How to Succeed in Economics?

Peter Leeson, Dan Klein, Peter Boettke and Frederic Sautet, and Peter Boettke have been discussing how to advance Austrian economics.

I find of particular interest the claim that, "Most economists will have no idea what you're talking about if you tell them you're working on 'capital theory'".

Against the Washington Consensus

The following worry that "third rank" economists and "cheerleaders" are insufficiently aware of the downside of "free trade":

• William J. Baumol (2005). "Errors in Economics and Their Consequences", Social Research, V. 72, N. 1 (Spring): 169-194.
• Alan S. Blinder (2007). "Offshoring: The Next Industrial Revolution?", Foreign Affairs (March/April)
• David Wessel and Bob Davis (2007). "Pain from Free Trade Spurs Second Thoughts: Mr. Blinder's Shift Spotlights Warnings of Deeper Downside", Wall Street Journal (28 March): A1
• Hat Tip: Max Sawicky
• Dani Rodrik (2007). "The Cheerleaders' Threat to Global Trade", Financial Times (27 March). (Hat tip to Christopher Hayes)
• Paul A. Samuelson (2004). "Where Ricardo and Mill Rebut and Confirm Arguments of Mainstream Economists Supporting Globalization", Journal of Economic Perspectives, V. 18, N. 3 (Summer): 135-146
• Joseph E. Stiglitz (2000). "What I Learned at the World Economic Crisis: The Insider", The New Republic. (I couldn't find an online link for this at TNR's site.)

Not to mention, myself.

The Unconscious Is Structured Like A Language

I find Zizek difficult to read in large doses. For instance, I did not even make it all the way through this. I don't think I retain much from the book containing the following:

"So what is hegemony? Those who still remember the good old days of Socialist Realism are well aware of the key role played by the notion of the 'typical' in its theoretical edifice: truly progressive Socialist literature should depict 'typical' heroes in 'typical' situations. Writers who, for example, presented a predominately bleak picture of the Soviet reality were not accused simply of lying - the accusation was that they provided a distorted reflection of social reality by focusing on phenomena which were not 'typical', which were sad remainders of the past, instead of focusing on phenomena which were 'typical' in the precise sense of expressing the deeper underlying historical tendency of the progress towards Communism. A novel which presented a new Socialist type of man who dedicated his life to the happiness of all the people, of course, depicted a minority phenomenon (the majority of people were not yet like that), but none the less a phenomenon which enabled us to identify the truly progressive forces active in the social situation.

Ridiculous as this notion of the 'typical' may sound, there is a grain of truth in it - it lies in the fact that each apparently universal ideological notion is always hegemonized by some particular content which colours its very universality and accounts for its efficiency. In the present rejection of the social welfare system by the New Right in the USA, for example, the very universal notion of the present welfare system as inefficient is contaminated by the more concrete representation of the notorious single African-American mother, as if social welfare were, in the last resort, a programme for single black mothers - the particular case of 'the single black mother' is silently conceived of as 'typical' of the universal notion of social welfare, and what is wrong with it... The same goes for every universal ideological notion: one always has to look for the particular content which accounts for the specific efficiency of an ideological notion. In the case of the Moral Majority campaign against abortion, for example, the 'typical' case is the exact opposite of the (jobless) black mother: a successful and sexually promiscuous career woman who gives priority to her professional life over her 'natural' assignment of motherhood (in blatant contradiction to the facts, which tell us that the great majority of abortions occur in lower-class families with several children).

The specific 'twist', the particular content which is promulgated as 'typical' of the universal notion, is the element of fantasy, of the phantasmic background/support of the universal ideological notion - in Kant's terms, it plays the role of 'transcendental schematism', translating the empty universal notion into a notion which directly relates and applies to our 'actual experience'. As such, this phantasmic specification is by no means a mere insignificant illustration of exemplification: it is on this of which particular content will count as 'typical' that ideological battles are won or lost. To go back to our example of abortion: the moment we perceive as 'typical' the case of abortion in a large lower-class family unable to cope economically with another child, the perspective changes radically...

[Footnote] Another name for this short circut between the Universal and the Particular, by means of which a particular content hegemonizes the Universal, is, of course, suture, the operation of hegemony 'sutures' the empty Universal to a particular content. For that reason, F.W.J. Schelling must be considered the originator of the modern notion of critique of ideology: he was the first to elaborate the notion of 'false' unity and/or universality. For him, 'evil' lies not in the split (between the Universal and the Particular) as such but, rather, in their 'false'/distorted unity, that is, in a Universality that effectively privileges some narrow particular content and is impenetrably 'anchored' in it. Schelling was thus the first to elaborate the elementary procedure of the critique of ideology: the gesture of discerning beneath the appearance of neutral universality (say, of 'human rights'), the privileged particular content (say, white upper-middle-class males) which 'hegemonizes' it...[End Footnote]

'Single unemployed mother' is thus a sinthome in the strict Lacanian sense: a knot, a point at which all the lines of the predominant ideological argumentation (the return to family values, the rejection of the welfare state and its 'uncontrolled' spending, etc.) meet. For that reason, if we 'untie' this sinthome, the efficiency of its entire ideological edifice is suspended. We can see now in what sense the psychoanalytic sinthome is to be opposed to the medical sympton: the latter is a sign of some more fundamental process taking place on another level. When one claims, say, that fever is a symptom, the implication is that we should not cure only the sympton, but attack its causes directly. (Or, in the social sciences, when one claims that adolescent violence is a sympton of the global crisis of values and the work ethic, the implication is that one should attack the problem 'at its root', by directly addressing problems of the family, employment, etc., not only by punishing the offenders.) The sinthome, in contrast, is not a 'mere sympton', but that which holds together the 'thing itself' - if one unties it, the 'thing itself' disintegrates. For that reason, psychoanalysis actually does cure by addressing the sinthome.

This example makes it clear in what sense 'the universal results from a constitutive split in which the negation of a particular identity transforms this identity into the symbol of identity and fullness as such': the Universal emerges from the Particular when some particular content starts to function as the stand-in for the absent Universal - that is to say, the universal is operative only through the split in the particular. A couple of years ago, the English yellow press focused on single mothers as the source of all the evils of modern society, from the budget crisis to juvenile delinquency - in this ideological space, the universality of the 'modern social Evil' was operative only through the split of the figure of 'single mother' into itself in its particularity and itself as the stand-in for the 'modern social Evil'. Owing to the contingent character of this link between the Universal and the particular content which functions as its stand-in (i.e. that fact that this link is the outcome of a political strugle for hegemony), the existence of the Universal always relies on an empty signifier: 'Politics is possible because the constitutive impossibility of society can only represent itself through the production of empty signifiers.' Since 'society doesn't exist', its ultimate unity can be symbolized only in the guise of an empty signifier hegemonized by some particular content - the struggle for this content is the political struggle. In other words, politics exists because 'society doesn't exist': politics is the struggle for the content of the empty signifier which represents the impossibility of Society. The worn-out phrase 'the politics of the signifier' is thus fully justified: the order of the signifier as such is political and, vice versa, there is no politics outside the order of the signifier. The space of politics is the gap between the series of 'ordinary' signifiers (S2) and the empty Master-Signifier (S1)..." -- Slavoj Zizek (1999), The Ticklish Subject: The Absent Centre of Political Ontology, Verso: 174-177, 180.

