Petri 2001 Burgstalerclasicoyneoclas

Metroeconomica 52:2 (2001)

162±180

BURGSTALLER ON THE COMMON CORE OF CLASSICAL AND WALRASIAN ECONOMICS Fabio Petri Universita di Siena

1.

Burgstaller's Property and Prices 1 is a collection of exercises in the determination of full-utilization, in®nite-horizon, perfect foresight competitive paths of a series of economies differing in the kinds of resources and of technologies. On the basis of his exercises he advances two main claims. The ®rst is that value theory has underestimated the importance of portfolio equilibrium, i.e. of the no-arbitrage condition that, where titles of property to stocks of income-producing resources can be traded, these property titles (or `equities') will tend to have such values as will yield a uniform expected rate of return. One little-noticed consequence, he claims, of admitting arbitrageurs and speculators who perform the above task is that equilibrium is reached without any need for the Walrasian auctioneer in economies where all outputs are durable (or `basic' in Burgstaller's sense); another is that Walras was mistaken in the way he interpreted his own equations of capital formation. The second claim is that, since `classical and neoclassical value theory both operate through arbitrage and speculation in ®nancial markets' (p. 1), he has found, in the quasi-Hamiltonian system of equations describing the perfect foresight competitive equilibrium paths over in®nite  I thank H. D. Kurz and M. De Francesco for critical comments. I acknowledge ®nancial support by MURST (ex 40%). 1 I apologize if some arguments in what follows will be obscure to readers unacquainted with this book, but space limitations made it impossible to render this note self-contained. In the present note, when no other indication is given, the page number refers to Burgstaller's book.

# Blackwell Publishers Ltd 2001

Burgstaller on Classical and Walrasian Economics

163

time, `the common theoretical core of classical and Walrasian economics' (p. 10). In what follows attention will be mainly focused on the second claim, with only brief remarks on some aspects of the ®rst claim. I shall argue that the models which Burgstaller appears to consider representative of classical economics do not correctly re¯ect the way classical economists viewed the working of market economies, and betray the uncritical acceptance of neo-Walrasian theoretical choices, not only alien to the classical approach but also highly criticizable. Brie¯y, the picture of classical value theory which emerges from Burgstaller's book is indistinguishable from neo-Walrasian theory except for one difference: in classical analyses the real wage is given. Further differences, concerning for example what are presented as the classical preferred assumptions as to substitutability in technology or in consumption, are viewed in the end as minor, since they do not disturb the prediction, common (according to Burgstaller) to both classical and neoclassical theories, that market economies evolve along a full-utilization path which tends to a steady state; the main difference in the economy's evolution over time, stemming from the different assumption as to real wages, is that in neoclassical models labour is fully employed and the real wage is determined endogenously, while in classical models it is labour employment which is determined endogenously. This picture of classical theory misses nearly all the true differences between the classical and the neo-Walrasian approaches to value and distribution: the differences at the level of method (the abandonment in neo-Walrasian economics of the traditional method of long-period positions); and the differences as to the forces determining distribution and outputs (the absence in the classical authors of the neoclassical factor substitution mechanisms, an absence which explains the different treatment of distribution, and also makes the classical approach open on the issue of the validity of Say's law, thus making it compatible withÐ indeed, upon re¯ection, in need ofÐthe Keynesian principle of effective demand). Without clarity as to these differences, the one difference Burgstaller does grasp, the given real wage in the classical approach2 , is insuf®cient 2 Still, Burgstaller, when examining `classical' models, takes the real wage as ®xed all along the growth path leading to the steady state; in Marshallian terminology, he takes the real wage as ®xed even when determining the secular tendencies of the economy; classical authors would here disagree with himÐthey did not deny changes of the real wage in the course of accumulation.

# Blackwell Publishers Ltd 2001

164

Fabio Petri

to distinguish the classical approach from a neoclassical one where the real wage is ®xed (e.g. by trade unions) above the full-employment level. Readers therefore may be misled by Burgstaller's book into thinking that a resumption of the classical approach to value and distribution would make very little difference to received theory, while the opposite is the case. 2.

Let us start from the differences at the level of method. The classicals distinguished market prices and natural prices. The former (the day-byday observed prices) are in¯uenced, they believed, by accidental and transitory causes which make their determination generally impossible and also generally uninteresting. It is only the results of the persistent forces acting on relative prices which, they esteemed, economic theory can try to determine. These persistent forces, it was argued, push the market prices of products to gravitate, in competitive conditions, toward the relative prices yielding a uniform rate of return on the supply price of capital goods. Fundamentally the same conception also characterizes the analyses of traditional marginalist authors such as Jevons, Wicksell, J. B. Clark, Marshall, Walras (in the ®rst three editions of his EleÂments), D. H. Robertson etc. The object of value theory at the economy-wide level was therefore, for both groups of authors, the determination of long-period relative prices. The de®ning element of natural or long-period prices is that they satisfy the condition of a uniform rate of return on supply price (URRSP). This is not simply the no-arbitrage conditionÐwhich is also satis®ed in neo-Walrasian equilibriaÐof an equal convenience of investment in the purchase of any income-yielding asset; it additionally requires that, for all producible assets, their value should equal their cost of production. This condition is a necessary ingredient of the attempt to determine the prices which market prices may be gravitating toward in real time (i.e. through time-consuming processes), because only when the URRSP condition is satis®ed can the forces (the reallocations of investment), which tend quickly to alter the relative amounts of capital goods in existence and hence relative prices, be assumed to be at rest. Now, this condition requires an endogenous determination of the relative endowments of capital goods. Thus it is not surprising that Arrow± Debreu equilibria, or more generally neo-Walrasian equilibria, where, owing to the given initial endowments of the several capital goods, in # Blackwell Publishers Ltd 2001

