Topics in Classical Micro- and Macroeconomics

This chapter on the “transformation problem between labor values and prices of production”¹ shows that Lipietz’s analysis of the Marxist transformation procedure represents but a simple, though useful reinterpretation of obvious mathematical consequences of a standard Sraffa model – by making appropriate use of its known degrees of freedom. Labor values are not involved in this new interpretation of conventional prices of production. A proposal is therefore made how the role of labor values can be investigated further in such a framework, from the perspective of Marx’s “Capital” and on the basis of Lipietz’s theorem and its reinterpretation of the “value of labor power”. Our additions to Lipietz’ definitional procedures suggest that important labor value aggregates such as the average value rate of profit and the value rate of exploitation may be of use in analyzing the systematic consequences of changes in the sphere of capitalist production, while the effects of the actual price dynamics that drive these changes (not yet accounted for by total labor costs) may be unsystematic and may therefore represent distortions of secondary importance. The issues considered here will be further investigated in the next chapters where also Marx’s (1954, p. 48) view that labor values are measures of labor productivity, and thus also important in their own right, is explored from the perspective of Richard Stone’s System of National Accounts. From this perspective, labor values concern the accounting side of an economy, constructed from the observed dynamics of nominal magnitudes in order to understand in a conventional way or in a Marxian sense what is going on behind the surface of nominal magnitudes.

The dominant price theory from the perspective of models of general equilibrium is in terms of rigor the Arrow-Debreu General Equilibrium Theory (GET) of so-called (neoclassical) perfect competition. The most developed framework for national accounting is the System of National Accounts (SNA) of the United Nations in its current form. Both approaches towards a classification and analysis of microeconomic structures flourished in the 1960s and 1970s, but lost in importance thereafter, in the first case, due to the internal limitations of GET in the fulfillment of Smith’s conjecture on the working of market economies and, in the second case, due to a dilution of the current SNA as a rigorous and coherent approach to input–output structures within the System of National Accounts as it was originally formulated by Richard Stone and his research group. Moreover, the Arrow-Debreu world pays little attention to the need for a System of National Accounts (though there have been some attempts to combine these two approaches in the study of the “real” magnitudes usable to characterize market economies).¹ It is therefore basically a purely “nominal” approach,² despite the fact that it is in fact solely a theory of relative prices and thus faces the problem of the choice of a numéraire, which however is not supposed to reflect something truly “real”. It therefore seems to suggest that there is nothing “real” behind the “nominal”, not even as a theoretical construction that can help to understand the movement of “nominal” magnitudes. In addition to its pure “surface” orientation, GET pursues a theory of competition that does not reflect any competition at all, since all individuals and firms are isolated utility or profit maximizing price-takers without any interaction with each other.

In this chapter we provide theoretical and empirical examples for the usefulness of the Marxian Dual System Approach (MDSA) to the LTV, here from a very pragmatic perspective, namely concerning their role to serve (in reciprocal form) as measures of labor productivity which allow to discuss the sectoral implications of technological change as we observe it happening now in more and more rapid terms. Already Marx supplied such an interpretation of his measure of labor values, see for example Marx’s (1954, p. 48), where he discusses the reciprocal relationship between labor values (total labor costs) and the measurement of labor productivity in the production of commodities by means of commodities and labor. Moreover, there are theoretical links between cost-reducing (profitable) technical changes and decreases in the labor content of commodities that assume various forms, depending on the type of technical change that is occurring. We show in the next section of the chapter that conventional measures of labor productivity, see United Nations (1993), can be very misleading in grasping what is going on in the production side of the economy.¹ Compared to these measures the Marxian view to use labor values for this purpose in reciprocal form is shown to be well-defined and superior. This indicates again that the strength of the labor theory of value lies in its use as a system of national accounts and not as a means to understand price formation in a capitalist economy (though total labor costs are clearly an important – if not the central – component in prices as measured by Keynes (1936) wage-units. In addition we will consider in Sect. 3.3 theorems that reveal the consequences of cost-reducing technical change for labor values as well as their interpretation as indexes of labor productivity. These propositions provide theoretical explanations for the law of decreasing labor content, in addition to what has been shown by Farjoun and Machover (1983) from a probabilistic point of view. In this section we also provide some empirical applications of these propositions and show that this law has much wider applicability then is suggested on the purely theoretical level.