Depreciation of the One Hoss Shay

1.0 Introduction
Some economists have mistakenly thought that depreciation is merely a matter of capital goods wearing out:

"One of the advantages of the von Neumann model is that it can handle capital goods without fuss and bother. A nondepreciating capital good simply enters both as input and as output in the corresponding process. If the capital good depreciates 3 per cent per unit of time, 1 unit of the good may appear as input, and 0.97 unit as output." --Robert Dorfman, Paul A. Samuelson, and Robert M. Solow (1958: 382-383)

The above is an incorrect characterization of the von Neumann model. Von Neumann got depreciation right, unlike Dorfman, Samuelson, and Solow in that quotation. (Luigi Pasinetti points out this error.)

2.0 A Three-Period Example
2.1 Production
As an example of the correct calculation of depreciation, consider a machine of constant efficiency that lasts three production cycles. Each cycle takes a year. Table 1 summarizes the Constant-Returns-to-Scale production processes assumed to be in use for this example. The left five columns show inputs applied over the course of the year. The three right-most columns show outputs available at the end of the year. Oil is representative of inputs used up in producing the output, which the machine is an example of fixed capital. Suppose this machine, at whatever age, is only used in producing wheat; it is not used as an input in any production processes other than those shown in Table 1.

Table 1: Three Production Processes

1 New Machine	&	a Barrels Oil	&	l Person Yrs	Produce	1 Quarter Wheat	&	1 One-Year Old Machine
1 One-Year Old Machine	&	a Barrels Oil	&	l Person Yrs	Produce	1 Quarter Wheat	&	1 Two-Year Old Machine
1 Two-Year Old Machine	&	a Barrels Oil	&	l Person Yrs	Produce	1 Quarter Wheat

This data illustrate the phenomenon of joint production. A process exhibits joint production when its output consists of more than one good. Because the von Neumann model is a model of general joint production, it "can handle capital goods without fuss or bother." Capital goods of different ages and history are distinguished as different goods; capital goods differing only in age are not treated as different quantities of identical goods. This is the point Dorfman, Samuelson, and Solow get wrong in the above quote.

A firm can be thought of as using all three of these production processes side by side. The managers of a firm will want to know how much to enter on thier books for old machines of different ages. They will also want to know the rate of (accounting) profits that they are making. The firm's book prices will be such that the firm is making the same rate of profits in all three process:

(1)

(2)

(3)

where:

• p0 is the price of a new machine,
• p1 is the price of a one-year old machine,
• p2 is the price of a two-year old machine,
• pa is the price of a barrel oil,
• pw is the price of a quarter wheat,
• w is the wage, and
• r is the rate of profits.

A little algebra is of interest here. Multiply each of Equations 1, 2, and 3 by the appropriate power of (1 + r) to obtain Equations 4, 5, and 6:

(4)

(5)

(6)

In summing, the prices of old machines drop out:

(7)

Or:

(8)

In the price equations for an input-output system, Equation 8 can replace the system of equations specified in Displays 1, 2, and 3. Suppose the original system can be solved for prices, given the numeraire and, say, the rate of profits. Then the new system can be solved, as well. And the price of old machines does not appear in the system.

One can think about Equation 8 as follows. A wheat-producing firm buys a new machine that lasts for three production cycles. It doesn't make sense in calculating profit to charge the cost of the machine totally at the time it is bought. The later two production cycles make use of the services of the machine. The cost of the inputs for all three cycles should include some part of the cost of the machine. Equation 8 shows how much the machine should contribute to costs of the inputs of each year's production process, where the costs are assessed at the end of the year.

2.2 An Annuity
Consider an annuity, where (equal) payments are made at the end of three consecutive years. If the interest rate is such that the present value of this stream of payments is equal to the price, p0, of the annuity at the start of the first year, Equation 9 must hold:

(9)

where x is the payment made at the end of the year. Summing the terms on the right, one obtains:

(10)

That is, an annuity of:

(11)

paid at the end of three years has a present value of p0.

The charge for the machine at the end of each production cycle, inclusive of profit and depreciation, is then the value of a fixed annuity paid at the end of each production cycle over the lifetime of the machine.

3.0 Generalizations and a Limit
The above analysis is easily generalized to a machine of constant efficiency that lasts for n years. The annual charge is:

(12)

One can also figure out the the price of the machine of constant efficiency at any age as a ratio of the price when new:

(13)

Figure 1 shows this ratio, for various rates of profits, for the above example of a machine that lasts three years. (Sraffa provides a graph for machine that lasts 50 years, and the rate of profits in his example ranges up to 20%.) A machine that lasts forever would have a charge of p0 r. This is a charge only for profit; there is no depreciation in the case of a machine with an infinite lifespan. This conclusion correctly suggests that joint production provides a framework in which to analyze the rent of land.

Figure 1: Dependence of Variation in Capital Value With Rate of Profits

The analysis can also be generalized to consider machines of varying technical efficiency throughout their age. An (industrial) plant might be analyzed as a collection of processes, where each process uses more than one kind of machine. These generalizations lead to more equations being appended to the system, as well as matching prices for machines of distinct ages and history. In principle, if the efficiency of the machines dependes on the history of the machines it is combined with as inputs in the processes, the number of equations can be countably infinite (Roncaglia 1978). The analysis must also be one of the choice of technique, where the technique includes the possibility of junking a machine while processes still remain that can use it. That is, the economic life of a machine may be shorter than its technical life.

It seems to me incredible that conventions for depreciation in practice could be the solutions of the general theory of joint production. One of the world’s foremost experts on the theory of joint production has this to say:

”Every economist knows that there is indeed much arbitrariness in accounting for depreciation or in the prices set for different derivatives from crude oil. Of course, competition always settles the matter somehow, but whereas it was easy – as de Quincey knew ... – to predict the value of shoes produced by a shoemaker in the nineteenth century, it is very difficult to predict on the basis of cost calculations how a modern refinery will recover its costs by setting administered prices for different refined products. Its rate of return for all its processes taken together can in general not deviate much from the rate of profit of the economy, but this observation does not explain how the relative prices of its individual products are set. Is this therefore another area where history must (as in the case of distribution) supplement theory because it is open-ended? The example of public goods as a form of joint social costs proves that there are cases of indeterminancy of possibly growing historical importance, but Sraffa has shown that there is a solution to the problem of the evaluation of joint products that does not require any explicit reference to the subjective elements of demand.” --Bertram Schefold (1989: 32)

The question becomes whether the number of cost-minimizing processes is equal to the number of products in the general case of joint production, except at flukes. I’m not convinced that the answer to this question is in the affirmative.

