ccx+6 unhs of N. These produce x units of N. Therefore the growth rate of N is 'V— -1 which
ax+b
X
must be equal to the growth rate of the economy g. Hence ■■■■■■■■ -1 = g => x ~ 1.85 . Equally, the
ax+o
input requirements for M of the next cycle are ßMx for sector 1 and eM for sector 2, that is a total of ßx+ £ units of M. These provide one unit of M giving a growth rate equal to
—-i— = g~ 49.22% . This is the gist of the von Neumann (1937) growth model. In the latter. ßx+e
things are more complicated since each production process is visualised as a number (less or equal to n) of inputs producing a number of outputs (also less or equal to n, where n is the total number of goods in the economy). For example, a very elementary von Neumann economy would, be one with two goods (chicken and eggs) and two processes (laying and hatching). In the laying process, one chicken (the input) could lay 12 eggs and the output would be 1 chicken (the original) and the 12 eggs. In the hatching process one can have as inputs one chicken and 4 eggs and get as output 5 chickens (the hatched eggs and the original); see Kemeny et al (1966).
p{\ - a) - ¡3 - wy (1 — e) -/j<5 -
7 Which can be easily computed as gH =--- — = ---——
pa + j3 pS + £
g The mathematics are tedious but straightforward. Since,
p(\-a)-(3-wy (l-c^g* +l))/?-/3(gif +l)
„ ...........—-=> w= -—..................
pa + fi y
or in our numerical example vv = (l - 0.4(g„ +1))/> - 0.2 (gfl +1)
Since pQ-<x)-P~wY = pS~w£
pec + P pd + s
we get that
[' P{\ - «) - j3] (p5 + e) - [(1 - e) - pS](pa + p)
which in our numerical example becomes
w =..............—
~p
and get a more complicated expression for p.
[l + 0.2(g„ +1)] + J[l + 0.2(g„ +1)] + 8[5 + (l - 0A(g„ +1))
2[5 + (l-0.4(ÏB+l))]
which forg// = 0 gives ap of around 0.714 and a vv of 0.229. Note that if g„ is higher than 49.22%, w becomes zero and 49.22% is the upper bound for the growth rate of the economy.
9 In equations 4.1 and 4.2 the inequalities become equalities, i.c.p =pa + q\S + wyand q = p§ + q£ + You could check by substituting our numerical examples noting that p~0.714, vv~0.229 and q= i.
10 This is nicely consistent with the film’s theme of a wholesale war launched by killer machines against the band of human rebels who plot to rescue their brothers and sisters from the Matrix, thus (one presumes) making human heat available to machines more scarce.
11 This is due to the fact that this particular Matrix Economy is assumed to rely more on the machinery produced in sector 1 than those in the second sector (recall that a = 4/10 and (3 ~ 2/10 whereas 8=5/10 and e = 3/10).
12 A somewhat different criticism of the Ricardian labour theory of value was raised by proto-Marginalist economists like Nassau W. Senior, who asked whether ‘wine in a cellar, or oak in its progress from a sapling to a tree’ were also creating value (Senior 1836, p. 152). Indeed, the whole discussion about ‘natural agents’ that led to the definition of ‘factors of production’ was inspired by an attempt to dethrone labour and ascribe value creating properties to ‘natural agents’. But as Marx (1875 [1962], p. 15) wrote: ‘Labour is not the source of all wealth. Nature is ,.. [But] to the extent that man from the beginning behaves towards nature, the first source of all means and subjects of labour, as an owner, treats her as belonging to him, his labour becomes the source of use values, and also of wealth’ (emphasis in the original). See Theocarakis (2010). So natural processes in themselves do not create value.
13 When astronomers are speculating regarding some distant planet where a kind of murky atmosphere may be maintained by bacteria and other relatively simple organisms, by the ebb and flow of gamma rays emitted from its sun and by various other organic and inorganic forces, they too speak of the function that each of these life forms and inorganic factors play. Nothing would be added to their analysis by bringing into the discussion the concept of value.
14 This does not mean that our position is shared by all. Indeed, a common mathematical structure of certain problems leads some to conclusions that their essence is similar. In the natural world this may lead to the so-called pathetic fallacy: ascribing consciousness to inanimate objects. In economics it can be the reverse: to assume that economic problems are problems similar to those of the natural world. The great Paul Samuelson was fascinated by the mathematical structure of economics and attempted to make maximisation under constraint almost tantamount to the definition of our science. See in particular his 1970 Nobel Prize Lecture: ‘Maximum principles in analytical economics' (Samuelson 1970) and the striking opening paragraph of his Foundations of Economic Analysis (Samuelson 1947): 1 The existence of analogies between central features- of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features ... It is the purpose of the pages that follow to work out [this fundamental principle’s] implications for theoretical and applied economics’ In linear programming, for example, the same tools were used for a variety of different uses. It is in fact ironic that the most supposedly strategic branch of the social sciences, Game Theory, still has a JEL classification which bears the historical marks of its being perceived through its mathematical structure, rather than through its strategic insights. In neoclassical economics, after Robbins redefinition of our science as ‘the science which studies human behavior as a relationship between given ends and scarce means which have alternative uses’ (Robbins 1932, p. 16), one has the impression that the human economy of free agents is a Matrix Economy brought about bv its human slaves. The inevitability of rationality coupled with an obsession with harmonious efficiency, makes a centrally planned economy tantamount to a perfectly competitive one in its results, like the body of Leviathan that was composed of 300 homunculi in the famous frontispiece of Hobbes’ magnum opus created by Abraham Bosse.
15 Just as nothing would have changed in Ricardo’s com model if the gold turned into dust every now and then - recall Box 3.5.
16 In chess, the German term Zugzwang applies to situations where a player would be at a disadvantage when it is their turn to move. In some cases a move is forced. In checkmate you just lose. In Ken Loach’s The Navigators (released in 2001) Gerry, a British Rail (former) employee, plays chess against himself. When Fiona asks him ‘who’s winning?’ he replies ‘Checkmate’. Fiona asks again: ‘Checkmate, what’s that mean?’ to get the reply ‘Whatever move you make, you lose.’ Fiona then chuckles and says ‘Story of my life’.