In contrast to counterfactual linear programming definitions of labor values this chapter introduces an at least equivalent definition of such values for the general case of joint production which is exclusively based on actual data. This task is accomplished by extending Marx’s concept of “individual values” from multiple activities to joint production by means of certain price ratios at those points where production data are insufficient to ensure the positiveness of “embodied labor time”. Our approach generalizes the simple formula that relates labor values to monetary input–output tables, and it reformulates the labor theory of value in such a way that the “theoretical priority” of the case of a uniform composition of capital is reaffirmed. In the concluding pages of his book, Marx’s Economics, it is suggested by Morishima that Marxian economists “ought radically to change their attitude towards the labor theory of value” since in general the value system of the methods of production actually adopted in a capitalistic economy “may be determined to be negative, indefinite or even contradictory to the postulate of the uniform rate of exploitation” (Morishima 1973, p. 193). He then continues by proposing that “optimal labor values”, the shadow prices of certain linear programming problems which minimize the amount of labor needed to produce given bundles of net output, should take the place of “actual labor values” when production models of a more general kind than the simple Leontief model are to be considered, an interpretation of labor values which has been worked out in detail in Morishima (1974) and has become a widely accepted approach to labor values and the labor theory of value for all types of multiple production systems.

There have been numerous attempts to measure total employment effects and productivity indexes since the early work of Leontief (1944). These measurements have been based on the Leontief inverse (I − A) ^{− 1} of recorded input–output tables. Examples of this are Bezdek’s (1973) manpower analysis and the employment multiplier study of Diamond (1975). However, not much attention has been paid in these investigations to the derivation of the coefficients of the input–output matrix A, although at least two fundamentally different procedures exist in this respect. This may be due to the fact that the two procedures lead to different input–output tables only when subsidiary production is present in the classification of industries and commodity groups. The objective of this chapter is to show that these two input–output accounting schemes, recommended by the United Nations (1968) in the case of insufficient information about subsidiary production, generate two different measures of total factor requirements (Sect. 6.2). In the Sect. 6.3 attention is focused on the case of pure joint production. Sraffa’s interpretation of joint production and employment multipliers is summarized and a new concept of average labor content, or in reciprocal form: of labor productivity, is introduced and compared. It is shown in Sect. 6.4 then, that the UN method for calculating total labor requirements per dollar of output value from input–output tables leads either to Sraffa’s or to the new interpretation of physical total input requirements, depending on how the A matrix is derived. Subsequent sections examine additional properties of these employment multiplier calculations and productivity concepts.

Since Stone’s original work, input output methodology has taken a great step forward in standardizing the procedures employed for the derivation of monetary input output tables which in turn, e.g., are used to measure the energy requirements of commodities. In this methodology there exist two basic (mechanical) ways, or “technology” assumptions, by which such measures under circumstances of joint production can be defined. The physical effects of these assumptions on the measures obtained, however, have not yet been analyzed sufficiently. This chapter presents such an analysis on the basis of technological conditions of a quite general kind, including joint production, and shows that even then these two measures of energy requirements will give rise to economically well-grounded expressions, i.e., do not represent measurement without theory. The expressions obtained will allow us to prove several assertions within their respective ranges of applicability, which complement each other to some extent.