Burgstaller on Classical and Walrasian Economics

165

the initial period(s) the URRSP condition is not satis®ed except by a ¯uke (because the capitalized values of some capital goods may easily be less than their costs of production, entailing a zero production of those kinds of capital goods)Ðit is not surprising that these equilibria cannot be interpreted as centres of gravitation of actual, time-consuming adjustment processes. (The processes which might be envisaged to bring about the neo-Walrasian equilibrium corresponding to a given vector of capital goods endowments must be assumed to be instantaneous, a reason for frequent complaints.) Nowadays it is often forgotten that in this respect these equilibria represent a break not only with the classical approach but also with earlier neoclassical analyses, which had attempted to determine long-period equilibria, i.e. equilibria embodying the URRSP condition, and accordingly had treated (with the exception only of Walras who was simply contradictory) the relative endowments of the several capital goods as variables which the equilibrium had to determine endogenously (which is the reason why the notion of `capital' as a single factor, an amount of value, given in total endowment but capable of changing `form', was indispensable to these authors; cf. Garegnani (1990a), Petri (1999)). Now, the prices Burgstaller determines are neo-Walrasian equilibrium prices, in the precise sense that they equate supply and demand on all markets (except on the labour market when the real wage is given) on the basis of data which, when there is more than one capital good, include given endowments of each type of capital goods. Accordingly, he correctly calls temporary equilibria the equilibria he determines. This obviously raises the problem of the right to consider Burgstaller's analyses of the `classical' economies he calls VON NEUMANN I, II and III, MARX±SRAFFA, or RICARDO, as not unfaithful to these authors, who never attempted the determination of temporary-equilibrium prices. This problem is nowhere discussed by Burgstaller. What makes it possible to leave it undiscussed? Two perplexing aspects of his book. First, Burgstaller never mentions (is unaware of?) the role of classical natural prices as centres of gravitation of prices in economies all the time in disequilibrium. Actually, Burgstaller appears to be more neoWalrasian than most neo-Walrasian theorists, because he appears to have no qualms with the assumption of continuous equilibrium, i.e. of instantaneous equilibration. He appears to feel no need to confront himself with the problems raised by Hicks's admission that `the adjustments needed to bring about equilibrium take time' (Hicks (1946, p. 116)). He never admits the possibility of time-consuming disequilibria, and writes that `the market economy represents a saddle-path quasi-Hamiltonian # Blackwell Publishers Ltd 2001

166

Fabio Petri

system' (p. 41), as if the equilibrium paths determined by his analyses could be assumed perfectly to coincide with the actual path a market economy follows 3 . This is surprising because, although he has some arguments to the effect that, for economies where all products are `basic' in his sense (i.e. durable, not perishable), arbitrageurs make the Walrasian auctioneer unnecessary (these arguments will be discussed later), he does not deny that the Walrasian auctioneer remains necessary in order to avoid `false-price' transactions when there are markets for perishable goods. So, it would seem, on his own grounds he cannot avoid the criticism, repeatedly advanced in recent years against the neo-Walrasian versions of general equilibrium theory, that, since in real economies there are disequilibrium transactions and productions, sequences of neo-Walrasian equilibria cannot claim to describe the paths of real economies (Fisher (1983), Garegnani (1990a), Petri (1999)). But he never mentions this criticism. Second, in all his exercises Burgstaller avoids the kinds of technology which might have obliged him to admit the possibility that a URRSP condition might not be satis®ed in a temporary equilibrium, and thus he can avoid distinguishing between the no-arbitrage condition (satis®ed in Arrow±Debreu equilibria) of a uniform rate of return on the value of equities and the different, long-period URRSP condition. Let us take for example the VON NEUMANN I economy, a surprising case where the URRSP condition is satis®ed from the initial instant (prices are longperiod prices, and constant through time), in spite of the given initial relative stocks of the two inputs corn and steel. This result is due to the peculiar technology assumed: there are only two products which are also inputs, corn and steel; the production of steel requires only corn, and the production of corn requires only steel, with ®xed coef®cients. These assumptions ensure that the possibility of full utilization of both stocks is guaranteed in spite of the ®xed technical coef®cients4 . Had Burgstaller 3 Also cf. p. 5: `I will argue that any economy that (a) possesses a well-de®ned system of private property and (b) is competitive, must be governed by two fundamental laws of motion', these laws being then indicated in the quasi-Hamiltonian system which traces out the perfect foresight full-utilization competitive path. 4 The reason why prices are long-period prices from the very beginning is that production is assumed to be instantaneous and the two goods, when utilized as inputs, are assumed to be durable capital goods which evaporate radioactively, so that a unit of for example steel surviving from the past is a perfect substitute for a newly produced unit of steel. Then the prices of corn and of steel as inputs and as outputs must be identical, and no need arises to determine product prices through a ¯ow equality condition between supply and demand for newly produced corn and steel: any difference between ¯ow supply and ¯ow demand will be