4.0 Conclusion
Suppose an economist claims that firms maximize profits. And that economist depicts depreciation as a technical datum, not dependent on prices and the rate of profits. Then, that economist has made a mistake in mathematics.

References

• Robert Dorfman, Paul A. Samuelson, and Robert M. Solow (1958). Linear Programming and Economic Analysis, Dover
• Luigi L. Pasinetti (1977). Lectures in the Theory of Production, Columbia University Press
• Alessandro Roncaglia (1978). Sraffa and the Theory of Prices (English translation), John Wiley & Sons
• Bertram Schefold (1989). Mr. Sraffa on Joint Production and Other Essays, Unwin-Hyman
• Piero Sraffa (1960). Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory, Cambridge University Press

Some Other Blogs

• I used Google's translation services to read this explanation of the Cambridge Capital Controversies, titled, "What is wrong with Neoliberalism".
• I thought interesting this comment on the attitude to economics among Cal Tech students. Presumably, given their economics department, some MIT students would not agree.
• This blog has something to say about general equilibrium theory. I haven't formed an opinion here, though the mention of Gödel raises my suspicions.

Hayek and Socialist Calculation

Gabrial Mihalache says that the Socialist Calculation debate is "a sort of Capital Controversies in reverse, on the Left-Right spectrum." I don't know what this is supposed to mean. Perhaps it is a sociological claim that the side presented as winning in the hegemonic discourse, for the next couple of decades, actually lost at the time, I'd like to say, by any rational standard. The caveat is there because Michael Greinecker is much less enthusiastic about Hayek's position on this particular topic. (I've noticed before that Michael and I have divergent views on Hayek, but I do not want to do the work to clarify my position with respect to his.)

One study of this debate I like is David Ramsay Steele's From Marx to Mises: Post-Capitalist Society and the Challenge of Economic Calculation (Open Court, 1992). Steele is clear, I think, that he is only addressing a very small part of Marx's output. And that Mises and Hayek were only attacking complete central planning. Work would need to be done to use their position to attack mixed economies, as in western Europe.

Michal Kalecki, One of the Greatest Economists Ever

Kalecki is probably most famous for having invented the theory of effective demand, as in Keynes' General Theory, prior to and independently of Keynes. I cannot read Polish, so I cannot document this claim. I have read a later 1965 work of Kalecki's, in which he lays out his views on business cycles and the level and the rate of growth of the national income.

But I want to describe another aspect of Kalecki's work. Kalecki demonstrates that at least some of those who advocate Keynesian policy do not think of government as staffed by far-seeing and disinterested philosophers working entirely for the good of society, whatever that may mean. Rather, Kalecki described government policy as refracting conflict within society, including conflict resulting from the divergent interests and views of members of different classes.

For instance, in Kalecki (1967), he analyzed the prospects of governments coming to power in third world developing economies in which representatives of the lower middle class do or do not find themselves serving the interests of big business, in alliance with remnants of the feudal system. Kalecki analyzes, for example, how land reform can be expected to change the balance of class forces.

Apparently that article was of importance in the literature on development economics. But I am more aware of Kalecki (1943). In this article, Kalecki explains why a government in a first world country might be unwilling to maintain full employment through increased deficit spending. Kalecki's explanation has several aspects:

• Full employment policy threatens big business' ability to carry out a capital strike.
• Public spending might start with "objects which do not compete with the equipment of private business, e.g., hospitals, schools, highways", but is unlikely to stop there, and might lead to newly nationalized industries and subsidization of consumption.
• Under full employment, if maintained, '"the sack" would cease to play its role as a disciplinary measure.'

Still governments have been thought for many decades accountable for downswings in business cycles. How can governments manage this tension between the needs to maintain full employment at election time and to maintain the social position of business leaders? Kalecki suggests one can expect large scale spending on armaments, an emphasis on tax cuts (as opposed to increased spending), and the emergence of a political business cycle. Kalecki's observations on political economy might have something to do with, say, United States government policy over later decades.

References

• Kalecki, Michal (1943). "Political Aspects of Full Unemployment", Political Quarterly, V. 14 (Oct.-Dec.): 322-331
• Kalecki, Michal (1965). Theory of Economic Dynamics: An Essay on Cyclical and Long-Run Changes in Capitalist Economy (Second Edition), George Allen & Unwin
• Kalecki, Michal (1967). "Observations on Social and Economic Aspects of 'Intermediate Regimes'", Coexistence, V. 4, N. 1: 1-5

History Needing Revision

I'm fairly sure this is not how it actually happened:

"The next king, I was told, was a priest of Vulcan, called Sethôs. This monarch despised and neglected the warrior class of the Egyptians, as though he did not need their services. Among other indignities which he offered them, he took from them the lands which they had possessed under all the previous kings, consisting of twelve acres of choice land for each warrior. Afterwards, therefore, when Sanacharib, king of the Arabians and Assyrians, marched his vast army into Egypt, the warriors one and all refused to come to his aid. On this the monarch, greatly distressed, entered into the inner sanctuary, and, before the image of the god, bewailed the fate which impended over him. As he wept he fell asleep, and dreamed that the god came and stood at his side, bidding him be of good cheer, and go boldly forth to meet the Arabian host, which would do him no hurt, as he himself would send those who should help him. Sethôs, then, relying on the dream, collected such of the Egyptians as were willing to follow him, who were none of them warriors, but traders, artisans, and market people; and with these marched to Pelusium, which commands the entrance into Egypt, and there pitched his camp. As the two armies lay here opposite one another, there came in the night, a multitude of field-mice, which devoured all the quivers and bowstrings of the enemy, and ate the thongs by which they managed their shields. Next morning they commenced their fight, and great multitudes fell, as they had no arms with which to defend themselves. There stands to this day in the temple of Vulcan, a stone statue of Sethôs, with a mouse in his hand, and an inscription to this effect - 'Look on me, and learn to reverence the gods.'" --Herodotus, The History, Book 2, Sect. 141

Neoclassicalism as Lysenkoism in the U. K.

I previously mentioned Fred Lee's work in the history of heterodox economics. In one of those papers, he and a co-author predicted that the implementation of the Research Assessment Exercise (RAE) would make British economics less diverse and less tolerant of non-mainstream economics. Lee (2007, "The Research Assessment Exercise, the State and the Dominance of Mainstream Economics in British Universities", Cambridge Journal of Economics, V. 31: 309-325) has recently confirmed the validity of this prediction.