In this chapter we go from the sphere of the production of commodities to the sphere of their circulation, by means of the theoretical as well as the empirical investigation of the Classical concept of prices of production which is based on the principle that there is a single uniform rate of profit for all activities that are organized on a profit-oriented basis. We start the Classical theory of price formation at first in its most basic setup, and then with increasing generality, in order to show how long-period prices of production may be formulated in more and more general models of production. We also provide a brief survey on the mathematical tools that are needed for the proof of basic Classical assertions on the properties of such long-period accounting prices which shows that indeed quite sophisticated mathematical theorems are needed for this purpose, for proving things that the Classical authors (including Marx) simply took for granted. Our findings will be that the search for the foundations of a Classical theory of competition has by no means been a successful one so far. On the theoretical level, we find that the analysis of the process of the circulation of capital has by and large ignored the many factual accounting principles that are involved in and indeed are governing this process and that are needed for proper production price calculations in general production systems. And on the empirical side, we come to the conclusion that the principle of imposing a single uniform rate of profit on all profit-oriented activities of the (world) economy is simply going too far in the pursuit of finding useful and applicable long-period prices for the factual analysis of existing economies. Sectoral profitability studies are urgently needed for the proper formulation of long-period prices but are rarely done by the proponents of the Classical theory of prices of production.

The concept of a basic commodity as introduced in Sraffa’s (1960) well-known book: ‘The Production of Commodities by Means of Commodities’ has often been treated and reformulated in the literature under the presupposition of a square single-product system. Its various formulations in terms of direct and indirect – or solely in terms of direct – relationships between the production accounts of the commodities produced can be easily understood from a mathematical as well as from an economic point of view. This situation, however, changes drastically once joint products are taken into account. In this general case the various definitions at hand not only lose their equivalence, but are – following a proposal made by Sraffa (1960, 60) and formalized by Manara (1980) – in fact replaced by a new and much more complicated definition, which, in addition, does not give a complete generalization of the original concept of basic commodities (as we shall see in Sect. 9.4). The proposed new formulation of basic commodities for joint production systems is based on linear combinations of the direct relationships which describe the production of commodities by means of commodities for this case, and Sraffa (1960, 57) explicitly states that ‘the criterion previously adopted…(in terms of direct and indirect relationships, P.F.) now fails, …’. It is the aim of the present chapter to demonstrate that this view need not be conclusive. In fact, we shall see in Sect. 9.2 that our four equivalent ways of generalizing the single product approach to the case of joint production (among them one which generalizes this approach in a very natural way), give rise to a concept of ‘basics’ which differs from the Sraffian one. Section 9.3 presents several properties of this alternative notion of basics and it also provides a motivation for their denomination: Leontief-basics, to be suggested in this chapter. In Sect. 9.4 we shall then briefly consider their known alternative, the Sraffa-basics, by utilizing two simplifications of their original definition which have been provided by Steedman (1980) and Pasinetti (1980). This section also completes their up to now incomplete characterization if the set of singular output matrices is excluded from consideration.

Regarding these views we shall show in the following that this assertion is a completely misleading one. The Standard Commodity and the therewith derived linear wage-profit curve \(\tilde{w}(r)\) do not simplify the theory of income distribution, but in fact make it more obscure, i.e., either incomplete ore more complex, as compared to its presentation by means of a conventional nonlinear w(r)-curve, e.g., based on a numéraire which keeps national income fixed when changes in the distributional variables w and r are considered. Furthermore, our way of demonstrating this claim will to some extent indicate that Sraffa’s composite commodity may be of dubious economic significance quite generally, i.e., will not serve as an appropriate ‘measure of value’, also cf. Burmeister (1968, p. 86–87) for an early remark on this and Flaschel (1980). The present chapter thus should be conceived as a first argument towards the conclusion that an analysis based on Sraffa’s Production of Commodities by Means of Commodities should dispense with his hypothetical composite commodity, the ‘Standard Commodity’.

