Piero Sraffa - Free

44 Piero Sraffadistribution of the products and makes it possible for the process tobe repeated’.If the economic system under consideration is able to produce a surplus,‘the distribution of the surplus must be determined through the samemechanism and at the same time as are the prices of commodities’. (Sraffa1960: 6). If the wage can exceed the subsistence level, the relative pricesand one of the two distributive variables – wage or rate of profits – arejointly determined, once the technology and the other distributive variableare known. The higher the wage, the lower the rate of profits will be. 5Let us recall here Sraffa’s equations for this case (Sraffa 1960: 11):(A a p a B a p b … K a p k ) (1 r) (L a w) Ap a(A b p a B b p b … K b p k ) (1 r) (L b w) Bp b. . . . . . . . . . . . . . . . . .(A k p a B k p b … K k p k ) (1 r) (L k w) Kp kwhere A a , B a , … , K a ; A b , B b , … , K b ; … ; A k , B k , … , K k and L a , L b , … ,L k are the quantities of the various commodities and of labour requiredfor the production of quantities A, B, … , K of the same k commodities;p a , p b , … , p k are the prices of the k commodities; w is the wage rate and r isthe rate of profits. We thus have k equations for a system with k commodities,and k 2 unknowns (k prices, the wage rate and the rate of profits).Let us choose a commodity as the standard of measure (so that weremain with k – 1 relative prices as unknowns). Let us then consideras exogenously determined either the rate of profits or the wage rate(which is a real wage rate, being expressed in terms of the commoditychosen as the standard of measure). The k equations are now sufficientfor determining the k remaining unknowns.Let us go on to assume that the system produces a surplus: namely,for each commodity the total quantity required as means of productionin the various sectors is less or equal to the quantity produced, withthe strict inequality holding for at least one commodity. It can then beproved that the system has economically meaningful (i.e. positive) solutionsfor the unknowns. It can also be shown that the rate of profits isa decreasing function of the wage rate, varying from a maximum correspondingto a zero wage rate (the case in which all the surplus accrues toprofits) down to zero when the wage rate is maximum (and the wholesurplus accrues to wages).5Cf. Pasinetti 1975, Chapter 5, for a broader mathematical treatment of thissimple model.Production of Commodities by Means of Commodities 45When there is a surplus, the possibility opens up to produce ‘luxury’commodities, that is, commodities which are neither means of productionnor part of necessary (subsistence) consumption. On the oppositeside, we have ‘basic’ commodities, which are directly or indirectlyrequired as means of production in all production processes. We shalldiscuss this distinction in greater detail in Chapter 4. Sraffa then brieflyillustrates the distinction between prices of production and marketprices, followed by the distinction between necessary and surpluswages, before presenting the general solution for the model in the casewhere each industry has a single product (thus leaving aside by assumptionthe case of joint production, to be considered in the second partof his book).Sraffa (1960: 12–13) goes on to analyse changes in relative prices connectedto changes in income distribution. As the classical economistsand Marx already knew, such changes are determined by ‘the inequalityof the proportions in which labour and means of production areemployed in the various industries’. Indeed, ‘it is impossible for pricesto remain unchanged when there is inequality of “proportions”’.Two chapters (Sraffa 1960: 18–33) are then devoted to constructing aparticular analytic tool, namely the ‘standard commodity’, and to provingthe uniqueness of the underlying ‘standard system’. Thanks to thisconstruct, as we shall see later (Chapter 5), Sraffa is able to tackle theRicardian problem of an invariable measure of value and to illustrateimportant characteristics of his own analysis.Part 1 of the book closes with a chapter (Sraffa 1960: 34–40) on the‘Reduction to dated quantities of labour’. This analysis is relevant to anumber of issues, including the Smithian idea that the natural price canbe resolved into wages, profits and rents (see § 3.3) and the Austriantheory of capital, developed by Böhm-Bawerk and adopted by Hayek,whereby capital is measured in terms of an ‘average period of production’(discussed later, § 6.2).In Part 2 of the book Sraffa’s analysis of production prices goes onto consider the case of joint products and, within this category, fixedcapital goods and scarce or non-reproducible means of production suchas land. 6 The book closes with Part 3, consisting of a single chapter onthe choice between economically alternative methods of production in6On the problems which arise with transition from single product systems tojoint production – problems concerning the positivity of prices, the definition ofbasics, the monotonicity of the wage–profit curve, the choice of the methods ofproduction – there is an ample literature, referred to later (§ 8.3).