherent thread running through these seemingly disparate views, or areMarx's various accounts hopelessly muddled and inconsistent?

It seems to me that we can extract a fairly coherent Marxian theory ofwage and hours determination if we consider the entire structure of Marx'sargument as it progresses through Capital, and its implications. This is exactlywhat is attempted in this paper. The language and modes of analysis are not,to be sure, exactly those used by Marx. Indeed, the use of some neoclassicalanalytical tools may strike some as novel, if not downright inappropriate, butI think their 'utility' is amply demonstrated in what follows. Also, on groundsof superior transparency, the analysis here is carried out in terms of the metricof the only commodity in a one-commodity economy rather than in Marxianvalue terms. Because of these analytical heresies, I do not feel inclined topersuade the dogmatic of this paper's Marxian intellectual pedigree. But I do


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92 ECONOMICA [FEBRUARYclaim that, over all, my premises are reasonably consistent with Marx's andthat the derived implications tally with his.A major point of emphasis, in this paper, is that what seem to be invariantMarxian premises are, rather, results. For instance, rather than being anexogenously given determinant of wages, the value of labour-power is alower-bound frontier of wages as a function of hours, to which labour marketoutcomes tend to evolve. Likewise, class struggleis not the exclusive mechanismwhereby hours are determined for the labour market. Rather, the evolution ofutility-reducing labour marketoutcomes for workers sparksa political struggleto limit the workings of the market by restricting hours.The focus on wages and hours determination, in terms of consistent costminimization by capitalistic firms and maximal, feasible preference satisfactionby workers, is what makes the analysis in this paper microeconomic. To keepthis focus sharp, I have purposefully avoided some difficult interconnectionswith the determination of other crucial magnitudes, particularly those of amore macroeconomic stripe. Clearly, for instance, the structure of the modeldoes not allow effective demand (or realization) considerations to arise in aninteresting way. Furthermore,the capital stock, and its commitment to produc-tion, is taken as exogenous. Unemployment, on the other hand, is endogenouslydetermined and is featured in an important way with respect to the implicationsof the model. However, cyclical aspects of unemployment are not dealt with,and possible feedback ramifications of unemployment on worker productivityand discipline are ignored. Nevertheless, the sharp insights generated by thismodel argue in support of its fruitfulness and are suggestive of how it mightbe used to provide a foundation on which these broader considerations canbe integrated.The plan of this paper is first to represent the production technology andcost characteristics of the one-commodity Marxian economy (in Section I).In Section II, some care will be taken to identify the most salient wage-determining characteristics associated with the concept of the value of labour-power, and to link these to a plausible mechanism for their realization inappropriate circumstances. A static, one-period labour market equilibrium ischaracterizedin Section III. The comparative-static effects of capital accumula-tion, changes in the supply of workers, technological change and fixed capitalformation are then analysed in Section IV. In section V this analysis is shownto be basically consistent with Marx's pronouncements about the role of theindustrial reserve army in the determination of wages, and with his viewsconcerning the sources of class political conflict over the length of the workingday. Section VI contains some final thoughts.

I. A REPRESENTATION OF THE PRODUCTIVE TECHNOLOGY AND COSTThe economy to be analysed produces one all-purpose commodity, X. Thisputty-clay commodity can be pressed into wage goods, fixed capital goods orcirculating capital raw materials. However, to reflect the fact that businessfirms cannot instantaneously adjust their technologies and capital goods tothe current state of the labour market, it is assumed that firms must committhemselves to a particular technology prior to the realization of the labourmarket outcome for a given production period. It is consistent with attempted