RAE Ranking Levels

5*	Level of international excellence in more than half of the research activity submitted and attainable levels of national excellence in the remainder
5	Levels of international excellence in up to half of the reseach activity submitted and attainable levels of national excellence in virtually all of the remainder
4	Levels of national excellence in virtually all of the research activity submitted, showing some evidence of international excellence
3a	Levels of national excellence in over two-thirds of the research activity submitted, possibly showing some level of international excellence
3b	Levels of national excellence in more than half of the research activity submitted
2	Levels of national excellence in up to half of the research activity submitted
1	Levels of national excellence in virtually none of the research activity submitted

The RAE impacts how research funds are allocated to British universities and, indirectly, hiring and promotion decisions. Lee found that publication in the "Diamond List" of 27 mainstream journals raised a department's ranking. In 1992, many believed that assessors had an unofficial extended list, which included, for example, Kyklos and the Manchester School of Economic & Social Studies. Apparently, though, publication in the journals added in the extended list does not count positively in the RAE ranking. Furthermore, "the lower the department ranking, the greater the percentage" of publications in heterodox economics, history of economic thought, and methodology. Personally, I would be honored to be published, or even cited, in the Cambridge Journal of Economics, the Journal of Economic Issues, the Journal of Post Keynesian Economics, the Review of Political Economy, or the Review of Radical Political Economics.

"Furthermore, in the West, in a climate of intellectual intolerance charmingly reminiscent of Sino-Soviet totalitarianism, all varieties of non-mainstream economics - including Marxism, Post Keynesianism and the 'old' institutionalism - have systematically been driven out of university departments in several countries in the 1980s and 1990s. Contrary to the more pluralistic state of affairs in the 1950s and 1960s, non-mainstream economists are increasingly rare in economics departments in Britain, the United States, Germany and elsewhere. Against such developments, 'A Plea for a Pluralistic and Rigorous Economics' was signed by 44 leading economists - including four Nobel Laureates - and published in the May 1992 edition of the American Economic Review. This plea included the words:

We the undersigned are concerned with the threat to economic science posed by intellectual monopoly. Economists today enforce a monopoly of method or core assumptions, often defended on no better ground than it constitutes the 'mainstream'. Economists will advocate free competition, but will not practice it in the marketplace of ideas."

-- Geoffrey M. Hodgson (1999). Economics & Utopia, Routledge: 263.

Non-Communication

Mark Thoma has put up a couple of posts defending mainstream economics from critics. Or, perhaps, he is writing about methodology. It's all at a very abstract level of generality.

My favorite commentator in these threads is "piglet". But then I've described myself on occasion as a "bear of very little brain".

Courageous Karl Liebknecht

"Once the war broke out, Social Democrats - German, French, and Austrian (Lenin did not attend the Brussels meeting and disassociated himself from his government's actions) - declared their support of the war and of their governments by voting for war appropriations... On 30 October 1914, a Swiss newspaper, the Berner Tagwacht, carried a 'Declaration' signed by Clara Zetkin, Franz Mehring, Karl Liebknecht and Rosa Luxemburg. In one brief paragraph they disclaimed their allegiance to the official party line and assured foreign comrades that they, like many other German Social Democrats, held a view on 'the war, its origin and character' different from that of the SPD." - Elzbieta Ettinger (1986). Rosa Luxemburg: A Life, Beacon Press: 194.

"Karl Liebknecht went to Liège in October, met with the secretary of the International, Huysmans, saw the devastation wrought by his countrymen, and departed saying: 'Now I know what has happened and I shall do my duty.' In December he voted, a lone voice, against renewal of war appropriations. Contacts were made with antiwar groups abroad with the vague hope that the carnage might somehow still be stopped." -- ibid: 195 (my emphasis)

"The Spartacists put enormous effort into the May Day celebration in 1916. Luxemburg wrote the leaflets distributed in factories, and 10,000 antiwar demonstrators gathered in Potsdam Square. The demonstration was led by Liebknecht, dressed up in a soldier's uniform, shouting, 'Down with the war! Down with the government!' Luxemburg marched at his side. Arrested on the spot, he was stripped of his [parliamentary] immunity, and was sentenced to four years and one month of penal servitude." -- ibid: 208

Interest Rate Still Unequal to Marginal Product of Capital (Part 2/2)

4.0 Wicksell Effects
The model from the previous post shows how the value of output and of capital per worker depend on the interest rate. In effect, I have traced out a parametric specification of a continuously differentiable aggregate neoclassical production function q(k), where both output and capital per capita are specified in common units. This production function can be differentiated:

(13)

The numerator is easily found:

(14)

The denominator is more interesting. From the chain rule for differentiation, one obtains:

(15)

The first term on the right shows the variation in the value of capital by a change in the optimal technique. This variation is known as the real Wicksell effect. The optimal technique changes with the interest rate, although the real Wicksell effect is evaluated at a given value of the interest rate. The second term on the right hand side of Equation 15 shows the variation of the value of capital with changes in the interest rate, given the technique. This term is the price Wicksell effect.

Wicksell effects can be calculated for this particular model. The price Wicksell effect is easily found from Equation 7:

(16)

For this simple model, the price Wicksell is always positive:

(17)

The determination of the real Wicksell effect requires the calculation of the partial derivative of the value of capital with respect to its first argument, the optimal process length:

(18)

Evaluating for the optimal process length, as given by Equation 10, this partial derivative is considerably simplified:

(19)

Suppose price Wicksell effects were zero, which they are not. Then one would have for the marginal product of capital in this model:

(20)

But, since price Wicksell effects are positive, the denominator in Equation 13 exceeds the real Wicksell effect. Consequently, the marginal product of capital is, in equilibrium, less than the interest rate in this model:

(21)

Because of non-zero price Wicksell effects, the marginal product of capital is generally unequal to the interest rate.

One generally cannot place any restriction on the direction of (price or real) Wicksell effects. They may be either positive or negative. Austrian-Wicksell flow-input flow-output models and the Sraffian analysis of the choice of technique are two examples of classes of models I consider reasonably general.

Suppose one were only willing to consider model solutions in which the real Wicksell effect is negative. That is, one considers variations in the optimal technique with changes in the interest rate. One assumes that the value of the newly selected capital goods, evaluated at non-varying prices, is such that a higher interest rate is associated with a lower capital intensity. If one does make Burmeister's arbitrary regularity assumption, Chmpernowne's chain index for capital is well-defined. This chain index is found by adding up real Wicksell effects from an interest rate of zero to the interest rate in which one is interested. Using this measure and a corresponding chain index for output, the equilibrium interest rate is equal to the marginal product of capital. One should note that the wage is no longer equal to (discounted) marginal product of labor for these measures. Nor are they empirically observable. I don't think that this approach is all that interesting; its only purpose seems to be to defend the failed aggregate neoclassical model.

Notice that the above analysis uses a smooth aggregate production function. In the model, the value of all capital goods is easily aggregated in the same units of measurement as the single consumption good. The value of capital is a well-defined quantity. All firms are identical, and net output consists of a single commodity. The modeling of production makes it apparent that the inequality between the marginal product of capital and the interest rate is not driven in other models by adopting a discrete model of production. The inequality is the result of non-zero price Wicksell effects.