17 ‘Life has been integrated into the market as easily as could be imagined because it has been a progressive process. It started with something that was symbolically far removed from mankind, the vegetable domain; from there it passed to the micro-organism, then to the most rudimentary forms of animal life like the oyster. The whole of the animal kingdom is now targeted and we are on the verge of the human, weighed down with precedents which ensure the closure of the system and make any resistance difficult. The work of man, which must be remunerated, claims repayment from the whole realm of nature which has traditionally been free of any property claims.’ Edelman (1988 [1997]), p. 197.
18 ‘in a perfectly competitive market, it really doesn’t matter who hires whom: so have labor hire “capital” Samuelson (1957, p. 894).
19 When one agrees to buy apples or generators for a given price, the moment this agreement is concluded signals the end of the economic relation between buyer and seller. In the case of the labour contract., its signing signals the very beginning of the economic relation between employer and employee.
20 Speaking of complex mathematical functions, there is no dearth of explanations in which ‘effort, ‘diligence’ or ‘performance’ has been attempted to be determined as a result of a complicated mathematical formula. Once the mainstream economic theory decided to extend its scope to the black box of the labour process and allow for asymmetry of information and uncertainty in its assumptions, it proposed the so-called agency model in which the employer, as the principal, and the employee, as the agent, attempt to enter into a mutually acceptable contract in which the employer will pay the wage in such a specific manner that it would be rational for the worker to apply the specified level of effort, thus escaping the dreaded indeterminacy. This research programme has created a veritable sub-industry in modern labour economics with dumbfounding mathematical sophistication (see for an advanced textbook treatment Cahuc and Zylberberg. 2004, Ch. 6. For a survey of the literature see Malcomson, 1999.) The new branch of 'personnel economics’ has been extremely fruitful (see Lazear, (1999) and Lazear and McNabb 2004). The Human Resources literature is naturally even more voluminous. The problem with such attempts is that they insist in an asocial model in the determination of effort. On the contrary, what the industrial relations and the industrial sociology literature has demonstrated time and again is that of work literature which shows that the determination of effort is either hard to quantify (e.g. Baldamus,
] 961) or that workers react strategically to attempts by management to set rules by which the latter try to control them. This literature goes way back in time (see e.g. Goodrich, 1920 [1975]; Mathewson, 1931; Roy, 1952; Lupton, 1963; Burawoy, (1979); Arthur Marsh (1979, p. 37) offers a litany of names for restricting output: ‘ca’canny, go-slow, siow-gear strikes, lazy strike, folded arms strike, stay-in strike, working without enthusiasm, restrictive practices, protective practices, craft control, quota restriction, gold bricking7. Geoff Brown in his Sabotage (1977) studied conscious attempts by workers to disrupt production even if there was no rational reason to do it. For a more plausible view of managing remuneration and productivity see especially the work of William A. Brown (1979, 1989, Brown and Nolan 1988), Moreover, issues of trust, not contractually achievable, become paramount (Fox, 1974). In the industrial relations literature it is a commonplace that the motivation of workers is not achieved through the labour contract, however skilfully managed. Notions of fairness, unrelated to the rational opportunistic worker, are important in the process of motivation (Hyman and Brough, 1975). Job evaluation schemes, for example, are less linked to the external labour market and more aimed at creating a wage and salary structure that respects norms of fairness of the employees (Doeringer and Pior, 1971; Theocarakis, 1991, ch. 5). Research from experimental economics demonstrates that in labour contexts notions of instrumental rationality do not apply (Fehr and Gächter, 2000). Ideologies at large in society serve to bolster the authority relationship (see Bendix, 1956).
21 Marx’s exact words were: 'Capital is thus the governing power over labour and its products’.
22 Again, we have paraphrased. His own words are: ‘Modern bourgeois society with its relations of production, of exchange and property, a society that has conjured up such gigantic means of production and of exchange, is like the sorcerer, who is no longer able to control the powers of the netherworld whom he has called up by his spells.’ (The Manifesto of the Communist Party, Marx and Engels {1848 [1998]), p. 41.
23 Marx here speaks specifically of Political Economy rather than Capital, but it is clear from his discussion that his analysis concerns both.
24 Lenin wrote in 1913 that the ‘Marxist doctrine ... is the legitimate successor to the best that man produced in the nineteenth-century, as represented by German philosophy, English political economy and French socialism’. (‘The Three Sources and Three Component Parts of Marxism’ in Collected Works, 1977, Vol. 19, pp. 21-8.) We believe that the influence of Ancient Greek philosophy was as important.
25 See G.W.F. Hegel (1807 [1931] p. 103). Ten years later he expanded on the theme thus: ‘The concrete return of me into me in the externality is that I, the infinite self-relation, am as a person the repulsion of me from myself and have the existence of my personality in the being of other persons in my relation to them and my recognition of them which is mutual.’ Hegel Enzyklopädie der philosophischen Wissenschaften: Ul Philosophie des Geistes (1817, 2nd 1827, 3rd 1830) Hegel 1894, §490.
26 To be fair to Smith, he did not suggest that human nature was immune to all experiences. For example, he was worried that his cherished division of labour might turn human labourers into automata. To combat this danger Smith prescribed education as an antidote to such alienation. Nevertheless, along with David Hume, Smith held to the belief that, systematically adverse situations notwithstanding, human nature was more or less fixed and only the social norms governing behaviour changed in response to changing circumstances.
27 David Hume, (1748 [1902]) Sec. ViII, Part 1, §65.
28 Hegel (1894) I. The Logic, §131.
29 All the quotations in this paragraph are from The Manifesto of the Communist Party, by Karl Marx and Friedrich Engels, published in 1848. In the same passage Marx and Engels extol the bourgeoisie’s contribution to the demise of the old, anachronistic ways; of the stagnation that typified the Middle Ages. ‘The bourgeoisie’, they wrote, ‘cannot exist without constantly revolutionising the instruments of production, and thereby the relations of production, and with them the whole relations of society. Uninterrupted disturbance of all social conditions, everlasting uncertainty and agitation distinguish the bourgeois era from all other ones.’ Marx and Engels 1848 [1998], p. 38.