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1990] MARX'S LABOUR MARKET THEORY 93profit maximization, in the model specified below, to suppose that capitalistschoose the technology that they believe will minimize unit cost. Furthermore,even though the technology chosen for a given period is independent of thatperiod's labour market outcome, over time firms will adjust their technologiesto trends in labour market outcomes, as will be discussed in Section IV. Butinitially, given the available technologies, let us suppose that all of a largenumber of identical capitalistic business firms commit themselves to the sametechnology, which generates the following rate of output for a productionperiod:(1) x=ehpwhere e is the number of workers employed, h is the number of hours workedby an employee2 and p is an employee's output per hour. The technology thatyields this productivity can be adequately described by stipulating the fixedand circulating capital requirements.Fixed capital is the machinery and other means of production that are notused up or incorporated into individual commodities in a single labour process.Fixed capital, rather, maintains an independent material form that can beemployed as a use value in a succession of repetitions of the labour process(see II: ch. 8). But fixed capital does depreciate, so it will be assumed that itcan be used unimpaired for the duration of a single production period andthen will depreciate completely. Let the amount of fixed capital, f, be given by(2) f =aewhere a is the number of units of X that must be moulded into fixed capitalfor each worker employed. This formulation captures some important Marxiannotions which deserve further comment.First, the parameter a is a direct index of the technical composition ofcapital, which is the amount of fixed capital relative to the amount of livinglabour-power (I: p. 612). The importance of the technical composition ofcapital is that its increase over time is the primary source of intertemporalincreases in productivity. Increases in a must be mirrored by increases in theproductivity parameter, p. Another important point is that, since a is unrelatedto h, we have the polar case of the proposition that the increased usage offixed capital resulting from longer hours will be proportionately smaller thanthe increase in output3 (I: pp. 404-5).The last part of the technology description is the required amounts of rawmaterials, called the circulating capital (II: ch. 8). The usual assumption isthat the amount of circulating capital used up in a production period isproportional to the rate of output. Therefore the amount of circulating capital,c, is given by(3) c =f3pehwhere /3 is the amount of X that must be used as raw materials for each unitof X produced. The cost of producing X can now be represented as a functionof wages and hours.Letting y be the amount of X advanced as wages per employed worker,we can use equations (2) and (3) to express total cost, T, as(4) T = e(y + a +/3ph).


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94 ECONOMICA [FEBRUARYDividing T by the output obtainable for given levels of e and h, which is pehaccording to equation (1), we obtain average cost, A, as being(5) A={(y+a)/ph}+,3.Implicit differentiation of equation (5) characterizes a family of iso-average-cost curves which can be graphed in (y, h) space.Iso-average-cost curves are linear and positively sloped because(6) dy/dh = (y + a)/h >O,and d2y/dh2 =0. Equation (5) also indicates that lower values of y and/orhigher values of h generate lower levels of average cost, so the direction ofunambiguously decreasing average cost is to the south-east. Equation (6), then,indicates that iso-average-cost curves to the south-east are less steeply slopedthan those to the north-west. A representative iso-average-cost map is shownin Figure 1, with curve A1 indicating the highest and A4 the lowest level ofaverage cost.

YA Al A2A1~~~v AA4

hm hFIGURE 1

The representation of average cost just arrived at plays an important rolein the determination of labour market equilibrium. But before moving on toa characterization of equilibrium, the concept of the value of labour-powermust first be dealt with.II. THE VALUE OF LABOUR-POWER

To start, note that what Marx calls the value of labour-power can, in theone-commodity model, be expressed directly in units of X, and its magnitudewill be designated by V. Now clearly, the value of labour-power is supposedto play some wage-determining role in Marx's theory, but the theoretical andempirical grounding for this in Capital is, to say the least, insecure. Neverthe-less, Marx's consistent emphasis is on the notion of reproduction, both ofindividual workers and of the class of workers. But it is important to note thathis first and primary emphasis is on the reproduction of individual workers,and not just as beings who are able to subsist, but as productive labouring