References

• Ahmad, Syed (1991). Capital in Economic Theory: Neo-Classical, Cambridge, and Chaos, Edward Elgar
• Baldone, Slavatore (1984). "From Surrogate to Pseudo Production Functions," Cambridge Journal of Economics, V. 8: 271-288
• Bidard, Christian (2000). "Wicksell and Douglas on Distribution and Marginal Productivity," in Critical Essays on Piero Sraffa's Legacy in Economics (edited by H. D. Kurz), Cambridge University Press
• Burmeister, Edwin (1987). "Wicksell Effects", in The New Palgrave (edited by J. Eatwell, M. Milgate, and P. Newman), Macmillan

Interest Rate Still Unequal to Marginal Product of Capital (Part 1/2)

1.0 Introduction
I thought I would try to explain again why, in equilibrium, the interest rate is typically unequal to the marginal product of capital. This explanation is based on a model with a different structure than in a previous explanation.

Sometimes you will find, in textbooks and journal articles, claims that, in equilibrium, the interest rate and the marginal product of capital are equal. You may also find economists who claim to be putting forward disagreggated models. They may include production functions in their models with arguments that include the quantities of individual capital goods. Yet those quantities are measured in numeraire units. Such economists are just making a mathematical mistake.

2.0 The Model
Consider a simple economy in a stationary state whose output consists entirely of wood. A worker plants trees at the start of the process of production, which lasts for t years. No labor is required for the trees to grow or to harvest the quantity of wood, q(t), available at the end of t years. Assume that lengthening this process increases the harvest, that is, q'(t) > 0. Also assume that each additional increment of time increases the output less than the previous increment, that is, q''(t) < 0. (This is stronger than needed.) The production function, on a per worker basis, q(t), is graphed in the upper-right quadrant in Figure 1.

Figure 1: Optimal Length of Production Dependent on Interest Rate

Assume wages are paid immediately to workers. Competitive firms take the wage, w, and the interest rate, r, as given. Suppose the wage was above the present value of output q(t). The firm could either deposit w in a bank at the interest rate or produce wood. No profit-maximizing firm would do the latter if the wage was this high. But if the wage were below the present value of output, firms would expand production upon seeing an opportunity to make pure economic profit. Thus, competition enforces an equality between the wage and the present value of output.

Table 1: Compounding Interest

Number Of Compounding Periods	Value
0
1
2
3
.	.
.	.
.	.
t n

What is the present value of q(t)? The annual rate of interest is 100 r%. Suppose the interest rate is compounded n times per year. By definition, the per period interest rate is 100 (r/n)%. Table 1 shows the effects of compounding the wage. Since the wage is equal to the present value of output, Equation 1 holds:

(1)

Or:

(2)

where:

(3)

Take the limit as gamma increases without bound, with the process length fixed. One obtains the wage for the case of continuous compounding of interest:

(4)

At this point, I have adopted a notation that emphasizes the wage depends on the process length and the interest rate.

Consider a firm producing a stationary state output of q(t). What is the value of the firm's capital at a given point in time? The firm's capital consists of goods in process for producing output from this point until t years in the future. The value of these goods in process is the wages, expended from -t years in the past until the current instant, compounded to that instant:

(5)

This integral is easily solved:

(6)

Or, using Equation 4:

(7)

Notice that the wage and the value of capital satisfy an accounting identity:

(8)

3.0 The Optimal Process Length

The period between planting and harvesting of timber is a choice variable in this model. The firm's managers choose the process length, given the interest rate, r*. From the construction of the so-called factor price frontier, one knows that the optimal technique maximizes the wage. Hence:

(9)

Thus, the optimal length, t*, of the process length is implicitly defined by Equation 10:

(10)

One can also find the optimal process length by equating the marginal return to waiting to the marginal cost of borrowing finance capital for the required time increment, dt. The increased output of extending the length of the process used in production, evaluated at the instant in which output originally becomes available, is q(t + dt) - q(t). The extra charge for interest is q(t) r* dt. Equation 11 follows from the usual equilibrium assumption that marginal returns and marginal costs are equal:

(11)

Taking the limit as dt approaches zero yields Equation 10. It is not an accident that these two derivations give the same result.

The visualization, in Figure 1, of the choice of the process length, is most easily explained by a transformation of Equation 10. Equation 12 is equivalent to Equation 10:

(12)

The given interest rate is measured downward from the origin in Figure 1. The
reciprocal of that interest rate is measured leftward from the origin. The southwest quadrant in the figure shows a hyperbola, which relates the interest rate and its reciprocal. The slopes of the parallel lines extending into the northwest quadrant are the ratio of output per worker (measured upward from the origin) and the reciprocal of the interest rate. From Equation 12, one can see that the derivative of the production function is equal to this ratio for the optimal process length. In terms of the geometry, the lower of the two parallel upward-sloping lines is tangent to the production function.

Propaganda From Landsburg

Michael Greinecker comments on game theory. His post reminds me that I've been meaning to point out some nonsense for a while. One should believe nothing one reads in a Wall Street Journal op ed:

"Competition is often destructive. Everybody knows that. The remarkable exception, enshrined in Smith's enduring metaphor of the Invisible Hand, is that in the presence of free competitive markets, functioning price systems and well-defined property rights, the 'best result' (in a sense that can be defined precisely) does come from everyone in the group doing what's best for himself.

That's not obvious, but it's true. It was proved, as a matter of pure mathematics, by economists like Gerard Debreu, Kenneth Arrow and Lionel McKenzie, beginning around the time Nash was supposedly having that fateful drink. Surely that would have been good enough for Nash, who through all his breakdowns never lost his respect for mathematical reasoning.

In the real world, as opposed to the movie, Nash complemented Smith without supplanting him. The Invisible Hand tells you that good things happen when people compete in free markets. Nash laid the game-theoretic mathematical foundations for figuring out what happens when people compete in other ways. It turns out that without markets, many different things can happen, not all of them good. That means we should have more respect for markets, not less." -- Steven A. Landsburg, (22 February 2002)

Arrow and Debreu did not show that competitive markets lead to the "best result". Their conclusions have nothing to do with what Adam Smith was talking about with his metaphor of the invisible hand. Von Neumann and Morgenstern, not Nash, laid the foundations for game theory. Game theory is not confined to explaining competition outside of "free markets" or "without markets".

Conquering the Worm

Sraffa's Production of Commodities by Means of Commodities is good to think with in examining several issues. One issue is in exploring the misdirections of neoclassical economics, a major theme of this blog. Another issue is what needs to be the case in a society that continually reproduces itself (either simply or on an expanded scale).

Even for economic reproduction, more needs to be reproduced than simply inputs into production. Norms, institutions, conventions, and social knowledge of all sorts are also (re)produced in a capitalist society. This brings us to culture and the sign.

A lot of academics study cultural criticism. Often they read various French thinkers and jesters. Some of these academics may, when they turn to economics, want to resist neoclassicalism. And so they might be interested in exploring Sraffa. I'm never sure what advice Sraffians can give on the topic of the production of consciousness. It seems to me Sraffa carves out a space where such issues can be explored. Part of his point might be how little formal mathematical economics can say about how to fill that space.