30 Paul MacCready was, amongst other things, the inventor of the solar powered airplane. A commit, ted environmentalist, he argued vehemently about the unsustainable imbalance between the biomass under our control and the biomass in the ‘wild’. The figure reported here is pan of tha* argument. MacCready’s figure concerns the mass of land animals, that is, of terrestrial vertebrates He did not include insects, worms or the fish in the sea. What he found was that humans plus their livestock overtook wild animals (in weight) at the beginning of the twentieth century. Humans alone (without livestock) began out-weighing wild animals only after World War II. In the past decades the combined footprint of humans and cattle has all but eclipsed all other land-based animals.
31 Paul B. MacReady, (2004) p. 8 [emphasis in the original].
32 In this context, it is possible to argue that twentieth-century communism committed precisely this type of fundamental error: it concentrated on the top-down Central Plan while ignoring the ways in which bottom-up ‘natural selection’ (i.e. decentralised activity by individuals) would alter, affect and, eventually, undermine the Plan. They behaved like genetic engineers who unleash their designer organisms in the ecosystem on the assumption that they will neither mutate nor interact unpredictably with existing organisms.
5 Crises: The laboratory of the future
1 ‘In the market, as the owner of the commodity “labour-power”, [the worker] stood face to face with other owners of commodities, one owner against another owner. The contract by which he sold his, labour-power to the capitalist proved ... that he was free to dispose of himself. But when the transaction was concluded, it was discovered that he was no “free agent”, that the period of time for which he is forced to sell his labour-power is the period of time for which he is forced to sell it, that in fact the vampire will not let go ‘ “while there remains a single muscle, sinew or drop of blood to be exploited’” Marx, Capital., Vol. 1, (1867 [1976]), p. 416. Marx quotes from Engels' “Die eng* lische Zehnstudenbill” [The English ten-hour bill].
2 Marx in Wage-Labour and Capital, (1849 [1902]), p. 58.
3 Marx in Grundrisse, (1857 [1973]), p. 361.
4 Neoclassical economics denies the fact that there is an essential difference between the two. in a famous article Armen Alchian and Harold Demsetz argue that the difference between the pairs' ‘grocer-customer’ and ‘employer-employee’ is in the ‘team use of inputs and a centralized position of some party in the contractual arrangement of all other inputs’ [Alchian and Demsetz (1972), p. 778], In the Markets and Hierarchies paradigm Oliver E. Williamson argues that due to the existence of uncertainty, adaptation is needed for the changing circumstances and therefore the need for flexible contracts arises. There are four types of possible contracting modes: (1) ‘contract now for the specific performance of X in the future’ (a sales contract); (2) ‘contract now for the delivery of X, contingent on event et- obtaining in the future’ (contingent claims contract); (3) "wait until the future materializes and contract for the appropriate (specific) X at the time’ (seijuemiai ‘■po: extract); (4) ‘contract now for the right to select a specific X from within an admissible set X, the determination of the particular Xto be deferred until the future’ (authority or employment contract). [Williamson et al. (1975)]. Ronald Coase in a celebrated article made efficiency decide where the limits are set between markets and firms. The limits of the authority relationship are set according to this view by transaction costs (Coase (1937)).
5 In the next section we discuss the reason why the labour market must be Jill’s only fallback position: her only outside option. If she has alternative options, e.g. can go into business for herself, she has no reason to accept a labour contract of the form discussed here.
6 In Section 4.5 we explained that workers are offered a labour contract only when they work in the context of social production such that the link between Jill’s output and her labour input is opaque (see also Box 4.8). If this link is transparent, we claimed, there is no reason why the employer would want to employ Jill on a labour contract, as opposed to contracting work out to her; effectively turning her into a sub-contractor.
7 This point was made powerfully by Sue Himmelweit in her 1995 paper entitled 'The Discovery Unpaid Work: The Social Consequences and the Expansion of Work’, Himmelweit (1995).
8 Marx, Capital, Vol. 1, (1867 [1976]), p. 932.
9 Referring to E.G. Wakefield’s account of capitalism in the colonies, Marx writes: ‘First oi >‘>s-Wakefield discovered that in the Colonies, property in money, means of subsistence, inachniwx and other means of production, does not as yet stamp a man as a capitalist if there be wanting
correlative - the wage-worker, the other man who is compelled to sell himself of his own free-will. He discovered that capital is not a thing, but a social relation between persons, established by the instrumentality of things’. Marx, Capital, Vol. 1, (1867 [1976]), p. 932.
10 Seaford’s address was partially reprinted in Seaford (2009).
11 Seaford (2009) relates another pertinent Greek myth according to which a man called Erysichthon 'cut down a sacred grove to make himself a banqueting hall and is punished by being made insatiable. No food is enough - whether from land, sea, or air - to satisfy him. He is driven to sell his daughter in marriage, from which she returns to him, and the process is constantly repeated. In the end he eats himself’. Money, therefore, is spreading its poisonous web, making it impossible for mortal men to satiate their cravings, commodifying trees and women alike, consuming everything in its path, including the very flesh and blood of the man who craves it the most.
}2 See Marx’s Economic and Philosophical Manuscripts, 1844, and in particular the chapter on The Power of Money’ where he also writes: ‘If you suppose man to be man and his relation to be a human one, then you can only exchange love for love, trust for trust’. Money on the other hand ‘changes fidelity into infidelity, love into hate, hate into love, virtue into vice, vice into virtue, slave into master, master into slave, stupidity into wisdom, wisdom into stupidity. It is the universal confusion and exchange of all things, an inverted world’. Marx (1844 [1977]), p. 111.