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1990] MARX'S LABOUR MARKET THEORY 95individuals. According to Marx, a worker must receive means of subsistence'sufficient to maintain him in his normal state as a labouring individual'(I: p. 171). Employed workers, then, must receive wages 'sufficient' to achievethis 'normal state'. Wages higher than the required minimum are sufficient toachieve this, but wages lower than the required minimum are not, so I takethis to mean that there is some minimum payment required for a worker'sphysical and psychical reproduction that allows him/her to be advantageouslyemployed by a capitalist, which takes account of the 'historical and moralelements' mentioned by Marx (I: p. 171).Essentially, if this were the only component of the value of labour-power,the value of labour-power would be the minimum amount that capitaliststhemselves would want to pay as wages. Moreover, this component of thevalue of labour-power has a mechanism, grounded in unit cost minimization,to assure its realization, as we shall soon seen. But according to Marx, thereis more to the value of labour-power than this.After discussing the reproduction of individual workers, Marx also notesthat the perpetuation of the working class requires that workers' incomes besufficient to cover the costs of replacing individual workers as they withdrawfrom the labour market and die (I: p. 172). This means that the cost of raisingchildren can also play some role in the determination of the overall level ofwages. But how?Marx, after all, basically rejects the Malthusian population dynamics thatenforce the realization of Ricardo's 'natural price of labour'.4 In fact, Marxmakes almost nothing out of this component of the value of labour-power inthe rest of Capital, and nowhere does he specify a mechanism specificallylinking the rearing of children to wages. Furthermore, the mechanism of theindustrial reserve army is certainly a poor candidate for providing such a link.As a result of these considerations, I think it reasonable to ignore this secondcomponent of the value of labour-power, and to associate the value of labour-power exclusively with the first component described above. Of course, I amalso ignoring Marx'sconsiderations concerning the different values of differen-tially skilled labour-powers (I: p. 172), because such considerations lie outsidethe scope of this paper and, in any event, are not obviously at odds with therole I assign to the value of labour-power. Before leaving the general conceptof the value of labour-power, as I will employ it, two more things shouldbriefly be said about it.First, by associating the value of labour-power with the reproduction ofindividual labouring persons, I also embrace the characterization of it as theminimum amount that capitalists themselves would want to pay as wages. Thisdoes not mean, however, that workers have no role in establishing what thisminimum is, because the individual and collective behaviour of workerscertainly does help to determine the normal state of a labouring individual.Nevertheless, this characterization raises another issue, because, by definition,capitalists would never cut wages below the value of labour-power, althoughit is possible for wages to be higher.This characterization is consistent with the assumption often made by Marx'that the price of labour-power rises occasionally above its value, but neversinksbelow it' (I: p. 519); but there are notable exceptions. The most importantis the second counteracting influence to the falling rate of profit, which Marx


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96 ECONOMICA [FEBRUARYlabels 'Depression of Wages Below the Value of Labour-Power' (III: p. 235).Below this heading Marx says:

This is mentioned here only empirically, since, like many other things which mightbe enumerated, it has nothing to do with the general analysis of capital, but belongsin an analysis of competition, which is not presented in this work. However, it isone of the most important factors checking the tendency of the rate of profit to fall.

This is all that Marx says on the topic, so it is not clear what we should makeof it. Its theoretical efficacy is suspect because Marx never got to his analysisof competition; and as an assertion about the empirical evidence he had athand, this statement simply does not hold water, as is partially evidenced bythe failure to present the data. The empirical truth being asserted would haverequired a far more precise description of the value of labour-power thanMarx ever gave, because in its absence we do not know if the value oflabour-power fell or if wages fell below the value of labour-power, not tomention a host of other empirical issues. Therefore, I am inclined to stick withmy basic characterization and move on to more detailed analysis.Although its overall determination is complex, Marx is clear that the valueof labour-power does vary in predictable ways with such things as the intensityof labour and the length of the working day. With respect to the working day,which is the exclusive focus of this paper, Marx assumes that, over some initialrange of hours, the value of labour-power is essentially constant, but abovethat range it increases at an increasing rate (I: p. 527). This relationship canbe represented by V = g(h), with g'=0 for some initial range of hours butafter that having the characteristic that g'> 0, as well as g > 0. In Figure 1,the value of labour-power is represented by curve V.It turns out that a lower-bound constraint on wages, like the one representedby curve V, falls rather naturally out of cost minimization considerations, ifthe production description given in Section II is modified slightly. Supposethat the productivity parameter, p in equation (1), is not determined solelyby technology but is also functionally related to y and h, so that p = p(y, h),with the characteristics py> 0, pyy< 0 and Ph < 0. For a number of individualand social reasons, productivity increases as income increases, but at a decreas-ing rate. Also for a number of reasons, productivity per hour falls as hoursincrease. Now, under quite general conditions, there would be a global average-cost-minimizing point, and a map of nonlinear closed contour iso-average-costsaround it, in (y, h) space. Then, for any level of h, there would be an average-cost-minimizing level of wages, such that lower wages would actually increaseaverage cost. The locus of average-cost-minimizing wages for alternative levelsof h thus satisfies my characterization of the value of labour-power and is thesource of curve V. However, there is a simplification that makes the analysismuch more straightforward, while maintaining the appeal to cost minimizationjust discussed.The simplification that is the basis for the analysis, in this paper, is that pis not a smooth continuous function of y, but rather a step function. The ideahere is that there is a threshold level of wages, y,, varying with h accordingto y,=g(h), such that p=0 when yy,, and p= p>O when y2y,, where p3is a productivity level given by the technology and organization of production.On this reading, y, = g(h) is the value of labour-power and has the usualproperties associated with curve V in Figure 1. The convenience of this


