Sraffa and Modern Economics, Volume I

Roberto Ciccone, Christian Gehrke, Gary Mongiovi

• Publisher: Routledge
• Year: 2013
• ISBN:
  9781136717222
• Edition: 1
• Topic: Business
• Subtopic: Business generale
• Index: Business

Analyzing Sraffa, one of the key figures in the history of economics, this book explores his legacy and the relevance of his thought for modern economics. Written by an array of internationally respected contributors, including Schefold, Aspromourgos, Nell and Kurz it is an invaluable tool for all those studying the history of economic thought.

Part I

Capital and the critique of neoclassical theories

Savings, investment and capital in a system of general intertemporal equilibrium

Pierangelo Garegnani^†

1.1 Introduction

1. The criticism of the neoclassical theory based on the inconsistency of the concept of a ‘quantity of capital’ has been met from the orthodox side essentially with the claim that contemporary reformulations of the theory do not rely on any such concept.¹ The present chapter is intended to show that the claim is unfounded and that the deficiencies of the concept undermine the reformulations no less than they do the traditional versions.²

In Section 1.2 we shall introduce for this purpose, the very simple model of intertemporal equilibrium which Hahn put forward in 1982 to counter what he took to be the ‘neo-Ricardian’ critique. This model will allow us to bring out the decisions to save and to invest of any ‘year’ which are implied in an intertemporal general equilibrium (GE).³ In Section 1.3 we shall then define what can be described as the ‘general-equilibrium saving-supply schedule’ and the ‘general-equilibrium investment-demand schedule’ for such a ‘year’. The detailed determination of those schedules — which may be left aside at a first reading — has been postponed to Appendix I and to the Mathematical Note attached to the chapter. Section 1.4 will examine the general information which the schedules provide about the behaviour of the system, while Section 1.5 will deal with the effects on investment demand of changes in techniques and in consumption outputs as intertemporal prices change.

The above will enable us to approach in the final section the question of how a ‘quantity of capital’ enters intertemporal equilibrium. That will involve pointing out first how misleading can the idea be that the adjustments in intertemporal consumptions (i.e. in decisions to save and invest) raise no more problems than adjustments in contemporary consumption do.⁴ Whereas the latter imply a shift of resources between the respective contemporary productions and can be activated directly by the disequilibrium prices, the analogous disequilibrium in intertemporal prices (own rates of interest), due, for example, to excess savings, can only adjust the respective intertemporal productions indirectly, through the intermediate link of an incentive given to entrepreneurs to change methods of production and/or relative consumption outputs, so as to increase the ‘amount of means of production’ relative to labour and other primary factors employed in the economy in that year. The corresponding additional investment is indeed what should, on the one hand, absorb in the production of the capital goods, the resources of time (t − 1) set free by the additional savings of t and, on the other, increase the productivity of primary factors in (t + 1), (t + 2), etc. to provide for the future increased consumption which the savers have planned. It will then be seen how the impossibility of measuring that ‘amount of means of production’ independently of distribution entails that no such ‘increase’ in means of production needs to follow from the competitive fall of the prices of commodities of early, relative to those of later dates (fall of the respective own rates of interest) caused by excess savings. The conclusion will thus be that treating under the same heading inter temporal and contemporary consumptions can obscure, but not do away with the differences between the two cases — the “quantity of capital” re-emerging essentially unchanged in its relevance, and in its deficiencies, for the determination of the equilibria. Indeed in proportion to their value, heterogeneous capital goods are for savers perfectly substitutable means of transferring purchasing power over time, so that savers’ decisions about capital goods will refer to that ‘quantity’,⁵ which will accordingly have to be implicitly or explicitly present in the system like that of any other good on which individuals exert their demand and supply decisions.

Appendix II completes the chapter by examining some flaws in the mathematical argument Professor Hahn has conducted in his 1982 article. Those flaws will allow bringing out some misunderstandings which appear to have seriously hindered communication between the two sides in the course of the capital controversies.

Our analysis of general equilibrium will be conducted by analytical instruments, other than excess demands generated by treating all prices as independent variables and used since Hicks (1939). As indicated, we shall use ‘general equilibrium demands and supplies’ of particular commodities or factors, assuming that all markets other than the specific ones on which we focus our attention are in equilibrium.⁶ An equilibrium in the particular market considered will then imply an equilibrium of the whole system. The advantage of these instruments is the possibility they offer to trace the effects of peculiarities of that market on the general equilibrium and its properties. Thus we shall here centre on those commodity markets which constitute the savings-investment market, and study the effects of the phenomenon of ‘reverse capital deepening’ which directly affects such markets. The reader is thus asked for some effort in entering a less familiar method of analysis, which however, we hope, may turn out to allow for some novel results and for a better economic grasp of key phenomena affecting a general intertemporal equilibrium. In particular, the reader should try to take these unfamiliar instruments on their logic, and resist the temptation to translate them too quickly into the language with which he is more familiar.

1.2 Decisions to save and invest in a system of intertemporal general equilibrium

2. To have a first, bird’s eye view of the ground we shall travel, it might be useful briefly to focus our attention back on the traditional versions of the theory. We need to consider the seeming contradiction between the varying physical capital underlying the demand function and that underlying the supply function for capital,⁷ the single ‘factor’ characterising those versions.⁸ For the sake of a definite example we may refer to Wicksell’s “Lectures” (1901) where a ‘quantity of capital’ demanded, expressed as a value in terms of consumption goods, is equalised to the economy’s endowment of it (loc. cit. vol. I, 204–205).

The seeming contradiction lies in the fact that, whereas in the demand schedule the physical capital which the quantity K demanded at each interest rate should express is that corresponding to the techniques and outputs most profitable at such a rate and changes with it, the physical capital making up the supply, or endowment of K is the stock in existence in the economy and will of course generally differ physically from t...