I have read a little where some familiar with certain strains of cultural criticism have looked at economics. I think I understand Philip Mirowski to some extent. Other writers (e.g., Ruccio and Amariglio 2003) I may have followed as I read, but retain very little.

I also retain little when I read (translations of) some on their home ground. I have two books by Jean Baudrillard (1975, 1994) on my bookshelf. I'm not sure I even get the jokes in the latter. Maybe I'll try to reread one now that Baudrillard is in the news with his death.

References

• Baudrillard, Jean (1975). The Mirror of Production (trans. by Mark Poster), Telos Press.
• Baudrillard, Jean (1994). Simulacra and Simulation (trans. by Sheila Faria Glaser), University of Michigan Press
• Ruccio, David F. and Amariglio, Jack (2003). Postmodern Moments in Modern Economics, Princeton University Press

Sraffian Prices As Accounting Prices

I want to consider an issue raised by Andrew Kliman in chapter 6 of his new book. As part of his argument for the Temporal Single System Interpretation (TSSI) of Marx, Kliman considers a production period embedded in a discrete time sequence in which prices are changing over the sequence. He considers three cost concepts:

• Historical cost: The sum of the costs over time of the capital goods used in production discounted to the start of the production period.
• (Pre-production) reproduction cost: The cost, at the start of the production period, of producing the capital goods used as input into production.
• (Post-production) replacement cost: The cost, at the end of the production period, of producing the capital goods needed to continue production in the next period.

If profits were evaluated at the end of the production period by comparing output prices to replacement costs, inputs and outputs would be evaluated at the same set of prices. On the other hand, if profits are evaluated at the end of the production period by comparing output prices to reproduction costs, the price of an output can differ from the input cost of that good. Kliman argues Sraffians (and others) argue that replacement costs, not historical costs, are the relevant costs for calculating profits. He argues that Sraffians are correct to argue that historical costs are irrelevant, and that Marx agreed. Kliman, however, thinks that Marx (correctly) calculates prices of production with reproduction costs, thereby allowing inputs and outputs to differ in price.

I don't want to argue here about how to read Marx. Rather, I want to offer an alternative interpretation of the single (simultaneous) set of prices characterized by Sraffa's price system - that of accounting prices at the start of the production period for a stock equilibrium (as opposed to a flow equilibrium).

As an example, consider, at the start of the production period, a fictional vertically-integrated firm that produces a net output of corn. The managers of the firm know various processes for producing corn from inputs of labor, iron, and corn. They also know various processes for producing iron from inputs of labor, iron, and corn. The firm is supposed to start the production period with a stock of iron and corn, in appropriate proportions to continue production. The firm is assumed to have already sold its net output of corn (to consumers?) produced in the last production period. How much should the managers of the firm, at the start of the production period, say their stock of iron and corn is worth?

Although I don't present the results in this way, one can read my 2005 paper as stepping through the mechanics of answering this question. Managers are assumed to know, at the start of the production period, the current market price of corn and the wage. My paper formulates a Linear Program in which firms maximize how much the value of the firm is incremented over the production period. This formulation requires a known price for iron, which I am asserting here can be a book price. The wage and price of corn pin down accounting prices such that managers will be willing to continue production of both corn and iron, thereby allowing the firm to continue in existence into the future. The decision variable in the dual Linear Program is the rate of profits which minimizes the value of the initial stock of inputs. Adopting a convention of using a single set of prices for inputs and outputs prohibits the accountants from using one method to manipulate that measure of profitability. Have I not now presented Sraffa’s prices as a method of deriving Kliman’s pre-production reproduction cost, the cost measure that he says Marx uses?

Depicting Sraffa prices as a stock equilbrium is not original with me. Keiran Sharpe (1999) says the same, albeit he starts with time indices and different prices for inputs and outputs. Sharpe sets his discussion in an evolutionary context, with the rate of profits as a measure of fitness. Sharpe, after having dropped the time indices, is still explicit that Sraffa is not assuming "constancy of prices over time".

I forget where I read this - probably in a paper by Kurz and Salvadori, but an early twentieth century Italian accounting manual was apparently one work Sraffa used as a mathematical aid when developing his system. This may be one reason why some who worry about computability and economics might find something worthwhile in Sraffa.

References

• Kliman, Andrew (2007). Reclaiming Marx's "Capital": A Refutation of the Myth of Inconsistency, Lexington Books
• Sharpe, Keiran (1999). "On Sraffa's Price System", Cambridge Journal of Economics, V. 23: 93-101
• Vienneau, Robert L. (2005). "On Labour Demand and Equilibria of the Firm", Manchester School, V. 73, N. 5 (Sep.): 612-619

Just the Facts, Ma'm

As far as I am concerned, the marginal variable cost curve for an industrial plant is typically a reverse L-shape. Industrial firms generally practice some sort of administrative, full-cost, or markup pricing policy. Empirical work on this point, I guess, goes back at least to Hall and Hitch. Post Keynesians will look back to Kalecki. (Sraffians have argued that Kaleckian models should be modified to incorporate a dependence of relative prices on distribution.) Steve Keen cites a recent book by Alan Blinder et al to the same point. And James Galbraith's empirical results suggest Kalecki was on to something in his classification of economic sectors.

Tyler Cowen wants to know how to avoid teaching students these ideas. I do like “Person’s” query in that thread:

”Stupid question: how about just admitting that businesses price based on (expected) average cost, instead of carving out all these epicycles? I'm just asking, is all.”

(Tyler Cowen is amusing here, too.)

Ignorance and Arrogance

"[J. E.] King: You published your second thoughts on the capital controversies in 1976. Any third thoughts today?

[G. C.] Harcourt: Yes. I think the methodological nature of Joan Robinson's critique is the dominant one. And price as an index of scarcity cannot be made coherent in the supply-and-demand framework, which I think is the principal Sraffian critique. So that if the demand curve for capital is not well-behaved, and capital may be a Giffen good, you might as well give up neoclassical economics as a conceptual illumination because the results aren't robust enough to go through, though you can pretend that they do. All these one-sector models pretend that there's a well-behaved demand curve for capital.

King: And they are being revived right now.

Harcourt: Yes, it's terrible: at best a sign of ignorance and more probably a sign of intellectual arrogance. Hegemony has been re-established by the mainstream, and it's breathtaking arrogance.

King: I think you're wrong. I think it's mainly ignorance. But you regard the Cambridge controversies as more important than Joan Robinson did, towards the end?