# Blackwell Publishers Ltd 2001

Burgstaller on Classical and Walrasian Economics

167

assumed that both industries used both inputs, then with ®xed technical coef®cients (or limited substitutability) there would have been only a limited range of proportions of the given stocks of corn and steel compatible with the full employment of both stocks; outside that range of proportions, one stock would be necessarily not fully employed, hence earning a zero rental; the value (given by capitalization of future rentals) of an already existing unit of that good might still be positive, if a positive rental were expected in the future, but it would be anyway inferior to the cost of production, inducing a zero production of that good: the URRSP condition would not be satis®ed (although the noarbitrage condition would be). Another aspect of Burgstaller's analyses betrays the neo-Walrasian nature of his conception of equilibrium and con¯icts with classical value theory: the role of expectations. The neo-Walrasian notions of equilibrium must admit the possibility of quick changes of relative equilibrium prices over time, because of the arbitrary initial relative endowments of capital goods, which may be quickly altered in subsequent periods. This explains the need, in neo-Walrasian equilibria, to admit a possible relevant in¯uence of changes over time in relative prices on the initialperiod decisions. Thence the need to assume complete futures markets existing already in the initial period, or perfect foresight, or exogenously given expectation functions. Burgstaller assumes perfect foresight over the in®nite future. He offers no justi®cation for this assumption, except for the observation that the assumption of myopically stationary price expectations generally produces the same qualitative dynamic behaviour as perfect foresight5 . But stationary price expectations are just as made up by stock accumulations or decumulations; technology is also such (an extreme form of the Uzawa conditions) as to ensure that the continuous full employment of the stocks will guarantee convergence to the steady state; there is then no reason why relative prices should change through time, if they are from the beginning at the level which, if constant, guarantees a URRSP; and indeed any other initial relative price, in order to guarantee the URRSP condition, would require a change of relative prices over time, which, for reasons well known from the Hahn problem, would bring one price to zero in ®nite time, making the URRSP condition impossible to maintain any further. 5 Actually, Burgstaller also writes: `dropping the perfect-foresight (or rational-expectations) postulate means condoning the not less implausible idea that speculators make systematic mistakes from which they never learn' (p. 34, fn. 34). Thus Burgstaller appears to think that being unable instantly to guess the future equilibrium values of disaggregate general equilibrium variables after a parameter shift is synonymous with making systematic mistakes from which one never learns. Is it? The research on the plausibility of the hypothesis of rational, i.e. correct, expectations has con®rmed the traditional persuasion that time is necessary in order to reach them, so that `Rational expectations are, if anything, a long run rather than a short run phenomenon' (Bray (1982, p. 330)).

# Blackwell Publishers Ltd 2001

168

Fabio Petri

arbitrary an assumption as perfect foresight, in a world where there is no reason to have stationary expectations. Traditionally, expectations had no explicit role in value theory because the prices which the theory attempted to determine were long-period prices, i.e. prices which had no reason to change (quickly), because the composition of capital had adapted to the composition of demand. Thus price expectations in a long-period position were generally implicitly assumed to be both stationary and correct (or suf®ciently close to being so) because the situation determined by the theory was one of constant, or nearly constant, relative prices. Burgstaller unfortunately misunderstands this aspect of classical analyses (an aspect which, I insist, classical analyses shared with traditional marginalist analyses) as meaning that `the classical models preferred by Cambridge-UK theorists' are `con®ned to steady states' (p. 13). This is totally wrong: the neglect of the changes of relative prices over time in traditional analyses was not due to an assumption that there were no such changes, but only to the very reasonable thesis that, once the composition of capital had had time to adapt to the composition of demand, endogenous changes in relative prices would be so slow as to be negligible, even though the economy was not in a steady state (cf. Petri (1999, pp. 27±9)). With this misunderstanding out of the way, one can see that neoWalrasian analyses can only determine the behaviour of economies continuously in equilibrium, a very unrealistic assumption; on the contrary traditional (classical as well as old marginalist) analyses had no problem in admitting disequilibrium actions and time-consuming adjustments; they could nonetheless formulate explanations and predictions by arguing that market magnitudes gravitate toward normal long-period values. Of the two types of analyses, it is therefore rather to the neoWalrasian ones that the accusation applies, which Burgstaller levels at the classical approach, of being `non-causal . . . incapable of providing what a philosopher or a scientist would call an explanationÐa temporal cause-and-effect account anchored in arbitrary initial conditions' (pp. 10±11)6 . But Burgstaller appears unacquainted with the traditional method of connecting theory and reality; he appears to think that the

6

Cf. Petri (1999), where Burgstaller's claim (taken from Hahn (1982)) is also refuted that `the Arrow±Debreu framework is formally consistent with andÐnot being con®ned to steady statesÐmore general than the classical models preferred by Cambridge-UK theorists' (p. 13).