13 Karl Marx. 1856, April 19th, ‘Speech at the anniversary of the People’s Paper’, in Marx and Engels 1969, p. 500.
[4 Shaw, 1949, p. 19.
15 The Manifesto of the Communist Party, by Karl Marx and Friedrich Engels, (1848 [1998]), p. 37.
16 Marx in Wage-Labour and Capital, (1849 [1902]), p. 58 [original emphasis].
17 Supra-intentional causality refers to a social process culminating into a social outcome that was not part of the intentions which led the various actors to the actions that brought it about. Sub-intentional causality, on the other hand, refers to a process internal to the agent (i.e. one that operates at the level of psychology or of the subconscious) culminating in the motives and beliefs behind their acts.
18 Addressing the First International Working Men’s Association, June 1865. His talk was later published as Value, Price and Profit, Marx (1865 [1969]).
19 Note that Marx and Ricardo are speaking with one voice here. The Ricardian profit rate equation (3.4), in Box 3,4 and Marx’s own equation (5.2) tell a similar story: whenever the wage rate w rises, the profit rate suffers. This is not to say that Marx did not recognise that some prices would rise, following a wage increase. In Value, Price and Profit he agrees that the price of basic goods (that workers buy with their wages) will increase as workers have more money to spend. However, the profit rate in the relatively more labour-intensive sector (i.e. the capital goods sector) will fall, dragging employment down in that sector. Then workers will migrate to the other sector(s), which are growing. Thus the wages in the other sector(s) will dip a little (as labour supply there rises) and increase a little in the capital goods sector. The overall effect will be a long-term increase in the economy-wide wage (but not as much as the initial rise in the basic goods sector) and an economy-wide drop in the profit rate. All in all, commodity prices will be, in the long term, left unaffected.
20 Maxwell 1890, Vol. 1, p. 500.
21 The interested reader may consult Paul Sweezy, (1942 [1970]) Chapter 10, pp. 162-3.
22 An assumption we made also in the context of the Matrix Economy (see Box 4.5). Another way of grasping the importance of assuming that profit rates tend to equalise is to go back to our depiction of the Physiocrats’ model in Box 3.1. The inequalities at the end of that box cannot, by definition, be solved as a system that yields the prices consistent with growth. To do that, these inequalities had to be expressed as equalities. Since the difference between the left-hand side and the right-hand side of these inequalities is profit per unit of output; the assumption that profit rates are equal allows one to add the same profit component to the right-hand side of the inequalities in Box 3.1 thus turning them into equalities before solving the two as a system of equations for the prices of the two goods. Clearly, without the assumption of Ricardo and Marx that profit rates tend to equalise, there can be no determinate theory of prices or values.
23 See in particular the Appendix to Ch. 5 of his Lectures on the Theory of Production. Pasinetti : (1977).
24 The validity of Marx’s iterative procedure in moving from values to prices has also been shown by Anwar Shaikh in ‘Marx’s Theory of Value and the Transformation Problem’, in Schwartz (1977), pp. 106-39.
25 Recall Hegel’s dialectical argument, so influential in Marx’s thought, that no one can be free in a society where some are enslaved. History, being the factory of irony, many decades later in the communist Poland of the 1980s, would produce a piece of dissident anti-communist graffiti that proclaimed (in opposition to the threat of a Soviet invasion) that ‘No country that threatens to invade another can be free’. Marx was being used, quite correctly, to lambast Soviet socialism While we think that he would have sided with the graffiti writer, this incident underscores the Left’s massive political and moral twentieth century failure.
26 Piero Sraffa, Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory. Sraffa (1960),
27 As opposed to the ratio of labour inputs bestowed (during production) into the commodities under exchange.
28 Relative prices are determined by equation (4.5) solved explicitly in note 4 of Chapter 4. The interpretation of w in the present context is as the economy’s wage rate expressed in units of the numéraire that labour input is to be paid for per unit. The relationship between the economy's uniform (across the sectors) growth rate (which is the same as the profit rate) and the wage rate can be computed by plugging the value of/? above into equation (4.6). Note that in the original context of the Matrix Economy, w was not the wage but the relative weight attached by that economy’s' Overlord Program to the only natural resource: human heat.
29 Sraffa’s rationale is that labour is the only input not produced by some sector of the market economy and, for this reason, its price, the wage rate vv, cannot be computed by the model Indeed, all the model can do is tell us which profit rate corresponds to which wage rate (recall Box 4.6, Chapter 4), with the two variables being inversely related. This inverse relation captures the contest, or struggle, between the classes over the distribution of the surplus. Noting that it is fully consistent with Ricardo’s mode [see equation (3.4) in Box 3.4 of Chapter 3], Sraffa’s approach is understandably referred to as neo-Ricardian. So, in one sense, the idea of social power is preserved since the model itself suggests that the distribution of the surplus between capital and labour is not an economic matter, as it cannot be determined mathematically by the economic model. Distribution, thus, remains in the ambit of politics and, once history, politics and sociology has determined who gets which part of the surplus (i.e. the particular combination of K and w) economics kicks in and determines relative prices. For the strongest argument in favour of a Sraffian, physical output based, notion of extraction, exploitation and social power, see Garegnani (1984).
6 Empires of indifference: Leibniz’s calculus and the ascent of
Calvinist political economics
1 We assume here that capital utilisation, or the organic composition of capital (the k? s in equation (5S))t differ across sectors. Indeed, only by a rare fluke would they not differ.
2 E.g. (i) the conversion of a piece of metal into a magnet by passing electrical current through h and (ii) the fact that light exhibits wave-like properties in some, but not all, experiments.
3 Hegel in his Philosophy of History called it Zeitgeist; a stand-in for humanity’s collective consciousness.
4 To the sectors with higher profit rates.
5 Away from sectors with higher extraction rates.
6 E.g. due to the temporary effects of some innovation, before it spreads to many competing firms, or of geographically determined conditions of monopoly, like those experienced by rural communities* served by a single petrol station.