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1990] MARX'S LABOUR MARKET THEORY 97assumption is that, with p = p3 or all (y, h) combinations above V, iso-average-cost can be represented with the linear curves in Figure 1. Of course, theobvious modification to Figure 1 is that the iso-average-cost curves cannot berepresented below curve V, because average cost becomes undefinedly largewhen y


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98 ECONOMICA [FEBRUARYIt has been a common weakness in much Marxian analysis-and criticismsof it-to eschew considerations of worker preferences over the terms ofemployment.6 But it is absurd to deny that Marx-or anyonle else, for that

matter-thought that workers prefer higher income and shorter hours to lowerincome and longer hours under the production relations of capitalism. Nor isthere any good reason for attributing to Marx the position that there is notrade-off between shorter hours and lower wages. In fact, Marx approvinglydisplays factory inspector Horner's evidence that many workers would havepreferred lower wages and shorter hours than what they had (I: pp. 284-5).Suppose, then, that all workers have identical preferences over wages andhours, and that they can be represented by the preference function, u = u(y, h),with the usual assumptions that uv> 0, uh< 0, and indifference curves as convexfrom below. A representative indifference map is illustrated by curvesU1, U2, U3 and U4 in Figure 2, with unambiguously preferred combinationsof y and h lying to the north-west.

FIGURE 2Given the curvatures of the indifference and iso-average-cost curves, thereis, among all the points on an indifference curve, just one that minimizesaverage cost, and that occurs where the indifference curve is just tangent toan iso-average-cost curve.7 The locus of all tangencies between indifferencecurves and iso-average-cost curves is characterized by

where the LHS is the slope of the indifference curve at a given point and theRHS is the slope of the iso-average-cost curve at that point. Equation (10)generates curve LL in Figure 2.As dictated by the configuration of indifference and iso-average-cost curves,curve LL will initially lie above curve FF, but will descend at a faster rate tointersect FF from above, if such such an intersection occurs in the regionabove curve V where LL is defined. When there is such an intersection point,it is a locally stable (at least) equilibrium, under a reasonable description ofmarket adjustment processes, as can be seen by considering Figure 2.We already know that an equilibrium cannot occur below curve FF. Onthe other hand, the unemployment associated with points above FF would


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1990] MARX'S LABOUR MARKET THEORY 99enable firms to offer and induce potential employees to accept combinationsof wages and hours that are less preferred by workers but are average-cost-reducing to firms. This pushes any equilibrium back down to curve FF, aslong as value of labour-power restrictions are not binding. But all points onFF are not equilibria.

Consider the full-employment point to the left of point E, where indifferencecurve U3 intersects FF. An outcome here cannot be sustained, because competi-tive firms have an incentive to move along U3 to the point where average costis minimized on curve LL. When all firms do this, unemployment re-emergesand potential employees can then be induced to work for lower wages andlonger hours, which pushes the market outcome to the equilibrium point E,which is also on LL. Point E, then, is an equilibrium because it generates fullemployment and also yields the minimum average cost compatible with theutility level attained by workers.8 Call this type of equilibrium type 1.There is, however, no requirement for FF and LL to intersect in the regionabove and to the left of V,as is illustrated in Figure 3 by curves FF and L'L';and when they do not, there are two additional equilibrium types which areillustrated in Figure 3. (Ignore curve LL and point m' for the time being.)Note that in Figure 3 the iso-average-cost curves are bounded by V and shrinkdown to to a single point of global average cost minimization at point m, asrequired by our previous discussion of the value of labour-power. The exactnature of the equilibrium depends on whether curve FF intersects curve Vabove point m or below it, as happens with the alternative full-employmentlocus F'F'. When FF is the relevant curve, equilibrium occurs at point z,where it intersects curve V.At any other point on or above FF, and on or tothe left of V, there is unemployment and/or the possibility of firms loweringaverage cost without making employees worse off, so the outcome is drivento z. Call this kind of equilibrium type 2.When F'F' is the relevant curve, point m is the equilibrium outcome. Theemployee indifference curve passing through the point where F'F' intersectsV is less steeply sloped than the iso-average-cost curve starting at that point,