Harcourt: Oh, as a conceptual critique, yes. Joan must have known about the Steedman-Metcalfe critique of international trade theory, but by that time she was into the methodological points, and of course she didn't know about Colin Rogers's destruction of the Wicksellian foundations of modern monetary theory. I think Colin's work is extremely important. If you destroy value and distribution theory conceptually, and show that the central concepts are incoherent - you see, what I say is, the harder-line defence is, General Equilibrium theory is not affected, but G. E. is not descriptive, so it's not a theory about the world, and it means that the cruder versions of neoclassical economics are vulnerable. So either you've got a non-applicable theory or a vulnerable theory. If you then go on and say that the critique may be extended to the foundations of mainstream monetary theory as well, that's a pretty damaging critique. It means that orthodox development theory, orthodox trade theory, orthodox value theory, orthodox distribution theory and orthodox monetary theory are incoherent at their very foundations. Well, providing that us lot remain a minority, no one's going to take much notice of it, and people have become more and more ruthless in suppressing dissent. But the fact remains, from an intellectual point of view, that it's an absolutely vulnerable position for the mainstream to be in. Sadly, the students in the advanced theory classes quickly fade away from my lectures on all this, because I lecture at a conceptual level instead of just squiggles - though I do some squiggles - and because of the counter-attractions of game theory, or modern decision-making under uncertainty, where there are precise answers If you can get on top of the highly difficult technical stuff you've got ready-made answers, and it's all self-contained. I don't think that's proper honours work. I think a good honours question is one where you have to do a conceptual discussion, a critical discussion, and some analysis. That's what my courses and my questions are like. Well, the students have to pass exams and get good marks, and so on, and since many of the lecturers here would rubbish the whole thing anyway, you can hardly blame the students for not coming. Though I find it a very sad thing myself, because where's the intellectual curiosity, where's the intellectual honesty in it all?" -- J. E. King (1995). Converstions with Post Keynesians, St. Martin's Press

What does Harcourt mean in saying, "G. E. is not descriptive?" He probably has in mind his debating partner:

"[G.E. is] very useful when for instance one comes to argue with someone who maintains that we need not worry about exhaustible resources because they will always have prices which ensure their proper use. Of course there are many things wrong with this contention but a quick way of disposing of the claim is to note that an Arrow-Debreu equilibrium must be an assumption he is making about the economy and then show why the economy can not be in this state. The argument will here turn on the absence of futures markets and contingency futures markets and on an inadequate treatment of time and uncertainty by the construction. This negative role of Arrow-Debreu equilibrium I consider almost to be sufficient justification for it, since practical men and ill-trained theorists do not understand what they are claiming to be the case when they claim a beneficent and coherent role for the invisible hand. But for descriptive purposes of course this negative role is hardly a recommendation." -- Frank Hahn (1973). On the Nature of Equilibrium in Economics Cambridge: Cambridge University Press: 14-15

I don't think I've read that particular Hahn quotation in the original.

Challenge Yourself

I occasionally browse back issues of Challenge, published by Michael E. Sharpe. Some readers of this blog might enjoy this semi-popular journal.

Its articles are more practical and policy-oriented than my posts. Some of the authors of these articles have been mentioned here. For example, in Challenge one can read Dean Baker on health care (Jan-Feb 2007), James K. Galbraith on a war economy (Nov-Dec 2001), and Thomas Palley on developing the domestic market (Nov-Dev 2006).

Challenge also includes interviews with economists. For example, in one recently, Duncan Foley (Nov-Dev 2006) explored some of the themes of his recent book, Adam's Fallacy. And the journal covers trends among academic economics.

The journal's authors do not have uniform opinions. Here's an example. Gerald Houseman is laudatory on Stigliz's work:

"Progress does occur. The formidable myth of 'free enterprise,' a major crutch for the belief systems of those who see market economics as a be-all and end-all, has been dead since at least 1986, and a rather modest economist, Joseph E. Stiglitz, along with two fellow Nobel Prize winners in economic science, George Akerlof and Michael Spence, drove the final stake through its heart in the Stockholm Nobel Prize lecture of December 2001...

...Critical observers associate ['free enterprise'] with price-fixing, the Enron Corporation, environmental threats, consumer fraud, union-busting, anti-trust violations, deregulation, rationalizations for layoffs and for budget cuts in social welfare programs, privatization schemes, speculation, stock manipulation, chicanery, and corruption. Many of us have become weary of what is no more than a slogan that seems useful for the arsenal of those who are just plain greedy or who have divined, sometimes with assistance from On High, that 'free enterprise' legitimizes keeping people in their place as a part of the holy cause of inequality...

...For Stiglitz has destroyed the '[invisible] hand' as well, proving that markets do not really work in this way...

...Economics texts also generally ignore Stiglitz and his cohorts. Their micro-models are unaffected and the macro-talk has proceeded in much the same vein as ever, with only slight adjustments of various kinds over the years. (The Stiglitz economics text is the sole exception.)... Institutions claiming total devotion to market economics, as opposed to those that muddy this view by combining it with calls for government largess for certain corporations or industries (as in the cases of Bush's Medicare, energy, defense, and social security measures), are also still in business, even though they have no earthly reason, by intellectual measures at least, for continuing to exist. A few examples of purposeless ciphers are the Cato Institute propaganda mill, the Ayn Rand Institute, the Objectivist Society and its branches, the Club for Growth, and the law and economics sector of legal writing and academic work, which is headquartered at the University of Chicago and is closely associated with the eccentric Judge Richard Posner. Some of the verbal meanderings of former Federal Reserve Chair Alan Greenspan, a Randy ideologue, have and should be regarded as part of this genre, and these are equally baseless.

It can be readily appreciated that some of these people and their organizations should be given the message of information economics (for their own self-interest, if for no other reason); but there is also real cause for doubting the motives and sincerity of some of the corporations, media organizations, and various other right-wing clusters who continue to spout market economics ideology..." -- Gerald Houseman (2006). "Joseph Stiglitz and the Critique of Free Market Analysis", Challenge (Mar.-Apr.): 52-62

Houseman also says Stiglitz provides tools needed for policy for economic development. On the other hand, Lance Taylor, an advocate of structuralism, is not nearly so glowing:

"Contemporary mainstream economics resembles Greek theater. The chorus ... incessantly chants that the economic system is basically competitive, populated by 'agents' with good information... [Agent] choices lead to welfare level as high as it possibly can ... in ... a 'Walrasian equilibrium'... [Stiglitz's] main theme is how 'asymmetric information' between actors can force the system away from a Walrasian position... Contrast the mainstream picture ..., whether viewed as a whole by the chorus or in detail with the actors, with an alternative 'structuralist' perspective, rooted in sociology... In the 'classical' variant ... the focus was on neither the price-mediated function of the whole nor the actions of individual actors, but rather on ... organized groups or classes such as capitalists, landlords, and peasants... How does [the structuralist approach] differ from the mainstream focus on individual actors as refined by Stiglitz? ...

Economists playing statistical games that show that their formal models of imperfect information are 'supported by the evidence' in a given institutional context simply ignore how social structure underlies economic responses - an observation that was crystal clear to their classical predecessors. In the absence of social change, their policy suggestions about how to ameliorate the inequity built into sharecropping, and other exploitative systems are beside the point..." Lance Taylor (2007). "A Review of Making Globalization Work, by Joseph E. Stiglitz",Challenge (Jan.-Feb.): 115-123

Taylor does say some of Stiglitz's policy proposals are good ideas.