7 Note that the power of firms (or market power, as economists call it) differs crucially from the power that is, in Marx’s mind, capital. Capital is a mighty force whose origins lie in the peculiarities of the labour contract (see Section 4.5) and which survives perfectly well in a fully competitive world where everything sells at its value and no one can profit from buying and selling commodities. TIté power affirms, in contrast, goes beyond that and is related to insufficient competition; e.g. when firm* enjoy a degree of monopoly in the market for products or monopsony in the market tor labour power.
8 Keynes in his famous essay on Alfred Marshall provides another difference between physics ana economics. He writes: ‘Professor Planck, of Berlin, the famous originator of the Quantum Theory, once remarked to me that in early life he had thought of studying economics, but had found it too
difficult! Professor Planck could easily master the whole corpus of mathematical economics in a few days. He did not mean that! But the amalgam of logic and intuition and the wide knowledge of facts, most of which are not precise, which is required for economic interpretation in its highest form is, quite truly, overwhelmingly difficult for those whose gifts mainly consist in the power to imagine and pursue to their furthest points the implications and prior conditions of comparatively simple facts which are known with a high degree of precision’ (Keynes, (1924 [1972]) p. 186, n. 2). The preceding footnote in Keynes’ essay is also scathing on the lure of mathematics ‘ Mathematical economics often exercise an excessive fascination and influence over students who approach the subject without much previous training in technical mathematics. They are so easy as to be within the grasp of almost anyone, yet do introduce the student, on a small scale, to the delights of perceiving constructions of pure form, and place toy bricks in his hands that he can manipulate for himself, which gives a new thrill to those who have had no glimpse of the sky-scraping architecture and minutely embellished monuments of modern mathematics’ (ibid.). Modern mathematical economics have gone a long way since Keynes’s days but the thrill of toy bricks remains intact.
9 Simplistic in the sense that the multiple identities that classical political economics allowed for (e.g. of capitalist, landowner, productive or unproductive worker, etc.) are replaced by the juxtaposition of buyer and seller. Dualist because of the impossibility of a dialectical account of the sort explained in Box 4.10. Tony Aspromourgos (2009) in his book The Science of Wealth: Adam Smith and the Framing of Political Economy uses the acronym SAD for ‘supply and demand’. Francis Edgeworth speaks of the ‘catal lactic molecule’ (1881, p. 3 1), whereas Bishop Whately suggested that the proper name for political economy should have been ‘CATALLACTICS or the “Science of Exchanges (Whately 1831, p. 6, emphasis in the original). No wonder that Marx (Capital, Vol. I, (1867 [1909]), p. 196) speaks of the ‘sphere of simple circulation or of exchange of commodities, which furnishes the “Free-trader vulgaris” with his views and ideas’.
10 Ludwig von Mises (1949 [1996]), pp. 203^4-. For an early discussion of the impossibility of calculating value in its own terms but only in ratios of exchange between things, see A.R. Jacques Turgot (1769 [1919]), p. 96.
11 Known to economists as consumer surplus. Note how this notion of surplus, first suggested by Marshall in his Principles (1890), although 50 years earlier (1844) the French engineer Jules Dupuit described the concept, quickly moves from a material basis that it had in classical political economics (taking the form of corn or other material goods that society produces over and above the levels necessary to replenish the stocks consumed during the production period) to a purely subjective one in neoclassical theory (where a mere increase in Jack’s desire for something boosts his consumer surplus, even though nothing extra was actually produced).
12 Note that the logic here is similar to that of English auctions: the winner pays a price slightly above the valuation of the second keenest bidder but below his/her own. In ‘normal’ markets (as opposed to auctions where only one unit is usually for sale), it is the least keen buyer whose appraisal of the last unit determines the price at which all units will sell. However, there is a condition for this: that competition prevents sellers from charging different prices for different units. For if the seller could sell lemons at higher prices to Jack than to Jill, the ‘law of one price’ implied here will not hold. Competition usually enforces that ‘law’ simply because if Jack got whiff of the fact that Jill buys lemons more cheaply, he could always ask her to buy some for him too (and pay her a small premium for the service). So, as long as the seller cannot stop re-selling (i.e. the establishment of a secondary market), one price will emerge and it will reflect the lowest marginal valuation (that is, Jill’s valuation of the marginal, or last, lemon). W. Stanley Jevons in his The Theory of Political Economy (1879, p. 99) suggested the law of one price, or ‘The Law of Indifference’ as he called, i.e. 'in the same open market, at any one moment, there cannot be two prices for the same kind of article’ (emphasis in the original). This law is ‘one of the central pivots of the theory’.
13 Consider: ‘To be “on the margin” has implied exclusion from “the centre”. But social, political and economic relations which bind peripheries to centres, keep them together in a series of binary relationships, rather than allowing complete disconnection. In this way, “margins” become signifiers of everything “centres” deny or repress; margins as “the Other” become the condition of possibility of all social and cultural entities’. Shields, 1991, p. 276.
14 The young abbé Ferdinando Galiani in his Della moneta (1751) described value as a ratio of utility and scarcity: ‘Value, then, is a ratio (ragione), and this ratio is composed of two ratios, the names thereof I express with utility (utilitci) and scarcity (rarita). (...) It is obvious that the air and the water, which are elements extremely useful for human life, have no value whatsoever, because they lack scarcity. On the contrary, a small bag of sand from the shores of Japan would be a rare thing, but since it has no particular utility, it would have no value.’ (Gaiiani 1751 [1803] Voi j|{ at p. 59.) Gaiiani was closer to the subjectivists but he saw fatica (labour) as the main source of scarcity.