ya

0 ~~~~~~~~~~~~~hFIGURE 3


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100 ECONOMICA [FEBRUARY

so firms can make average-cost-reducing moves which initially do not makeemployees worse off, but do generate unemployment. The unemploymentcauses workers to accept lower wages and longer hours until the outcome isdrivento point m, where value of labour-power considerations prevents furthermoves to achieve neoclassical-type market-clearing. Since m is the globalaverage-cost-minimizing point, firms have no incentive or need to hireemployees on any other terms, regardless of the extent of unemployment. Callthis kind of unemployment equilibrium type 3.Equilibrium types 2 and 3 achieve wage outcomes equivalent to the valueof labour-power for the number of hours obtained, but type 1 has wages higherthan the value of labour-power. I think that Marx's position was that type 1equilibriawould tend to evolve into the other types, and that, ultimately, therewould tend to be a persistent succession of type 3 equilibria. The reason forthinking this is that, as compared with the others, type 3 equilibria give fullerplay to the industrial reserve army of the unemployed and greater credenceto the notion that the unfettered market determination of hours leads to apolitical struggle over the length of the working day.The prospects for this kind of evolutionary tendency can be surveyed interms of the comparative statics of labour market equilibrium. While purecapital accumulation and changes in the supply of labour-power are of someinterestand deserve brief consideration, the emphasis here is the same as thatof Marx: namely, on the productivity increases resulting from fixed capitalformation.

IV. VARIATION IN THE LABOUR MARKET OUTCOMEThe strategyhere is to focus on the comparative statics of a type 1 equilibriumto see if it tends to move towards one of the other types on curve V,especiallytype 3. Since the analysis is very simple, it is instructive to begin with increasesin the amount of capital, K, and the supply of labour-power, n.In terms of the graphical apparatus, increases in K or n cause a shift incurve FF only. Using (9) as an equality, we can compute that an increase inK causes a parallel upward shift in curve FF by the amount dK/n, while anincrease in the supply of workers causes a parallel downward shift in curveFF by the amount K dn/n2. Since the effects of capital accumulation andan increased supply of workers cause FF to move in opposite directions,the overall intertemporal effects of these changes depend on their relativemagnitudes.

With an initial type 1 equilibrium, if K increases by a proportionatelygreater amount than n, the new equilibrium is also type 1, but with higherwages and shorter hours. On the other hand, if the increase in n is proportion-ately greater, the new equilibrium is pushed towards the value of labour-powercurve, with lower wages and longer hours. Of course, if capital and the supplyof workers increase by the same proportion, FF is stable and there is nochange in wages or hours, with the wage result being the same as the stablelong-run equilibrium result of classical economics, which was based onMalthusian population dynamics.As mentioned in Section II, Marx thought that the Malthusian populationdynamic was nonsense for a number of reasons (I: ch. 25). While he had a


