Sraffa and the Assumption of Constant Returns to Scale: A Critique of Samuelson and Etula

In a recent paper Samuelson and Etula claim to have providedthree examples of the presence of a constant returns to scaleassumption in Sraffa's Production of Commodities. The presentpaper is a refutation of their interpretation of Sraffa's propositions.It shows that they mistakenly take Sraffa's logical propositionsfor empirical propositions. This article also provides evidenceto refute Samuelson's hypothesis that Sraffa consistently confusedthe concept of Marshallian "constant cost" with the generalequilibrium concept of "constant returns to scale". The paperalso argues that Sraffa's prices are not necessarily "equilibrium"prices, and that it is not true that Sraffa maintained thatchanges in demand had no impact on prices; his position appearsrather to be that the impact of demand on prices is unpredictable.     

Sraffa's system: Equal rate of profits and the notion of center of gravitation

This paper argues that the condition of uniform rate of profits in Sraffa's system is not based on his implicit assumption that the system is at the ‘equilibrium’ or the center of gravitation. It is rather a logical requirement of a reproducing system of basic goods as long as prices are not imposed from outside the system. This condition holds irrespective of supplies being equal to their respective effectual demands. It conjectures that Sraffa could have arrived at this conclusion through his analysis of the Standard system. On the basis of this result, a critique of the received interpretation, led by Garegnani, of Sraffa's prices is developed.     

Switches and fake switches in methods of production

It has long been recognised that Sraffa's analysis of the choiceof methods in joint production cannot be sustained, so thatpost-Sraffian economists have abandoned it. The paper returnsto Sraffa's own approach and identifies two characteristic elements:methodologically, it is of a ‘dynamic’ nature (itconsiders a potential move of the rate of profits) and, analytically,the switch-points are the common intersection of several wage–profitcurves. An internal critique consists in showing the existenceof fake switches, which are at the intersection of two wage–profitcurves but, unexpectedly, are not switch-points.     

On Sraffa's Standard commodity: is its price invariant with respect to changes in income distribution?

In his 1960 book, Sraffa suggested using a composite commodity,which he called the ‘Standard commodity’, to solveRicardo's search for an invariable measure of value, i.e., astandard capable of isolating the price movements of any othercommodity induced by changes in income distribution. The absencein Sraffa's book of an explicit proof of the invariance propertyof this standard gave rise to many misunderstandings about itsmeaning and its role as an invariable measure of value. In orderto clear up these questions, Bellino (On Sraffa's Standard commodity,Cambridge Journal of Economics, vol. 28, 121–32, 2004)has proposed a ‘proper’ definition of an ‘invariablemeasure of value’, showing that Sraffa's Standard commoditydoes fulfil the requirements of this definition. He claims thatthe fulfilment of this property (but not the constancy of its‘nominal’ price) qualifies the Standard commodityas an invariable measure of value. In this paper, a proof ofthe invariance of the price of the Standard commodity with respectto changes in income distribution is given, and the equivalenceof this property with Bellino's definition of invariance isshown.     

THOMAS TOOKE AND THE INFLUENCE OF THE RATE OF INTEREST ON PRICES: IMPLICATIONS FOR DISTRIBUTION THEORY

Thomas Tooke included money interest among the determinantsof normal money production costs, together with money wagesand production techniques. This inclusion permitted him to explainthe existence, in actual fact, of a direct relationship betweenthe rate of interest and the level of prices. He did not developthe implications for distribution theory of his view of theinfluence of the rate of interest on the price level. In thepresent article it is maintained that the rate of interest emergesfrom Tooke's analysis as the regulator of the ratio of pricesto money wages, with the corollary that there is implicit init a causal relationship between money interest and normal profitthat goes from the former to the latter. This may be connectedwith Sraffa's suggestion of a determination of the rate of profitby the money rate of interest and lend it the support of Tooke'sscrupulous analysis of facts.     

Hodgson on Hayek: a critique

In his book Economics and Evolution, Geoffrey Hodgson offersa detailed critique of F. A. Hayek's writings on cultural evolution.Certain aspects of Hodgson's treatment appear to be inaccurate.This paper criticises Hodgson's critique.     