Î5 Classical authors, of course, did not reject the importance of utility. But they did not see it as a determinant of value. Adam Smith spoke of the water and diamond paradox: ‘Nothing is more useful than water: but it will purchase scarce any thing; scarce any thing can be had in exchange for it. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it’ (Wealth of Nations, (1776 [1981]) Book 1. ch JV pp. 44-5). Ricardo wrote ‘Utility then is not the measure of exchangeable value, although it is absolutely essential to it.’ (Ricardo (1817/1819/1821 [1951]), p. 11). Marx gives short shrift to utility as a measure of value in the beginning section of Capital, Vol. 1 (1867 [1909], p. 46); ‘The utility of a thing makes it a use value. But this utility is not a thing of air. Being limited by the physical properties of the commodity, it has no existence apart from that commodity. A commodity, such as iron, com, or a diamond, is therefore, so far as it is a material thing, a use value, some' thing useful. This property of a commodity is independent of the amount of labour required to appropriate its useful qualities. (...) Use values become a reality only by use or consumption: they also constitute the substance of all wealth, whatever may be the social form of that wealth. In thé form of society we are about to consider, they are, in addition, the material depositories of exchange value’. He also makes the observation in a footnote that ‘In English writers of the 17th cenftiry we frequently find “worth” in the sense of value in use, and “value” in the sense of exchange value This is quite in accordance with the spirit of a language that likes to use a Teutonic word for the actual thing, and a Romance word for its reflexion’.
16 See for example Senior ( 1836, p. 138) ‘if all the commodities used by man were supplied bv nature without any intervention whatever of human labour, but were supplied in precisely the same quantities as they now are, there is no reason to suppose either that they would cease to be valuable, or would exchange in any other than their present proportions’. Note also that the first edition of Walras, Elements d’économie politique pure, 1874, was simply an exchange model with no production. The most extreme case of this inversion is the entry by J, Trout Rader in The New Palgrave (Rader 1987).
17 In the case where the Internet makes it possible to distribute an infinite number of copies at zero cost to the producer (i.e. endless downloads), one would expect that the utility of the last available copy of the particular video game will tend to zero. Then, its price would tend to zero too. But this not what we observe? Video game producers, for this reason, strive for ways either to stop frae downloads or to create online games which can only be played by logging on to some website. In the latter case, the software for playing the game is downloadable free of charge but access to the online site comes at a price. Which price? According to the Marginalists, the price is given by the utility of access to the least motivated (or marginal) player.
18 See Book V, Chapter II, § 1 of Alfred Marshall ( 1890). Principles of Economics. This example was there from the very first edition (at p. 390). Behind the vivid example lies, of course, a mathematical theory of differential calculus. In Note XII of the Mathematical Appendix he provides the necessary mathematics: ‘If, as in Note X., v be the discommodity of the amount of labour which a person has to exert in order to obtain an amount x of a commodity from which he derives a pleasure u, then the pleasure of having further supplies will be equal to the pain
c .. . , du dv
of getting them when _ ¡= — .
dx dx ,
du du .
If the pain of labour be regarded as a negative pleasure; and we write U == -v; then — + — U *
dx dx
i.e. u+U = a maximum at the point at which his labour ceases’. A similar analysis was provided by Jevons in his Theory of Political Economy, 1871 (Chapter 5, Theory of Labour).
19 That is, the more units of X we have the less utility we get from our last (or oui' marginal) unit of X*
20 Note the hidden assumption here: every dollar corresponds to the same amount of utility, irrespective of how many dollars Jill has. This is, clearly, too restrictive. Surely, the richer (or poorer) you are the different your subjective valuation of your last penny. However, it is not too hard, with a little mathematical wizardry, to correct for this. Since nothing much changes in the essence of % arguments here, we shall skip such complications.
?1 Those unfamiliar with utility considerations may ask: Why would Jill buy this unit when she gets the same utility as dis-utility? This is no different from saying that you are prepared to pay up to $300 thousand for an apartment and then find out that the lowest price the seller is willing to accept is ... $300 thousand. Then, you buy it at that price.
■yj The formal proof is as follows: Let Jill’s utility from X and Y be given by the function U=U(X, Y). Her total expenditure on X and Y must be such that the money in her pocket, M, must equal her expenditure on X and Y : M=pxX+piY. Thus, Jill is looking for the combination of quantities (X,Y) that will maximise U within her budget. This is, mathematically, equivalent to maximising without any constraints the function U(X,Y)+A.(M -pxX+pYY), where A is a mere constant (known as the Lagrange multiplier). Differentiating the above function subject to X and Y, and setting these derivatives equal to zero, respectively yields: MUX = Xpxand MUy = XpY. Dividing the first equation by the second we get this new version of the equimarginal principle: MUx/MUy = px/pY, which is equation (6.1) above. This is the famous Gossen’s second law, first proposed 20 years before the Marginalist revolution by Hermann Heinrich Gossen in his Entwicklung der Gesetze des menschlichen Verkehrs und der daraus fließenden Regeln für menschliches Handeln (1854). It appeared also in Jevons (1871). The usual formulation is that the ratio of marginal utility divided by the price of each good is the same across all goods.
23 For a detailed critique of utility calculus and the claim that rationality is synonymous with a capacity for utility maximisation, see Varoufakis (1998), Chs 3 and 4 in particular.
24 This is no exaggeration. The hapless Gossen put Schiller’s Ode to Joy at the beginning of his 1854 book, while Walras in 1905 asked his friends to propose him for the Nobel Peace Prize (See Sandmo (2007). He complained later to a friend that Ted Roosevelt ‘m’a soufflé le prix Nobel’ (snatched the Nobel prize from me).
25 Or perhaps Beethoven’s ninth. See the previous note on Gossen.
26 Hayek (1945).
27 That has been established quite early on by mercantilist writers. See in particular Jean Bodin (1568 [1934]). Also O’Brien (2000).
28 Hayek 1976.
29 This point was made by Joan Robinson, 1971, pp. 4—6.
30 See Radford (1945).
31 There must have been at least a few prisoners who thought that there was something slightly amiss with the sight of hundreds of officers and privates indulging in profiteering, under the watchful eye of Nazi guards, and not too far from other camps where countless less privileged skeleton-like prisoners were queuing up to enter the gas chambers. Arbitrage in the midst of the most crucial conflict humanity has ever staged against the forces of genuine evil may boost utility and be pretty disgusting at the same time.