The construction of Sraffa’s Standard Commodity is often motivated by the claim that it allows to isolate the price-movements of any other commodity, so that they may be observed as in a vacuum. This chapter shows that (a) A specific and complete solution to the problem of finding the conditions for such a Standard is indeed available, yet that (b) Sraffa’s Standard does not fulfill this list of conditions. The source of Sraffa’s error is then isolated and the true set of ‘invariable measures’ is determined and shown to be devoid of economic content.

This chapter shows that there is a natural extension of the conventional price tâtonnement procedure of pure exchange economies which significantly increases the stability properties of such adjustment processes from a local as well as a global point of view. This extension is motivated by the observation that market price adjustments should not only depend on the levels of excess demand, but also on their direction (and magnitude) of change. Taking these additional forces appropriately into account implies an adjustment process which is formally similar to the Generalized Newton Methods which have been construed in the search for price mechanisms that are ‘universally stable’. Furthermore, this adjustment process also generalizes the stability proof for the ordinary tâtonnement procedure in the case of gross substitutes (by means of a suitable Liapunov function) in a straightforward way.

Since the early investigations of Arrow et al. in the late fifties and early sixties with their optimistic views on the stability properties of general equilibrium systems, there have been numerous contributions which have favored the opposite view – due to the counterexamples found shortly afterwards and due to the theorems of ‘Debreu-Sonnenschein’ type which have been formulated in the sequel. A typical statement in this regard is that of Frank Hahn (1970, p. 2): ‘What has been achieved is a collection of sufficient conditions, one might almost say, anecdotes, and a demonstration by Scarf and later by Gale, that not much more could be hoped for.¹, ² Similar statements can be found in a variety of publications on the stability issue, cf. for example Dierker (1974, p. 115) and in particular the recent survey article of Kirman (1989)³. This latter article also discusses one important possible route of escape from (non-uniqueness and) instability in the context of general equilibrium models, i.e., the approach by Hildenbrand and others who introduce further restrictions on the distribution of the characteristics of economic agents in order to avoid the above problems.

In recent neoclassically and classically oriented literature on competitive processes several models have been presented which work not only with the ‘law of demand’ but also with the ‘law of profitability’. In such dynamical models a cross-dual process is stylized in which price changes are initiated by imbalances in supply and demand and changes of outputs are caused by profitability differentials. Such cross-dual dynamics can now be found in neoclassical tradition (Morishima 1976, 1977; Mas–Colell 1974, 1986) and in classical tradition. In classical tradition the analysis of such a cross-dual adjustment process was initiated particularly by some recent publications of Nikaido (1978, 1983, 1985) who questioned the stability of classical competition. In comparison to his results it is the purpose of this article to show that the classical approach to the dynamics of competition may be able to produce stability results which are of at least comparable interest to those of neoclassical stability theory.

This chapter attempts an integration of Keynesian dual and Classical cross-dual micro-dynamic adjustment processes in the framework of a standard Leontief model. It investigates why strategies which are capable of proving stability for each separate case cannot in general successfully be applied to the composite system, where both prices and quantities are each revised on the basis of two instead of only one principle, namely supply/demand – as well as price/cost – discrepancies. It will be shown that significant limits to the adjustment speeds in the Classical domain have to be postulated in order to prove stability for the composite dynamics by means of the standard tools of the Walrasian tâtonnement literature. In view of these results an alternative approach to the stability of such composite systems is then introduced and applied to this system. This approach takes explicitly into account the type of composition of our dynamic system, i.e., its set of negative feedback mechanisms and the various interactions that may in addition exist between such substructures, which makes this approach of great methodological interest.

Our central findings are that there exist three different ways which allow to prove stability for our composite Keynesian/Classical structure (diagonal dominance, quasi-negative definiteness and the above new approach with a two-level type of stability analysis). In each of these approaches, however, we have to assume relatively narrow limits for the strength of the Classical component to obtain a stable composite dynamics. In contrast, no such narrow restrictions can be detected when the eigenvalues of numerical examples are calculated for a wide range of adjustment coefficients, even though counterexamples to stability do indeed exist then as well in other cases (see the mathematical appendix, subsection 1).