# Blackwell Publishers Ltd 2001

Burgstaller on Classical and Walrasian Economics

169

only way one can explain the behaviour of economies is by determining every detail of their motions7 , for which purpose he appears to see no alternative to continuous-equilibrium paths. Here we ®nd perhaps some effects of the modern education in economic theory, which in most universities for some decades now has been introducing students exclusively to neo-Walrasian notions of equilibrium, and thus tends to make economists uncritically accept the assumption of instantaneous equilibration, and to maintain them in ignorance of the traditional method of explanation. A return to the fruitful traditional method appears to be the way to overcome the frequently recognized sterility of the assumption of continuous equilibrium. But such a return to a focus of value theory on long-period magnitudes entails that the endowments of the several capital goods must be treated as endogenously determined. Thus a theory is needed of normal outputs, and of distribution, capable of deriving, from the quantities to be produced and the cost-minimizing technical choices, the demands for capital goods to which the endowments will tend to adjust. This theory cannot be provided by a return to the older neoclassical authors, because they needed the indefensible conception of capital as a single factor in order to render their long-period equilibria determinate; and it cannot be provided by neo-Walrasian theory because the latter needs given capital endowments: the entire neoclassical approach must be abandoned (Petri (1991)). Even only the difference at the level of method between the classical and the neo-Walrasian approach has enormous implications for economic theory, which one would not in the least suspect from Burgstaller's book. Thus, had Burgstaller recognized even only the difference at the level of method between the classical and the neo-Walrasian approaches, he would have had to admit that he could not call `classical' a model where outputs are determined by the full employment of given vectors of endowments of capital goods; he would have had to ask, how did the classicals determine normal outputs?

7 It may be worth recalling that Alfred Marshall likened the equilibrium scale of production of a good to the position to which a stone, hanging by a string `in the troubled waters of a mill-race', tends continually to return (Marshall (1972 (1920), V, iii, 6, p. 288)). Does Burgstaller think that a natural scientist would aim at providing a full and perfectly correct description of the dynamics of the stone?

# Blackwell Publishers Ltd 2001

170

Fabio Petri

3.

With the last question we come to the connection between approach to distribution and approach to outputs and employment. A study of the theories of outputs of classical authors shows the existence of strong disagreements among them on the issue of the general level of employment and outputs. The reasons for these disagreements are better highlighted if one starts from a contrast between the classical and the neoclassical approaches to distribution. Burgstaller correctly takes the real wage as given when analysing `classical' models. But he does not discuss (1) why the classicals differed, in this respect, from neoclassical theory, or (2) whether this might entail some difference for other parts of the overall analysis as well. Brie¯y, the answer on the ®rst issue is that neoclassical authors could adopt a view of the real wage as determined by the equilibrium between supply and demand (which presupposes that the real wage is widely ¯exible, e.g. inde®nitely decreasing in the presence of involuntary unemployment) only because they thought that the demand for labour was suf®ciently elastic with respect to the real wage to guarantee that normally the equality between supply and demand for labour would be reached at plausible levels of the real wage. In the different approach of the classical authors, where the notion of a decreasing demand curve for labour was absent, the view of the real wage as determined by historically speci®c social conventions re¯ecting the relative bargaining power of classes was only natural. Thus behind this difference one ®nds an analytically prior difference, the presence in the neoclassical approachÐand absence in the classical approachÐof those factor substitution mechanisms from which the notion of decreasing demand curves for factors was derived. (One implication is that in the classical approach a decrease of real wages is not a prerequisite for increases of the level of employment.) This has important implications on the second issue mentioned above. The theory of the quantities produced, which Burgstaller adopts in his `classical' models, is the same as in the `neoclassical' ones: continuous full utilization of resources. (When, in the MARX-SRAFFA and the RICARDO models, the subsistence real wage is exogenously given and there is a given subsistence-wage fund,8 then, although labour employ8

Labour employment is then determined by the wage fund divided by the wage. Actually Ricardo did not entertain a wage fund theory of wages, or of employment (cf. Stirati

# Blackwell Publishers Ltd 2001

Burgstaller on Classical and Walrasian Economics

171

ment is endogenously determined, it is the wage fund which is fully employed, so the economy is still a full-utilization economy.) We must ask how classical is this treatment of outputs. We may start by noticing that this continuous full utilization of resources does not create problems for Burgstaller only because whenever necessary he makes the `Uzawa assumption' that no produced capital good is `self-intensive' in its production process. In some of the economies he considers, this Uzawa assumption is crucial to the convergence of the economy to the steady state and to the existence of an in®nite-horizon perfect foresight path;9 but Burgstaller is unperturbed by this factÐhe makes the assumption without spending one word to justify its (very doubtful) legitimacy. However, how can he then claim to have found a `fundamental mathematical isomorphism linking the classical and the neoclassical theory of value' (p. 165), in a quasi-Hamiltonian system tracing out a perfect foresight in®nite-horizon path, if this system in order to exist may require a restrictive hypothesis of which there is no trace in classical economics? The answer is, of course, that the classicals had no need for a `Uzawa assumption' because they assumed neither perfect foresight nor continuous full utilization of all resources; they admitted disequilibria in the composition of stocks of inputs, and even of outputs, relative to the composition of demand, disequilibria which would be corrected over time. Thus, again, we ®nd here the absence of continuous equilibrium and the endogenous determination of the stocks of capital goods. But we also ®nd an important difference from the neoclassical (traditional as well as neo-Walrasian) approach: the absence, in the classical approach, of solid arguments in support of Say's law, for reasons strictly connected with the reasons explaining the difference in the theory of wages. (1999)), but there is a long tradition of interpretations which argue that he did, so Burgstaller can be excused for making this mistake. Inexcusable, in contrast, is his attribution of a wage fund theory to Marx or Sraffa. One may notice here that references to the literature which has debated the interpretation of classical economics, and its differences from neoclassical economics, are very scanty in Burgstaller's book. For example no mention is made of the work of Pierangelo Garegnani, the author of a series of important `Sraf®an' contributions on this topic. Burgstaller appears to have been too quick also in reconstructing the thought of Walras: he does not seem to realize that the adjustments in Walras's Lesson 25, which he discusses (pp. 204±11), are intended to bring into equilibrium the supply and demand for the numeÂraire, a produced money good only desired for transaction purposes, and that, because of this, the corresponding equilibrium equation is not at all viewed by Walras as `an interest-rate determining loanable-funds equation' (p. 208). Space constraints prevent me from entering into a detailed demonstration of this point. 9 Burgstaller admits it, cf. p. 21, fn. 4, and p. 201.