32 Prisoners who, against their better judgement, would sell their food rations for more cigarettes.
33 In Marx’s mind, a society that has overcome scarcity and reached a condition of plenty is one in which: ‘nobody has one exclusive sphere of activity but each can become accomplished in any branch he wishes; society regulates the genera! production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticise after dinner ... without ever becoming hunter, fisherman, herdsman or critic’. Karl Marx and Friedrich Engels. The German Ideology (1845 [1932] [1998]).
34 The manna from heaven metaphor was evoked by C.E. Ferguson in his best-selling textbook Microeconomic Theory. Goods fall like m different types of manna from heaven on each trader’s parcel of land (Ferguson 1966, p. 354).
.35 Though an embryonic labour market emerged (usually some unlucky person willing to perform laundry services at two cigarettes a garment), the POW camp was as close to a pure exchange economy as it is possible to imagine.
-6 Note that this is precisely the same problem as the difficulty with different degrees of capital utilisation intensity in the economy’s different sectors first encountered by David Ricardo (and pointed out by Thomas Robert Maithus) (see Chapter 3, Section 3.4) and then again by Karl Marx who realised that his theory of value lacked consistency when different sectors or firms were characterised by a different organic composition of capital (see Chapter 5, Section 5.4).
37 Knut Wicksell (1901 [1934]).
Note that this resonates perfectly with all three incarnations of the equi-marginal principle; equations (6.5) and (6.1): The ratio of marginal utilities (from supplying capital) equals its relative price. In (6.1) the relevant exchange was units of X and Y; in (6.3) it was the labour required to clean someone else’s shirt in exchange for 2 teabags; and in (6.5), as interpreted by Wicksell here, it is monetary units of capital invested for units of monetary capital saved.
39 Suppose that, for some unspecified reason, capital has become scarcer than labour. Then the interest rate will rise. This condition means that all the firms and branches of production in the economv must simultaneously use a more labour intensive (and thus a less capital intensive) production technique. Moreover, this rate of substitution must be common to all firms.
40 The book was originally published in French in 1838 under the title Recherches sur les principes mathématiques de la théorie des richesses. See Cournot (1838 [1897]) Chapter VII (pp. 79 -89) for the relevant passage.
41 We say ‘partly’ because Cournot’s scheme, as pointed out earlier, requires that firms do not set prices and output, but only output. This led to the famous Bertrand critique who raised '(u}ne objection péremptoire’ against Cournot’s assumption. (Bertrand (1883), p. 503).
42 For more on this, see Hargreaves-Heap and Varoufakis (2004).
43 The original idea was to preserve Jeremy Bentham’s principle of the greatest utility for the largest number of people (An Introduction to the Principles of Morals and Legislation, 1781, influenced by Cesare Beccaria’s Of Crimes and Punishments (1764) where the principle appears as ‘the greatest happiness for the greatest number’ (la massimafelicità divisa nel maggior numéro). Beecaria (1764 [1768]) p. 2 (emphasis in the original) However, Bentham’s principle was highly charged politically, since it allowed for comparisons between the utility the ultra-rich derive from their last dollar with the utility of the poorest from an additional dollar. Assuming diminishing marginal utility (which is necessary for the Marginalist calculus to make sense), this comparison led to a simple policy recommendation. Take the last dollar of the rich and give it to the poor, for this redistribution will increase average or social utility. To eradicate such a political implication, Marginalists abandoned the idea that Jill’s utility could be compared to Jack’s. Utility, therefore, became a private metric, or variable, which could not be compared across persons. (See Varoufakis (1998), chs 2, 3 & 4). While this move de-radicalised the calculus of utility, it killed off any chance Marginalism had to define the common good in an analytically defensible manner. Kenneth Arrow’s 1953 theorem that has come to be known as the impossibility Theorem put the final nail in that coffin (for an account, see Varoufakis, 1998, chs 8,9 & 10).
44 Notably, Mises, (1922 [1951]); Hayek 1935; Schumpeter, 1942. For a sympathetic view sec Boettke ( 1998).
45 According to anthropologist Evans-Pritchard, the Azande (first mentioned in Chapter 1) do not distinguish between the present and the future. In their mindset, one’s future health and happiness depend on future conditions that are regarded as already existing. Consequently it is believed that the mystical forces which produce those conditions can be tackled here and now. When the soothsayer predicted ominously that a man would fall ill in the near future, it was as if his illness was already present, his future already incorporated into present time. (Evans-Pritchard {1976 [ 1937}}, In a later study, Evans-Pritchard reports on another people, the Nuer, who have no equivalent for the word time. They cannot speak of it as something that passes or that can be either saved or wasted. Events follow a logical order but are not controlled by an abstract system. It seems that neoclassicism does possess a lineage. (Evans-Pritchard (1940)).
46 Elsewhere it has been argued that neoclassicism’s discursive power is, in fact, enhanced by its absurdity. See Yanis Varoufakis and Christian Arnsperger (2010).
47 It is useful to note here that Adam Smith, the patron saint of free market economic thinking, never used the term demand and supply, instead he referred to supply to demand. See Aspromourgo» 2009.
48 Indeed, Kenneth J. Arrow and Frank H. Hahn usher in the chapter on increasing returns in their book General Competitive Analysis (Arrow and Hahn 1971, p, 169) with the following lines from Milton’s Paradise Lost: ‘A gulf profound, as that Serbonian bog | Betwixt Damiata and mount Casius old, i Where armies whole have sunk’.
49 Walras (1874-1926 [1954]).
50 We are referring of course to the Walrasian deus ex machina, the fictitious announcer ot pnce>, whom Walras calls crieur and who is mistranslated into English as the ‘auctioneer’ but who dofo not perform an auction.