The exact limits for the stability of our composite system therefore remain an open question in the present chapter. Their determination may, however, be subordinate to another problem, which is the need for a more developed analysis of Classical dynamics itself before the stability properties of its integration with Keynesian types of adjustments processes are discussed in more depth.

This chapter generalizes Goodwin’s (1972) growth cycle model as reconsidered in :̧def :̧def Velupillai (1979) and it also extends the proofs of some assertions made by the latter author. This extended version which we shall introduce in Sect. 17.2 depends on a money-illusion parameter η in such a way that the Goodwin case becomes a bifurcation point between those parameter values (η > 0) where the extended model is globally asymptotically stable and those where it is totally unstable (η < 0). A by-product of this result is that Goodwin’s dynamical system obviously cannot be structurally stable. This method of demonstration replaces Velupillai’s formal proof by economic reasoning. Section 17.3 then shows why Velupillai’s demonstration of the closed-orbit structure of Goodwin’s model is not yet complete and it briefly indicates how to fill the existing gaps. Since this chapter is supplementary to :̧def :̧def Velupillai’s (1979) article, the reader should consult his paper for further explanations of the model and the symbols used.

This chapter provides an analysis of the effects on Goodwin’s (1967) process of the cyclical accumulation of capital which follow from employing a money wage Phillips-Curve that depends both on the rate of employment and on the rate of growth of the considered economy. This latter influence enters the scenario when the objective of the wage bargaining process is formulated in more detail. Our simple approach here is to assume that this objective is determined by the rate of inflation plus the rate of labor productivity growth and to assume additionally that more will be demanded in periods of very rapid growth, while the opposite occurs in times of subnormal growth. The target of workers’ wage claim will therefore be treated as endogenous, i.e., depending on the particular phase of the growth cycle to be analyzed below. Our above assumption represents one main modification to be incorporated into Goodwin’s well-known growth cycle model, whose real wage Phillips-curve is thereby reformulated in a twofold way (besides assuming that the rate of change of money wages depends on employment and the benchmark of a constant share of wages in an endogenous manner). We now have to formulate a hypothesis concerning the price-level, too. For the sake of simplicity we shall adopt a post-Keynesian mark-up equation here, but shall neglect – as in the original Goodwin model – all influences of effective demand. This is not to say that we regard these latter influences as purely secondary, but in the present chapter we prefer to concentrate on the interaction of wage-bargaining, mark-up induced inflation, accumulation, and employment without offering an explanation of the limits for the chosen mark-up. Focusing on the conflict over income-distribution and its effects on capital accumulation is – at least in our opinion – of some theoretical interest, since this conflict is, e.g., largely neglected in the monetarist approach to the phenomenon of stagflation, where a monotonic relationship between inflation and (un)employment is generally postulated. As we shall see in the following sections this monetarist viewpoint seems to be overly simplified.

Goodwin’s (1967) model of a growth cycle has since long been regarded as a model of class struggle and the conflict over income distribution which mirrors basic aspects of Marx’s “General Law of Capitalist Accumulation” in Volume I of “Das Kapital”. When rereading this chapter (Marx 1954, Chap. 25) with Goodwin’s model and its various extensions in mind, one indeed finds many observations of Marx – in particular in its Sect. 19.1 – which are strikingly similar to the assumptions and conclusions which this growth cycle model exhibits. However, Marx also very often stresses aspects of the behavior of “capital” which are not covered by this approach to cyclical growth (where profits are more or less mechanically invested by “capitalists”). These aspects typically concern the strategic possibilities of capitalists when faced with the profit squeeze mechanism due to a low number of unemployed workers in the reserve army. Such strategic considerations have, by and large, not found inclusion in the formal discussion of the Goodwin growth cycle. There exist attempts of Balducci et al. (1984), Ricci (1985) and in particular Mehrling (1986) where the theory of differential games is applied to this type of growth cycle model, but this seems to represent all efforts made to incorporate game-theoretic aspects into this conflict over income distribution. In this respect K. Lancaster’s (1973) related model on the dynamic inefficiency of capitalism has received much more attention in recent years, cf. Haurie and Pohjola (1987) for a typical article on this subject.