The equations unveiled: Sraffa's price equations in the making

In the first part of Production of Commodities by Means of Commodities,four equation systems are introduced: three are drawn up inorder to solve the problem of relative prices; the last oneis devised to define a suitable standard of prices. The bookwas published in 1960, but—as we are told in the preface—its‘central propositions’ and a first version of theprice equations had been originally conceived and written morethan 30 years before, when the author was still in his twenties.Having access now to the Sraffa Papers, preserved in the WrenLibrary, we can ascertain the intellectual origin of the equations.In this paper the analytical path that led to the final draftof the price equation is followed, step by step, and the linkbetween these equations and Sraffa's quest for an ‘invariablestandard of value’ is clarified.     

Revolution and counter-revolution: two views of unemployment

There is a view in economics that Keynes did not have a microeconomictheory underpinning his explanation of macroeconomics. For example,Friedman (1970) even goes so far as to maintain that pricesare arbitrary in Keyne's approach to economics. The conclusionwhich follows from this critique of Keynes is that Keynesianeconomics cannot explain the occurrence of unemployment in amarket economy except by invoking ad hoc assumptions. It isargued in this paper that the above critique is based on a misunderstandingof the focus of the Keynesian explanation of unemployment. Thefocus in Keynes is not choice, but exclusion from choice. Inconventional microeconomics, the concept of choice is not consideredproblematic. The observation that a particular action is takenis confused with the view that the action is voluntarily chosen.The Keynesian explanation entails an exploration of what theconcept of voluntary choice means.     

统一利润率与差别利润率——兼论两种均衡体系的比较

瓦尔拉斯把资本形成方程引入一般均衡体系后出现了内在的不一致性,从而在异质资本品的假设下,一般均衡体系只存在“差别利润率”。在斯拉法体系中,不同的资本品部门却拥有“统一利润率”。两种类型的利润率体现了两种均衡体系的对立。与“差别利润率”相联系的一般均衡体系只研究一般生产过程中的资源配置,体现技术关系;而与“统一利润率”相对应的斯拉法体系则涉及特定市场经济关系下的总量分配,体现社会关系。而后者才可以更好地解释市场经济中的现实问题。     

Sraffa and Goodwin: A unifying framework for standards of value in the income distribution problem

In this paper we show that direct links exist between Sraffian and Goodwinian methodologies in income distribution theory. In fact, Sraffa's Standard commodity approach and Goodwin's transformation of axes are shown to be different manifestations of the same structural approach. Both are brought under a unified framework in terms of transformations involving a transformation matrix of rank one. To obtain transparency Sraffa is shown to retain as much interdependency as possible while Goodwin sacrifies all interdependent structure. It appears that a central role is played by models related to closed models of input-output type.     

Computation and the Theory of Customs Unions

This paper reports on research that uses computational techniquesto assess whether or not various propositions that have beenadvanced as plausible in the literature on the theory of customsunions actually hold. This research blends theory and numericalsimulation to get insights into the likelihood that\ varioustheoretical propositions proposed in the customs union literaturehold. (JEL F10, F13, F15}     

The stock market and investment: another look at the micro-foundations of q theory

This paper introduces a novel distinction between real q andfinancial q. The paper examines three versions of financialq developed by Brainard and Tobin, Minsky and Hayashi, respectively.These theories differ regarding the nature of stock market pricedetermination and their use of marginal productivity theory.It is shown that non-profit maximising behaviour by managersdoes not invalidate q theory. It is also shown that if managersand shareholders have different profit expectations, this leadsto an equilibrium value of q that differs from unity. Lastly,the implicit claims in q theory regarding the efficient roleof stock markets as regulators of capital accumulation are shownto depend on assumptions about stockholder behaviour.     

Sraffian Indeterminacy in General Equilibrium

The indeterminacy claim for competitive price systems made by Sraffa (1960) is examined by placing Sraffa's work in an intertemporal general equilibrium model. We show that indeterminacy occurs at a natural type of equilibrium. Moreover, the presence of linear activities instead of a differentiable technology is crucial and the indeterminacy is constructed, as in Sraffa, by fixing some or all of the economy's aggregate quantities. On the other hand, an extra condition, that some factors have inelastic excess demand is necessary, and, unlike Sraffa's model, relative prices must be allowed to vary through time. Sraffian indeterminacy and the generic finiteness of the number of equilibria are reconciled by showing that indeterminacy occurs at a measure-zero set of endowments. We use an overlapping-generations model to show that these endowments nevertheless arise systematically and that indeterminacy does not occur when relative prices are constant through time.