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.     

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.     

Interpreting Ricardo: a rejoinder to Peach

This note answers Terry Peach's (1998) response to our criticismsof his interpretation of Ricardo. We show that the availableevidence supports Sraffa's interpretation. The arguments putforward by Peach, far from undermining that interpretation orfurthering an understanding of Ricardo's project, do littlemore than catalogue the already well-known difficulties thatRicardo encountered as he grappled toward a clearer accountof the laws that regulate distribution and prices.     

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.     

A note on the speculative demand for money

In the General Theory, Keynes argued that expectations about future bond prices tend to be “sticky”. A rise in bond prices causes more investors to “join the bear brigade” and so increases the aggregate demand for money. Since Tobin's classic article on liquidity preference, this explanation of the downward sloping demand for money curve has largely disappeared from the literature. This note introduces sticky expectations into the Tobin framework. It shows that the existence of such stickiness does not necessarily cause the demand for money to be more elastic because investors have expectations about the variance of future bond prices as well as about their mean. A sufficient condition for a more elastic demand for money under sticky expectations is that the Pratt-Arrow coefficient of relative risk aversion be either constant or decreasing in wealth.     

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.     

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.     

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.     

The impact of speculation on house prices in the United Kingdom

When house prices are expected to rise, the representative house mover has an incentive to secure his purchase price (i.e. exchange contracts) on the ‘new’ house before exchanging contracts on the sale price on his ‘old’ house. If all house-movers adopt this stance, the imbalance between buyers and sellers causes a self-fulfilling speculative price bubble. Transactions costs do not represent a barrier to such speculation in the house market, as such costs can be considered as being sunk costs for first-time buyers and owner-occupiers intending to move for non-speculative reasons. This idea is formalised and empirical evidence is presented which suggests that speculation is a significant determinant of house prices in the United Kingdom.     

Special offers and clustering under symmetric monopoly

A monopolist offerings variants on a Salop circle is analyzed with respect to his choice of product variants and prices. Although we assume a uniform distribution of tastes, the profit-maximizing pattern is not equidistant in variants and prices are not the same for all variants.Instead, under fairly general circumstances, there exists at least one cheap variant (special offer) around which the more expensive ones are clustered. This result depends on the assumption that the market size is not fixed as in most other models of this sort, but depends on prices in a straightforward manner.     

A necessary and sufficient condition for the equality of the expansion rates in the von Neumann growth model

We derive a necessary and sufficient condition for the equality of the maximal physical and the minimal economic expansion rate in a linear von Neumann model. It is a generalization of Gale's sufficient condition which postulates the absence of independent subsets of commodities. We argue that the von Neumann model is of little economic interest if this condition is not fulfilled, since then only free goods are produced and only some or all of those goods which are not produced at all have positive prices.     

Sraffa's legacy

This review essay of Critical Essays on Piero Sraffa's Legacyin economics situates Sraffa's work in relation to the Marshalliantradition and neo-Walrasian general equilibrium theory, andreviews the current state of debate between adherents of thesetraditions on the role of demand, returns to scale, capitaltheory and policy analysis. Other issues considered includethe corn model, Sraffa's critique of Hayek, and the extensionof the capital theory critique to the intertemporal equilibriummodel.     

Continuous choice functions and the strong axiom of revealed preference

Summary In this note, it is shown that a result due to Uzawa showing that the weak axiom of revealed preference together with a regularity condition implies the strong axiom of revealed preference can be derived from the regularity conditionalone, if the choice function is continuous in prices and in income. The observation that the weak axiom of revealed preference is not needed suggests that this regularity condition is remarkably strong. The main result of the paper is quite general in the sense that the only additional assumption on the choice function is that the whole budget be spent.I thank Charles Blackorby for his comments on an earlier version.     

Trade prices and supply in the UK economy

Current account imbalances are a major source of instability in the world monetary and trading system. Measures to correct these imbalances have largely involved adjustments to exchange rates. In the international trade literature, when the current account is in deficit, the Marshall-Lerner condition is sufficient for a successful devaluation. However, this partial equilibrium condition — apart from being based on the assumption that supply elasticities are infinite — abstracts from how the domestic economy responds to the change in relative prices. In this paper we develop a model of price and output determination in an open economy with imperpectly competitive markets, and draw a distinction between goods which are exported and those which are supplied to the domestic market. This means that we have to determine jointly both export prices and the domestic price of house sales. We show that as long as there is no money illusion in the labour market a fall in the nominal exchange rate raises domestic and export prices proportionally and leaves trade volumes unaffected. However, shifts in domestic absorption relative to overseas demand — by changing relative prices — cause shifts in the relative supply of exports and domestically sold goods and affect the trade balance. Thus fiscal and monetary measures directed towards reducing domestic absorption are more likely to be successful in correcting current account imbalances than exchange rate depreciation.     

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。     

A dynamical,pure exchange economy with feedback pricing

This paper examines a decentralized, dynamical, pure exchange economy in which changes in an individual consumers demand depend on his own consumption and on prices. An ‘instantaneous Walras law’ provides a sufficient condition for the existence of viable exchange trajectories. Such dynamic demand systems might result from goalseeking behavior of the March-Simon type, or when satisfaction of well defined preferences is continually improved through incremental adjustments in consumption. In contrast to Walrasian tâtonnement or Sinale's price adjustment model, prices in the present study follow a feedback control law that responds only to current consumer states. Various generalizations are also presented.