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1990] MARX'S LABOUR MARKET THEORY 101number of things to say about population and labour supply,9 the plain factis that, with respect to the effect of accumulation on workers' welfare, he didnot view the simple balance between the quantity of capital and the supplyof workers as being of primary importance. Of much greater significance isthatthe technical basis of production is continually revolutionized as accumula-tion proceeds, in order to heighten productivity. The technological changeengendered by capitalist social relations is the central core of the forces thatdrive the evolution of labour market outcomes.The struggle to survive in competition forces firms to adopt the bestaverage-cost-minimizing technology available (I: ch. 12). 0l1nMarx's view,modern industrial production based on machinery leads to a situation wheremost cost-reducing innovations are realized by increasing productivity throughfixed capital-deepening (I: ch. 13-15). In our model, this is represented by anincrease in the fixed capital coefficient, a in equation (2), and is reflected byan increase in the productivity parameter, p in equation (1). Although notnecessary, it is convenient to assume that the circulating capital per unit ofoutput remains unchanged. Recalling equation (5), average-cost-reducing-productivity increases from using more fixed capital must satisfy(11) dp/da > p/(y+ a),because, at a given initial level of hours and wages, the RHS of (11) is theproductivity increase needed to just offset the increased fixed capital expen-diture and leave average cost unchanged 1. Essentially, this is the cost screenused by capitalists for adapting their technology over time to realized labourmarket outcomes. Increases in a and p both affect labour market outcomes.Using equation (9), an increase in p causes FF to shift down by the amount(,fh) dp, which also means that FF becomes more negatively sloped. Theincrease in a reinforces the downward shift in FF, because equation (9)indicates an additional downward shift of (da) from this cause. This combinedeffect is illustrated by the shift from FF to F'F' in Figure 3. An increase ina also has other important consequences.First, curve LL shifts up and to the right, as is shown by the shift from LLto L'L' in Figure 3. The reason is that the slope of the iso-average-cost curveat any point, given by equation (6), becomes steeper and represents a lowerlevel of average cost. This means that, along all of the convex-from-belowindifference curves, new tangencies with iso-average-cost curves will be foundto the north-east. Obviously, the same reasoning implies that the minimum-average-cost point must move up curve V,because the now-everywhere-steeperiso-average-cost curves will shrink to a single global average-cost-minimizingpoint more to the north-east on convex-from-below curve V. In Figure 3, thisis shown by the shift from m to m'.Putting these effects together, technological change tends to transform anyinitial type 1 equilibrium, such as point E, into at least a type 2 and ultimatelya type 3 equilibrium, the latter being the new outcome at point m'. This is thekey mechanism that drives the evolution of Marxian labour market outcomes.In summary, the tendency of technological change to produce type 3equilibria results from: (1) a downward-shifting and more negatively slopedFF curve, which, combined with an upward shifting LL curve, makes itincreasingly likely that the two curves do not intersect in the region above


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102 ECONOMICA [FEBRUARYcurve V; (2) combined with the characteristic shift in FF, the movement ofpoint m up curve V makes it increasingly likely that FF intersects V belowpoint m. A succession of type 3 equilibria moving up curve V is consistentwith the role Marx assigned to the industrial reserve army, as well as withMarx's argument that, at least initially, the length of the working day was amore important point of class conflict than the level of wages.

V. THE INDUSTRIAL RESERVE ARMY AND THE STRUGGLE OVER THEWORKING DAY

The industrial reserve armyIn a descriptive overstatement, Marx says: 'Taking them as a whole, the generalmovement of wages are exclusively regulated by the expansion and contractionof the industrial reserve army. . . ' (I: p. 637).This is an exaggeration, but, given its context, it is also clear that Marx'smotivation was to oppose the Malthusian notion that wages depend solely onthe balance of accumulated capital and accumulation-induced population size.The point is that the technological dynamism of capitalist production tendsto create a relative surplus population that is unemployed by means otherthan pure population growth, and that brisk capital accumulation, particularlyin its cyclical rhythms, often does not increase wages but simply mops upsome of the pool of unemployed. The other side of this is that during investmentslumps full employment is not restoredby wage-cutting and hours-lengthening.This argument is consistent with type 3 equilibria, because, as long as FFcontinues to intersect V below m, capital accumulation which causes FF toshift up will leave wages and hours unchanged and will simply reduce thelevel of unemployment. The model in this paper also sharply identifies someof the other forces that check the depletion of the unemployed pool asaccumulation proceeds.We have already seen that technological change checks upward shifts inFF, while at the same time causing the average-cost-minimizing point to shiftupwards along V, making it more likely that FF will continue to intersect Vat a point below m. But if this fails, there is another mechanism that worksto restore this outcome. If accumulation is strong enough to force the intersec-tion between FF and V above point m, the wage level will rise above wagesat point m, and technologies using a higher proportion of fixed capital canthen pass through the average-cost-reducing screen of inequality (11) thanwould be the case at point-m wages. Technologies using more fixed capitalinduce a greater shift in point m up curve V and a smaller upward shift incurve FF, thus tending to re-establish an FF- V intersection below the newaverage-cost-minimizing point.In total, Marx's view was that technological change and the various sourcesof an increased supply of workers would tend to offset pure capital accumula-tion in a way that generates and reproduces type 3 equilibria over time. Withtechnological change producing the dynamic impetus, the secular path ofwages and hours would increase aiong the value of labour-power curve V-thatis, unless there were restrictions placed on the workings of the competitivemarket by union action or the state. It was exactly Marx's position that the