# Blackwell Publishers Ltd 2001

172

Fabio Petri

In Ricardo one does ®nd the acceptance of Say's law, and thus the tendency to assume that investment is normally determined by savings out of the income corresponding to the full utilization, on average, of the capital stock of the economy (he did not deny partial `gluts'). But his theory of value not only has no need for Say's law in order to determine values (it only needsÐcf. Garegnani, (1987, 1990b)Ðgiven quantities produced, i.e. a separate determination of quantities); even more importantly, it provides no support in favour of Say's law. The absence in the classical approach of the notion of a decreasing demand curve for capital, as well as of the connected notion of an investment schedule negatively related to the rate of interest, entails that in the classical approach the mechanisms which provide a foundation for Say's law in the neoclassical approach are missing: the rate of interest is incapable of acting as the `price' bringing investment into equality with full-capacity savings. Ricardo could only rely on Smith's belief that no one will be so foolhardy as to hoard money when he might earn an interest on itÐa very weak justi®cation, which Marx, for example, found easy to reject. The classical approach is therefore open on this issue; not only Marx and his followers but also Sismondi and the early J. S. Mill rejected Says' law, showing that Say's law is not a necessary component of that approach. Indeed, it may be argued that the moment one admits, following various hints of classical authors, some adaptability of production to demand, then Says' law becomes anyway untenable because any exogenous in¯uence (e.g. money creation, or, in the opposite direction, credit restrictions) on aggregate demand will have some in¯uence on the level of aggregate economic activity (for credit restrictions, this was admitted by Ricardo10 ), and then on income; thus the level of income can no longer be taken as given. Along this route, Kalecki, starting from Marx and Rosa Luxemburg, autonomously arrived at the Keynesian principle of effective demand. For the same reason, the modern advocates of a resumption of the classical approach, reinforced in their rejection of Say's law by the critique of neoclassical capital theory, all argue (Eatwell and Milgate (1983), Bharadwaj and Schefold (1990)) that the resumption of a classical approach to value and distribution can and should be coupled with the Keynesian principle of effective demand: the 10

`I am well aware that the total failure of paper credit would be attended with the most disastrous consequences to the trade and commerce of the country, and even its sudden limitation would occasion so much ruin and distress, that it would be highly inexpedient to have recourse to it as the means of restoring our currency to its just and equitable level' (Ricardo (1811, p. 94)).

# Blackwell Publishers Ltd 2001

Burgstaller on Classical and Walrasian Economics

173

principle that, through an endogenous determination of the level of income, investment determines savings and not vice versa. Now, this means that even in the long run there can be no presumption that growth is determined by savings: it will be the growth of the autonomous components of aggregate demand which will determine the growth of income and thus the growth of savings (Vianello (1985), Garegnani (1992). (Also compare the interventions in the Round Table on Accumulation, Effective Demand and Distribution in Bharadwaj and Schefold (1990). Particularly important here is this: because long-period positions are only centres of gravitation, which will themselves be shifting over time if the determinants of the quantities demanded are shifting, the fact that the de®nition of a long-period position includes fully utilized capital stocks does not imply that capital stocks are fully utilized all the time in the real economy, nor that capital stocks are fully utilized even only on average: it only means that capital stocks would be fully utilized if they had the time fully to adapt to demand, in which case they would be the stocks determined by the long-period position.) This means a subversion of the currently dominant views on macroeconomics and growth. These striking implications of a resumption of the classical approach can nowhere be glimpsed from Burgstaller's book. In the latter, the continuous full employment of resources is taken for granted, both for the `classical' and for the `neoclassical' economies. (That Marx, for example, rejected Say's law does not deter Burgstaller from using Marx's name for a model where Say's law is assumed.) The non-specialist reader cannot but be misled by Burgstaller's book into thinking that, on the issue of the determination of the general level of economic activity, there is no difference between the classical approach and a neoclassical approach where the real wage is for some reason ®xed and there is excess supply of labour. Thus Burgstaller's analyses of economies he calls by the names of classical authors contain only one element in common (up to a point) with classical analyses, the given real wage;11 but for the rest, in their assumptions of perfect foresight, of continuous equilibrium and of continuous full utilization of resources, they are neoclassical, indeed neoWalrasian. In those chapters he simply determines neoclassical perfect 11

This too may be disputed for the VON NEUMANN models, whose technology is not easily interpretable as including wages among the inputs, because both inputs are durable and depreciate radioactively (what was not the case in Von Neumann's own model, where the presence of circulating capital goods among the inputs made it possible to interpret the inputs as including wage goods). The `up to a point' quali®cation refers to the observations in footnotes 2 and 8 above.