In this chapter, we confront a simple extension of the Goodwin growth cycle model and its numerical investigation with corresponding phase plots of data on the wage share, the employment rate, the inflation rate, the profit rate and the output–capital ratio for eight OECD countries. Our modification of this growth cycle model gives rise to a locally unstable growth pattern which is turned into overall stability by an appropriate boundary behavior of investment and the inflation rate. The main finding of the chapter is that for some countries there are some similarities between the plots generated by the model and the data. This suggests that its long swing implications should be investigated further. Whenever it comes to a consideration of the work of Richard Goodwin there is one particular paper which is most often given special attention: his 1967 growth cycle treatment of the “inherent conflict and complementarity of workers and capitalists”. A recent example for this observation is Solow’s (1990) contribution to a collection of essays in honor of R. Goodwin where he not only provides a characterization of the merits and weaknesses of this prototype model, but also briefly discusses whether this employment-cycle model of the conflict over income distribution “fits the facts” (and what such a question may mean here).

In this chapter, we reconsider the simple empirical evidence for the existence of a long-phased cycle in the state variables employment rate e and wage share v that we have collected in Flaschel and Groh (1995) for a number of industrialized market economies, see the preceding chapter. We do this on the basis of 15 years of further observations and now also with quite modern econometric techniques. Our findings will be that – in the case of the US economy – the only three-fourths closed long phase loops we observed in this earlier paper can now be confirmed as by and large closed, giving in sum an approximately 50 years long cycle in employment rates and the wage share in its interaction with the six to seven business cycles observed in the US economy between 1960 and 2006. As basic theoretical explanation for the occurrence of such long-phased cycles the reference to the seminal papers by Richard Goodwin (1967), augmented by Rose (1967) type limit cycle considerations, and the many papers that are based on this work suggests itself. By and large this means that we consider a growth cycle model where the steady state of the model is repelling and where there are forces far off this steady state which imply constant or falling employment rates at the full employment ceiling e = 1 and falling wage shares in situations where income distribution squeezes profitability to a significant degree. We have supplied in Flaschel and Groh (1995) a model example for such a situation and will recapitulate in this chapter only the absolutely necessary ingredients that make a Goodwin–Rose growth cycle dynamics repelling at their interior steady state and bounded within the phase space [0, 1]². The implication of such a scenario will be a clockwise motion of the state variables (v, e) in the phase space [0, 1]² as it has been observed for a number of countries in Flaschel and Groh (1995).

In this chapter, we introduce a general model of monetary growth which contains several existing models as special cases. The model is complete in the sense that it allows for a full interaction among the three major markets (goods, labor and assets), and consistent in that the budget constraints for households, firms and the government are all respected. This gives rise to a four-dimensional differential equation system. The stability properties of some special lower dimensional cases of the model are characterized analytically, and the unrestricted model is then briefly examined numerically. Stein (1982, p. 191) defines a “Keynes–Wicksell model of money and capacity growth” as “one where there are independent savings and investment functions, but output is always at capacity”. The dynamic properties of general models of the Keynes–Wicksell type, consisting of fully interacting money, goods and labor markets, have not been systematically explored in the literature to date. Such models are of a very neoclassical nature with respect to their building blocks. Yet, despite their supply side orientation, our analysis reveals that a monotonic adjustment of real wages to the long-run full employment level cannot be expected to occur once the complexity of the various feedbacks and interactions between the major markets in a capitalist economy are adequately taken into account. This is the main finding of the chapter.