51 This the process of ‘groping’ or tâtonnement.
52 Note that if out-of-equilibrium trading were allowed between rounds, every transaction would invalidate the previous round’s information gathered by the program (as those who buy at the out-of-equilibrium prices will reduce their demand in the next round in ways that the program cannot anticipate). We would have ‘false trading’. This is no different from the problem that Cournot hit upon in 1838, which he ‘solved’ by assuming myopics firms. Walras’ solution was to ban time; just like John Nash Jr did in 1950 in order to prove his remarkable theorems about the Nash equilibrium in non-cooperative games and the theorem according to which there exists a unique solution to the Bargaining Problem, We return to the significance of Nash in Chapter 8. Hargreaves-Heap and Varoufakis (2004) present the theorems mentioned above is some detail.
53 Time and neoclassical price theory, as we have already shown, are like oil and water: they cannot mix. But what of space? If spatial distance is allowed between firms, and consumers are spread out over that distance, then some firms are closer to some consumers and, in principle, can exercise a modicum of market power over them. For example you may be prepared to pay a little more at the local store rather than travel to the nearest supermarket. But this means that distance is inconsistent with perfect competition since it contradicts the assumption of zero power over prices. How does neoclassicism respond to that? - by assuming distance away. In short, in its model of capitalism it is as if all firms and all consumers are living on a pin’s head, or on a proton to be more precise. And since time has also been reduced to a single moment, the space-time continuum is but a point,
54 Note that the mathematics of the original Walrasian General Equilibrium left much to be desired. ‘Counting equations and unknowns’ did not provide a solution. It was the mathematicians and economists such as Abraham Wald, Karl Schlesinger and John von Neumann of the Vienna mathematical Colloquium who salvaged mathematical respectability from the Walrasian system.
55 Okonogi (2008); or as The Telegraph put it in his obituary (14 Dec 2009) ‘he became disillusioned with Chicago where, even in the middle of the Depression, finer economic principles seemed to matter more than the dole queues’. Telegraph (2009).
56 Marx's phrase from The Manifesto of the Communist Party, by Karl Marx and Friedrich Engels, (1848 [1998], p. 38).
57 Here we borrow Joseph Schumpeter’s famous term from his Capitalism, Socialism and Democracy. (1943 [1994], Chapter VII “The Process of Creative Destruction”).
58 Sraffa, (1960), p.v,
59 But, for reasons already explained, end up creating single-person models as a price for retaining real time within their analysis.
60 The quotation comes from Marginalist Chicago economist, and 1982 Nobel Prize winner, George Stigler (1911-91). It was quoted in Clotfelter (1997), p. 95.
61 Alfred Marshall tried to steer a middle course. He focused on a single firm, which he thought of as representative of the average capitalist enterprise. This representative firm would embody the normal behaviour of every firm in the economy. L ikewise, the industry to which the firm belonged was to be taken as the representative industry which he evoked to represent the behaviour of the whole economy. Thus, Marshall teetered on the edge of Marginalism, struggling not to fall headlong into the neoclassical, Walrasian paradigm. He understood the centrality of productivity increases, of increasing returns, of time. Alas, his Marginalism left him nowhere to turn to and he ended up sitting on the proverbial fence incapable of turning back to classical political economics and unwilling to join the rampant neoclassicists.
62 The strategy is simple: first, they define preferences statically and assume that they are: (a) impervious to private experience (i.e. that what Jill does does not affect what she craves) and (b) independent of other people (i.e. that what Jack feels or does has no direct effect on Jill’s preferences). Then, they define as ‘special cases’ situations where (a) is relaxed (they call these endogenous preferences) or where (b) is ‘violated’ (they refer to interaction between Jill’s preferences and Jack’s utility/actions as externalities). Some play around with Marginalist calculus that permits departures from (a) and (b) before recoiling back (in horror at the impossible indeterminacy of the mathematics) to the ‘standard model’ where (a) and (b) are restored. In effect, typical features of human behaviour are defined as ‘special cases’ and the most extreme special case (a ‘static’ Jill bleached of all sociality and denied anything we would recognise as human psychology) is presented as the ‘standard model’. And all this because Marginalism cannot handle the mathematical complexity unleashed by real temporal change.
63 Suppose Jill is indifferent between basket X (2 kg of coffee) and basket Y (1 kg of tea). Then her preferences are convex if there exists a third basket Z combining some coffee (<2 kg) and some tea (<] kg) that is equally desirable to X. Such convexity is indispensable for the Marginalist price theory of equation (6.1) since, without it, the ratio of marginal utilities on the right-hand side of that equation is indefinable. Similarly with production theory: if the firm produces 100 widgets either by utilising a combination X of machines and labour (e.g. 1 machine and 10 person hours) or combination Y (e.g. 3 machines and 2 person hours), there must also exist an in-between combination (e.g. 2 machines and 5 person hours) that also produces 100 widgets. If not, no Marginalist theory of profit and wages is forthcoming. Marginalist price theory, therefore, requires that goods and factors of production are seen as infinitely substitutable by their ‘consumers’ (consumers and firms respectively) along a non-linear, convex indifference cw've first posited by Edgeworth (see Box 6.5).
64 For a complete account, see Hargreaves-Heap and Varoufakis (2004).
65 The very same ‘escape’ route was forced upon thinkers of a Marginalist disposition again and again. A celebrated example is that of John Nash Jr and his bargaining solution: The only way he could prove the existence of a uniquely rational agreement between bargainers was to abstract from any actual negotiations that, in reality, would yield the agreement. In Chapter 8 we shall be arguino that this ‘solution’ by the young Nash changed the course of post-war economics. Until then, the interested reader can turn to Chapter 4 in Hargreaves-Heap and Varoufakis (2004) for an account of Nash’s theorem.
66 There were 11 letters in all exchanged by the two men between 1873 and 1875. See Jaffé, 1965. See also Kolm (1968).
67 Walras wrote: ‘..we have proceeded in opposite directions. You start from monopoly to arrive at indefinite competition. I thought 1 had to start from indefinite competition, which I consider to be the general case, to arrive at monopoly, which seems to be a special case, This wpy k more difficult, but 1 believe it to be more beautiful and more complete’.