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1990] MARX'S LABOUR MARKET THEORY 103trend in hours sparked the struggle by workers to restrict labour marketoutcomes to a shorter working day.The length of the working dayUp to this point, class struggle has not appeared as an explicit, let alongexclusive, determinant of hours, although some elements of conflict andstruggle are surely embedded in the value of labour-power concept. There is,however, room for class struggle to emerge as an explicit determinant of hours,but as a political struggle, leading to a political intervention in the workingsof the labour market. 'Political' here is taken to mean the forcing of employersthat is enabled by union solidarity or explicit state action, which would notbe available to isolated workers in labour markettransactions. But the politicalclass struggle must be based on something that motivates it, and this paper'smodel identifies two potential candidates consistent with Marx's arguments(I: ch. 15), especially sec. 3b, and pp. 636-40).One possible motivation is that a restriction on hours might serve to reducethe unemployment associated with type 3 equilibria. To see this, suppose thatthe relevant curves in Figure 3 are L'L' and F'F', with a type 3 equilibriumoccurring at m'. Restrictions on h move the minimum attainable average costdown V and closer to F'F', thus dissipating some of the unemployment. Ofcourse, all unemployment is eliminated if the maximum number of hours isrestricted to the point where F'F' intersects V, but this obviously does nottake account of all possible longer-term ramifications that might argue for oragainst such a restriction. In any event, while political pressure from theunemployed and those feeling the threat of unemployment is perhaps straight-forward, the significance of this is unclear, mostly because it is not clearwhether those who are employed are made better or worse off. But Marxconsistently maintains that, even for the employed, the terms of employmentdeteriorate over time. This provides a second, if not entirely separate, possiblemotivation for class struggle over hours.We have seen that increases in fixed capital per employee cause theaverage-cost-minimizing point to move up curve V. If such a move makesemployees worse off, then it must be utility-reducing in terms of the preferenceordering over (y, h). While this is not required in the more general model, itdoes rest on the perfectly allowable additional assumption that indifferencecurves, as they pass through equilibrium outcomes on V,have steeper slopesthan V at such points. In this case, restrictions on h, which move the minimumattainable average cost down V,lead to more preferred terms of employment,as well as to a reduction in unemployment. Note, on the other hand, that aforced higher wage, by itself, would lead to less preferred terms of employmentand would increase the extent of unemployment. This special case clearlytallies with the priority that Marx gave to restrictions on hours as an initialobject of class struggle.

VI. CONCLUSIONBy viewing the value of labour-power as something that has to be realized inthe process of evolving labour marketoutcomes, and by takingthe class struggleto be a political strugglewhich emanates from the evolution of atomistic labour


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104 ECONOMICA [FEBRUARYmarket contracting, the analysis in this paper has been able to tie togetherwhat often seem to be incompatible parts of Marx's labour market analysis.Of course, once it is granted that the evolution of atomistic contractinggenerates political interventions in the labour market, the model of suchcontracting loses some of its precision as an indicator of labour marketoutcomes: then it becomes clear that the outcomes depend, in part, on thebalance of political forces. While this much must be conceded, the more purelyeconomic model does not lose all utility. It still emphasizes the sources ofconflict and indicates the likely direction of and limitations on political actionaimed at dictating labour market outcomes. It was part of Marx's genius torealize that, even though economic analysis can give a good survey of thebattlefield, it does not inevitably indicate the outcome of the battle.

NOTES1. All references to Capital are to Marx (1967), and will be given by a Roman numeral, indicatingvolume, followed by chapter and/or page reference.2. With more than one day in a production period, h is not the length of the working day butis proportional to, and hence an index of, it.3. In the more general case, we would havef = ea (h) with a'?' O, but with the crucial characteris-tic that d(f/x)/dh = {(a'/ph) - (a/ph2)}


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1990] MARX'S LABOUR MARKET THEORY 105MARX, KARL. (1967). Capital (3 vols.). New York: International Publishers.

(1968). Theories of Surplus-Value (3 parts). Moscow: Progress Publishers.RICARDO, DAVID. (1963). The Principles of Political Economy and Taxation. Homewood, Ill.:

Richard D. Irwin.STEEDMAN, IAN. (1977). Marx After Sraffa. London: New Left Books.WEST, EDWIN G. (1983). Marx's hypotheses on the length of the working day. Journal of PoliticalEconomy, 91, 266-81.

mumy (1990) - a microeconomic reconstruction of marx's labour market theory

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