# Blackwell Publishers Ltd 2001

174

Fabio Petri

foresight paths in economies with technologies reminiscent of those assumed in some works on value theory internal to the classical approach, and with real wages assumed rigid (so that labour may be replaced by wages in the speci®cation of technology). No wonder that he concludes that those analyses share with the analyses of `neoclassical' economies the characteristics of a neoclassical perfect foresight (`quasiHamiltonian') path. 4.

Is there then no common element in classical and in neo-Walrasian value theory? Yes, of course there is. The element common to long-period or natural prices and to neo-Walrasian equilibrium prices is the no-arbitrage conditions (one of whose implications is that product prices equal costs of production for produced goods). But this formal similarity is embedded in totally different frameworks: in the classical approach these conditions are only one part of a more exacting condition, the URRSP condition, because they are not conceived as capable of being established in the entire economy signi®cantly faster than the uniformity of rates of return on supply price; the situation in which the latter condition holds, the long-period position (which is not a steady state), is a situation of full (normal, optimal) utilization of the capital stocks present in it, but owing to its role as a centre of gravitation only and not as depicting the actual state of the economy it carries no implication that this full utilization is a normal, or even an average, characteristic of the real economy (thus it does not imply Say's law). Also, the no-arbitrage/ URRSP condition is not conceived as implying perfect foresight nor as extending over many periods into the future; it is only a fairly obvious aspect of a situation where relative prices have stopped changing (or nearly so). 5.

Now I come to a different issue. I wish to argue not only that the classical approach views things differently from the way Burgstaller depicts it, but also that it is correct in so doing. Burgstaller is wrong in believing, as he seems to believe, that the activity of arbitrageurs is by itself suf®cient to establish the full employment of resources, i.e. to guarantee Say's law; he is therefore also wrong in believing, as he seems # Blackwell Publishers Ltd 2001

Burgstaller on Classical and Walrasian Economics

175

to believe, that it is false that the justi®cation of Say's law, in neoclassical theory, is the equilibrating role of the rate of interest on the savings±investment marketÐin believing, in other words, that savings necessarily become investment owing to the operation of arbitrageurs. I may be mistaken in reading these claims in Burgstaller's analyses. I myself am not totally sure, because one would expect a very lengthy and detailed discussion of claims of such import by an author advancing them, and one does not ®nd this discussion in the book. But if I am mistaken, the fault must lie at least in part with Burgstaller's exposition. Burgstaller opens his sequence of economic models with the VON NEUMANN I economy, which is an economy where there is neither technical nor psychological substitution;12 so the mechanisms that according to traditional neoclassical theory should be pushing the economy toward a full-employment equilibrium are absent. Nonetheless, Burgstaller argues for this economy that `the economy's temporary equilibrium is instantaneously established through competition and the search for maximum pro®t aloneÐthat is, without recourse to a Walrasian auctioneer' (p. 26, italics in the original); and he then appears to believe that the same holds true for the other models in the book I ®rst comment on the `instantaneously' and on the claimed absence of the auctioneer. Even in the stock market,13 disequilibria are not instantaneously arbitraged away without `false-price' transactions. Offers are not provisional nor subject to revision, so although adjustments are quick, there are exchanges while prices change, and these exchanges are often afterwards regretted by at least one of the parties, so they must be seen as disequilibrium exchanges. Implicitly, Burgstaller is relying on the assumption he makes of perfect foresight, in order to have the equilibrium reached without `false-price' transactions. But, as is well known, bubbles which then burst are frequent in stock markets, so the assumption of perfect foresight cannot be defended by referring to the working of the stock market. The assumption of perfect foresight is simply a trick to hide the assumption of complete futures markets and the presence of the auctioneer, who, in the sense of some device to avoid 12

Consumption spending is assumed to be a ®xed proportion of wealth, and consumption is assumed to consist of corn and steel in ®xed proportions. 13 Burgstaller uses `equities' to mean alienable titles of property to durable and incomeproducing assets, but he also appears to think that selling equities in this sense is only performed on stock markets, and that, because of this, one has the right to assume that the elimination of arbitrage opportunities is extremely fast. It suf®ces to think of houses or small farms to realize that this is false, and that Burgstaller must still be imagining that all transactions happen in a single centralized place, as in the fairy tale of the auctioneer.