The Crisis of Vision in Neoclassical Economics

I think of the notion that prices act as scarcity indices and of the principle of substitution as central to the pre-analytic vision of neoclassical economics. (These principles should only be thought of acting reliably in the absence of imperfections in competition, complete knowledge, etc.) My view is not unique:

"The [Demand-and-Supply-based Equilibrium] theory visualizes the economy as an aggregate of atomistic individuals (producers and consumers) making their decisions autonomously, with no interference from the influence of 'externalities'. Relative prices and quantities are determined simultaneously in equilibrium as an outcome of the interplay of 'forces of demand and supply', generated by the optimizing behavior of individuals subject to their resource constraints. A certain symmetry characterizes the behaviour of producers and consumers. Each producer, given the technological possibilities, chooses the profit-maximizing activities and outputs, at the going prices; each consumer, given his budget constraints and scales of preferences, maximizes satisfaction at the going prices. It is through the operation of the 'fundamental' and 'universal' principle of substitution that individuals adjust their chosen quantities in response to the parametrically given prices...

Further, the notion of 'change' in the DSE theory gets restrictively predetermined by the theory in the following ways. First, all changes in quantities within the system are seen as the outcome of the ever-active principle of substitution. Thus the changes are primarily in relative quantities involving allocational variations. The role of prices as a scarce-resource allocator, given the resources, dominates the theory as contrasted with the resource-creational role of prices in classical theory... Secondly, all changes are explained as induced by changes in relative prices and operate through the decisions of individuals who are only 'quantity adjusters'; that is, all influences affecting quantities have to be necessarily mediated through relative prices or changes on the market and are outcomes of the atomistic responses of individuals. The relative prices acquire the all-powerful role of resource-allocation and the 'market' becomes the 'arena' of action." -- Krishna Bharadwaj (1989, p. 7-8)

Naturally, one can find many statements from advocates of neoclassical economics promulgating this vision. Here’s an example:

"It is indeed the great contribution of the Pure Logic of Choice that it has demonstrated conclusively that even such a single mind could solve this kind of problem only by constructing and constantly using rates of equivalence (or 'values' or 'marginal rates of substitution'), that is, by attaching to each kind of scarce resource a numerical index which cannot be derived from any property possessed by that particular thing, but which reflects, or in which is condensed, its significance in view of the whole means-end structure...

Fundamentally, in a system in which the knowledge of the relevant facts is dispersed among many people, prices can act to co-ordinate the separate actions of different people in the same way as subjective values help the individual to co-ordinate the parts of a plan. It is worth contemplating for a moment a very simple and commonplace instance of the action of the price system to see what precisely it accomplishes. Assume that somewhere in the world a new opportunity for the use of some raw material, say, tin has arisen, or that one of the sources of tin has been eliminated. It does not matter for our purpose - and it is significant that it does not matter - which of these two causes has made tin more scarce. All that the users of tin now need to know is that some of the tin they used to consume is now more profitably employed elsewhere and that, in consequence, they must economize tin. There is no need for the great majority of them even to know where the more urgent need has arisen, or in favor of what other needs they ought to husband the supply... The whole acts as one market, not because any of its members survey the whole field, but because their limited individual fields of vision sufficiently overlap so that through many intermediaries the relevant information is communicated to all. The mere fact that there is one price for any commodity - or rather the local prices are connected in a manner determined by the cost of transport, etc. - brings about the solution which (it is just conceptually possible) might have been arrived at by one single mind possessing all the information which is in fact dispersed among all the people involved in the process." -- F. A. Hayek (1945)

Here is an old textbook:

"Let us then suppose that...there is a strike on the part of one group of workers, say the plasterers, or that there is some other disturbance to the supply of plasterers' labour...The rise in plasterers' wages would be checked if it were possible either to avoid the use of plaster, or to get the work done tolerably well and at a moderate price by people outside the plasterers' trade: the tyranny, which one factor of production of a commodity might in some cases exercise over the other factors through the action of derived demand, is tempered by the principle of substitution." -- Alfred Marshall (1920, Book V, Chapter VI)

And here is exposed nonsense perhaps still being taught to some put-upon students:

"Suppose the number of carpenters suddenly increases, due to the immigration of thousands of new carpenters from Mexico. Both before and after the change, carpenters receive their marginal revenue product... But the wage after the migration is lower than the wage before. Since the supply of carpenters is higher than before, the equilibrium wage is lower.

...an increase in the supply of an input I own drives down its price (and marginal revenue product) and so decreases my income. The same is true for an increase in the supply of an input that is a close substitute for an input I own. If I happen to own an oil well, I will regard someone else's discovery of a new field of natural gas--or a process for producing power by thermonuclear fusion--as bad news." -- David Friedman (1990)

As leaders of mainstream economics know, this neoclassical vision has collapsed:

"Even people who have made no study of economic theory are familiar with the idea that when something is more plentiful its price will be lower, and introductory courses on economic theory reinforce this common presumption with various examples. However, there is no support from the theory of general equilibrium for the proposition that an input to production will be cheaper in an economy where more of it is available. All that the theory declares is that the price of the use of an input which is more plentiful cannot be higher if all other inputs, all other outputs and all other input prices are in constant proportions to each other." -- Christopher Bliss (1975).

I think the collapse of the underlying vision of neoclassical economics (Cohen 1993) leaves some questions open:

• Can the Arrow-Debreu model of intertemporal equilibrium, in its current state, serve as a foundation for price theory, including in applications (Rizvi 1994)?
• Can Sraffa effects be used, (and if so, how) to critique the Arrow-Debreu model?
• If the Arrow-Debreu model fails, how can mainstream economists understand prices? (Game theory is an obvious answer to explore (Rizvi 1999). Sraffians and Post Keynesians have other answers.)

References

• Bharadwaj, K. (1989). Themes in Value and Distribution: Classical Theory Reappraised, London: Unwin Hyman.
• Bliss, C. J. (1975). Capital Theory and the Distribution of Income, Amsterdam: North Holland Press.
• Cohen, Avi J. (1993). "What was Abandoned Following the Cambridge Capital Controversies? Samuelson, Substance, Scarcity, and Value", History of Political Economy, Annual Supplement, V. 25, N. 5: 202-219
• Friedman, D. D. (1990). Price Theory: An Intermediate Text, Second Edition, Cincinnati: South-Western Publishing.
• Hayek, F. A. (1945). "The Use of Knowledge in Society", American Economic Review, V. 35, N. 4 (Sept.): 519-530.
• Marshall, A. (1920). Principles of Economics: An Introductory Volume, Eighth edition. Macmillan.
• Rizvi, S. Abu Turab (1994). "The Microfoundations Project in General Equilibrium Theory", Cambridge Journal of Economics, V. 18: 357-377
• Rizvi, S. Abu Turab (1999). "Rationality, Evolution and Games", Strategic Rationality in Economics, Sant'Arcangelo di Romagna, Italy (26-27 August)