# Blackwell Publishers Ltd 2001

176

Fabio Petri

the implementation of disequilibrium decisions and transactions, must still be there.14 But even conceding, for the sake of argument, a very fast tendency to a correct equalization of rates of return on equities, this does not imply a tendency to the full employment of existing resources. Burgstaller makes a great deal of his assumption that goods are durable and storable; then, he argues, there is no obstacle to the continuous full utilization of resources because goods produced and not consumed simply increase stocks, i.e. increase the wealth of consumers, and as long as the no-arbitrage conditions are satis®ed consumers are content with holding their wealth in any form and therefore are ready to hold a portfolio of equities of the same composition as the real wealth, the stocks of resources, existing in the economy; and since their total wealth is the aggregate value of those stocks, their total portfolio of equities must by necessity equal in value the aggregate value of those stocks, which implies that they will willingly hold the entire stock of resources of which the economy is endowed. If this is true at each instant, it must mean that all production is sold without problems, because production minus (productive and consumers') consumption of stocks equals variation of stocks, and this variation of stocks is absorbed without problems by consumers if they are at each instant satis®ed with holding the existing stocks. But such an argument does not determine the levels of production. It simply says that, if all savings become investment, then arbitrageurs will ensure that savers are satis®ed with the composition of investment. But it does not guarantee the full utilization of resources: if these are underutilized, they are worth less than if fully utilized, and the wealth of consumers is correspondingly reduced, but the equality between wealth and value of stocks is not disturbed. This argument also has another weakness. It is of course true that at any moment the stocks of resources belong to somebody, but this somebody might be the owner of a ®rm who has produced some new units of, say, steel and would like to have sold them in order to repay his debts, but was unable to sell them and therefore has an incentive to decrease production.15 It is true that in this case there will be someone 14

A further objection to the claim of the non-necessity of the auctioneer is that, in economies with substitutability among inputs, the full-employment ratio between factor rentals must be brought about by the interplay of supply and demand, so, again, unless one uses the assumption of perfect foresight as synonymous with the instantaneous reaching of equilibrium, the auctioneer is necessary. 15 The peculiar technological assumptions of the VON NEUMANN model ensure that if only one price is positive then all prices and rentals are positive, which in that model

# Blackwell Publishers Ltd 2001

Burgstaller on Classical and Walrasian Economics

177

else in the economy who has credits for the value of the unsold inventory, but this someone else may need the debt to be repaid ®rst in order to be able to use that wealth to buy the unsold steel. Unless one implicitly appeals to the auctioneer, there is a sequence of payments to be respected in a market economy where goods are exchanged against money. The assumption, that wealth ˆ value of existing stocks ˆ demand for property of existing stocks, implicitly takes it for granted that existing stocks are with consumers, and not with ®rms who would have liked to sell them but were unable to. So this assumption implicitly assumes that there are no problems in selling the production of new capital goods. In a growing economy, in the absence of the auctioneer (and therefore with goods exchanging against money) this assumption runs against the problem that, in order to sell an increasing amount of goods at constant prices and with a constant velocity of money, there must be continuous money creation, otherwise purchasing power is insuf®cient (and notoriously, owing to past debts, price reductions are resisted16 ). And even in a stationary economy (in which the previously existing purchasing power would be suf®cient to buy the production at unchanged money prices), if for any reason someone starts hoarding money and hiding it in the mattress, there will be a corresponding decrease of money savings accruing to arbitrageurs for the purchase of equities representing capital goods, so there will be a corresponding inventory accumulation by some ®rms unless there is a corresponding compensating decision by someone else to borrow against money creation in order to invest. On the other side, the well-known ¯exibility of the credit system (which includes the possibility that ®rms pay other ®rms with promissory notes) makes it possible for investors to invest without any corresponding previous decision to save. Thus the problem arising from the separation of saving decisions and investment decisions of what mechanisms can bring the two into equality is notÐas one might have expectedÐeliminated by the presence of arbitrageurs who establish a uniform rate of return on existing equities. implies the full employment of resources, but only if producers do not have unsold inventories or are able anyway to offer them for productive employment. Anyway no argument resting on very special technological assumptions can be of great interest. 16 With durable goods, resisting price reductions is made possible by the possibility of storing them, and of reducing production below demand so as to get rid later of the excess inventories. This kind of quantity adjustment with price rigidity is widely recognized to be a very frequent occurrence. (For similar reasons, it is also possible that unemployment of a resource which deteriorates with use is not accompanied by a zero rental, but there is no space here to discuss this issue.)

# Blackwell Publishers Ltd 2001

178

Fabio Petri

One may therefore conclude that in Burgstaller's analysis the assumption of continuous full employment of resources is just that: an assumption, without justi®cation. It may of course be defended through standard neoclassical arguments for the models to which those arguments are applicable, but, except in one-capital-good models, the arguments will run against the well-known dif®culties brought to light in the Cambridge controversies. POST-SCRIPTUM

Some comments I received prompt me to return brie¯y to the roots of the difference between the classical and the neoclassical approach. Although Burgstaller never explicitly says so, the different hypotheses about technology in the `classical' and in the `neoclassical' chapters of his book may suggest that an important difference between classical and neoclassical analyses lies in the assumptions about substitutability in the production functions of the several industries or in the utility functions of consumers. This would be a misconception. The reason why in Ricardo or Marx one does not ®nd the neoclassical factor substitution mechanisms is not that they denied or neglected the existence of technical or consumer choice. Classical authors admitted the existence of those choices; they simply did not conceive that it was possible to derive, from those choices, factor substitution mechanisms depending on relative factor prices, from which one could in turn derive the decreasing demand curves for inputs which in the neoclassical approach give plausibility to an explanation of distribution in terms of an equilibrium between supply and demand for factors.17

17

The neoclassical factor substitution mechanisms resulted from a generalization of the Ricardian theory of intensive rent, deriving from the realization of the symmetry between the role of land and the role of capital-cum-labour (so that the reward of a unit of capitalcum-labour could be seen as the marginal product of that unit, just as the rent of land could be seen as the marginal product of land) and from the application of the same insight to utility functions. The road was thus open, it was (mistakenly) believed, to explaining on the basis of the marginal principle also the division of the product between wages and pro®ts, which the classicals had explained altogether differently. The reason why technical and consumer choices are given much less prominence in classical than in marginalist analysesÐ which may have given rise to the misconception mentioned in the textÐis then simply that in classical analyses these choices are not assigned the fundamental analytical role they have in marginalist theory.

# Blackwell Publishers Ltd 2001

Burgstaller on Classical and Walrasian Economics

179

It might then be thought that in this respect neoclassical theory constitutes an analytical advance, because it develops the implications of facts (the existence of technical and consumer choices) which the classicals were admitting. But modern research has shown that the neoclassical faith in the possibility of deriving demand curves for factors from those facts was ill-placed. For example, the demand curve for labour cannot be drawn, because it is impossible to specify the given endowment of capital which is kept fully employed as the real wage varies: one can take as given neither the vector of endowments of the several capital goods, because these would change during the disequilibrium, nor the endowment of `capital' measured as a single factor given in `quantity' but not in `form', because it would have to be measured as an amount of value. And even if one were to grant, for the sake of argument, either treatment of the capital endowment and the full employment of that endowment, the possibility of reverse capital deepening would anyway imply that the demand for labour would not be generally decreasing even when all possible perversities arising from income effects in consumer choices were set aside. Hence the interest of an approach, the classical one, which did not rely on notions which have come out to be illegitimate. If one were to believe that technical and consumer choices imply the neoclassical factor substitution mechanisms, and that the absence of a decreasing demand curve for labour in classical analyses derives from an assumption of ®xed technical coef®cients in production and of nearly ®xed proportions in consumption, then, since technical choices and consumption choices are undeniably present in the real world, it would be a short step to concluding that the classicals were unjusti®ably restrictive, that the standard decreasing demand curve for labour is a legitimate notion (at least, if perverse income effects are not present) and that the effect of a given real wage is therefore simply that of determining endogenously the demand for labour and hence employment. If on the contrary the criticisms of the logical consistency of the neoclassical approach are fully appreciated, the absence of demand curves for factors in the classical approach will be seen as a merit of that approach, and the classical analyses of distribution and of the effects of its changes, of wage differentials, of the working of competition, of taxation, of the causes and effects of technical progress, and so on, will appear of the utmost interest because unfettered by the straitjacket of the later misleading supply and demand framework. # Blackwell Publishers Ltd 2001

180

Fabio Petri

REFERENCES Bharadwaj K., Schefold B. (eds) (1990): Essays on Piero Sraffa, Routledge, London. Bray M. M. (1982): `Learning, estimation, and the stability of rational expectations', Journal of Economic Theory, 26, pp. 318±39. Burgstaller A. (1994): Property and Prices, Cambridge University Press, Cambridge. Eatwell J. L., Milgate M. (eds) (1983): Keynes's Economics and the Theory of Value and Distribution, Duckworth and Oxford University Press, London and New York. Fisher F. M. (1983): Disequilibrium Foundations of Equilibrium Economics, Cambridge University Press, Cambridge. Garegnani P. (1987): `Surplus approach', in The New Palgrave Dictionary of Economics, Macmillan, London. Garegnani P. (1990a): `Quantity of capital', in Eatwell J., Milgate M., Newman P. (eds): Capital Theory, Macmillan, London. Garegnani P. (1990b): `Sraffa: classical versus marginalist analysis', in Bharadwaj K., Shefold B. (eds): Essays on Piero Sraffa, Routledge, London. Garegnani P. (1992): `Some notes for an analysis of accumulation', in Halevi J., Laibman D., Nell E. (eds): Beyond the Steady State: A Revival of Growth Theory, Macmillan, London. Hahn F. H. (1982): `The Neo-Ricardians', Cambridge Journal of Economics, 6, pp. 353±74. Hicks J. R. (1946): Value and Capital, 2nd ed, Clarendon Press, Oxford. Marshall A. (1972): Principles of Economics, reprint of the 8th edn. (1920), Macmillan, London. Petri F. (1991): `Hicks's recantation of the temporary equilibrium method', Review of Political Economy, 3, pp. 268±88. Petri F. (1999): `Professor Hahn on the ``neo-Ricardian'' criticism of neoclassical economics', in Mongiovi G., Petri F. (eds): Value, Distribution and Capital: Essays in Honour of Pierangelo Garegnani, Routledge, London. Ricardo D. (1811): High Price of Bullion, in The Collected Works of David Ricardo, edited by P. Sraffa, Cambridge University Press, Cambridge, 1951±73, vol. III. Stirati A. (1999): `Ricardo and the wages fund', in Mongiovi G., Petri F. (eds): Value, Distribution and Capital: Essays in Honour of Pierangelo Garegnani, Routledge, London. Vianello F. (1985): `The pace of accumulation', Political Economy: Studies in the Surplus Approach, 1, pp. 69±87. Dipartimento di Economia Politica UniversitaÁ di Siena Piazza San Francesco, 17 I53100 Siena Italy

# Blackwell Publishers Ltd 2001