Saturday, May 18, 2019

Elsewhere

Thursday, May 16, 2019

How To Defend Capitalism?

1.0 Summary of Defense

Last month, Mike Munger purports to "summarize the basic argument for capitalism" (emphasis added). He acknowledges his argument is superficial. I find it excessively so. Munger argues that capitalism:

  • Supports the division of labor
  • Provides price signals so as to direct production appropriately
  • Promotes economies to scale

Ultimately, this defense is that capitalism delivers the goods. Here's a well-expressed, simple defense that, partially, argues along these lines:

It is possible to defend our economic system on the ground that, patched up with Keynesian correctives, it is, as he put it, the 'best in sight'. Or at any rate that it is not too bad, and change is painful. In short, that our system is the best system that we have got.

Or it is possible to take the tough-minded line that Schumpeter derived from Marx. The system is cruel, unjust, turbulent, but it does deliver the goods, and, damn it all, it's the goods that you want.

Or, conceding its defects, to defend it on political grounds - that democracy as we know it could not have grown up under any other system and cannot survive without it.

What is not possible, at this time of day, is to defend it, in the neoclassical style, as a delicate self-regulating mechanism, that has only to be left to itself to produce the greatest satisfaction for all.

But none of the alternative defences really sound very well. Nowadays, to support the status quo, the best course is just to leave all these awkward problems alone." -- Joan Robinson (1962). Economic Philosophy, p. 130

2.0 Division of Labor and Efficiencies of Scale

I am not sure that Munger has three principles. I think of the division of labor and efficiencies of scale as closely related. But are either specific to capitalism, as opposed to any society with large scale production? In some sense, Munger is not necessarily attacking a strawperson. Here's an expression of a wish for a post-capitalist society that is arguably not consistent with large-scale production:

"...in communist society, where nobody has one exclusive sphere of activity but each can become accomplished in any branch he wishes, society regulates the general 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, just as I have a mind, without ever becoming hunter, fisherman, herdsman or critic." -- Karl Marx, The German Ideology.

But, maybe with enough automation, such a society would be possible.

I find it of interest that Marx, in The Communist Manifesto and in Capital describes how capitalism brought about a remarkable increase in productivity. I find Marx, on the division of labor, much more concrete and extensive than Adam Smith, even though he is writing about the abstraction of capital in general. How much has been written about what Marx took from Charles Babbage's On the Economy of Machinery and Manufactures? This book has a lot to say about what would now be called Command, Control, Communications, and Intelligence (C3I)?

Anyways, questions arise when a defense of capitalism echoes capitalism's greatest critic.

3.0 Price Signals Consistent with Market Socialism

Munger's second principle, about price signals, draws, I assume, on Friedrich Hayek. I do not see how this is a defense of capitalism, as opposed to markets. Whatever you think of it, a large literature on market socialism exists. Private ownership of capitalist enterprises is not necessary for the existence of price signals. I suppose one could argue about incentives in this context, which I do not think Munger does.

4.0 Other Arguments

I think interesting that Munger does not say anything about the efficient static allocation of resources or the first and second welfare theorems. In some sense, he is correct to put these ideas aside, since a good apologetic argument for capitalism cannot be fashioned in these terms.

On the other hand, Munger avoids all of the issues that John Quiggin brings up in his recent Economics in Two Lessons. Issues with unregulated capitalism include externalities, the assignment and distribution of property rights, and periodic bouts of widespread unemployment. (I find unpersuasive talk of "government failure" as a response to the demonstration that unregulated capitalism is bound to misallocate resources. Is a claim being made that anybody can calculate a closed-form optimal allocation at any point in time?)

5.0 What is Capitalism?

I suspect that Munger supports a fairly hierarchical version of capitalism, with widespread private, brutal, and authoritarian institutions (for example, corporations). Inspired by Chapter 9, "Security and Freedom", of Hayek's The Road to Serfdom, I would ask what is compatible with Munger's apologetics for capitalism? Widespread co-operative, syndicates, and and factory councils? Co-determination, in which union representatives are on corpation boards? Sovereign Wealth Funds, Employee Stock Ownership Plans, Universal basic income, government insurance, and social security?

So Munger's three principles do not seem to rule out either an extensive social democracy or even democratic socialism.

Tuesday, May 07, 2019

Positive Real Wicksell Effect, Forward Substitution Of Labor

Figure 1: Wage-Rate of Profits Curves

Consider a comparison of stationary states. Net output is taken as given, and a unit of net output is the numeraire. Technology consists of a finite set of techniques. In each technique, net output is produced from inputs of labor and produced circulating capital goods. No fixed capital is used, and land of the best quality is in such abundance that it is free. Also assume constant returns to scale.

One can find a wage-rate of profits curve for each technique. The cost-minimizing technique at is the technique its wage curve on the outer envelope, also known as the wage-rate of profits frontier, at that wage. Switch points are points at which two or more wage curves intersect (on the frontier). Suppose the same gross vector commodities are produced, albeit in different proportions, at a switch point. Generically, the techniques differ in the process in use for one industry. The same processes are in use in all other industries. (I have argued that fluke switch points in which wage curves for more than two techniques intersect at a single switch point are of importance for understanding how qualitative changes in the properties of the wage frontier can come about from, for example, technological progress.)

A generic switch point can exhibit positive or negative real Wicksell effects. And it can exhibit a forward or reverse substitution of labor.

Around a switch point with a positive real Wicksell effect, a higher wage is associated with firms wanting to employ more labor throughout the economy, per unit of net output.

Around a switch point with a reverse substitution of labor, a higher wage is associated with firms, in the industry in which the process of production varies, wanting to employ more labor per unit of gross output.

I have previously given a numerical example that illustrates switch points with:

  • A positive real Wicksell effect and a reverse substitution of labor.
  • A negative real Wicksell effect and a reverse substitution of labor.
  • A negative real Wicksell effect and a forward substitution of labor.

Figure 1 illustrates a switch point can have a positive real Wicksell effect and a forward substitution of labor. Suppose that the wage curves for two techniques have three intersections. One intersection is between a rate of profits of negative one hundred percent and zero. The other intersections are at two feasible poisitive rates of profits. Then the switch point at the largest positive rate of profits has a positive real Wicksell effect and a forward substitution of labor. (I have not actually specified a technology, with three or more produced commodities, that generates wage curves like those illustrated.)

Since all four possible combinations are possible, the direction of real Wicksell effects and the substitution of labor are independent of of one another. The choice of technique results in variation in gross outputs in multiple industries, for given net outputs. These variations also result in variation in the amount of labor firms want to employ. This variation in aggregate employment is consistent with any direction in the variation in the labor coefficient of production in the industry with the varying process.

If somebody explains wages and employment by supply and demand for labor, they are making a political point. This holds even if they argue that a supply and demand explanation provides a baseline. They may be demonstrating that economists continue to adopt a price theory that has been known for decades to be incoherent nonsense.

Friday, April 19, 2019

Some Experts On The Cambridge Capital Controversy

Many years ago, I used to argue, on Usenet, about the Cambridge Capital Controversy. Many mainstream economists used to ignorantly assert, when pretending to respond, that an application of the CCC to labor economics was my idea alone. So I used to demonstrate that this was false by quoting from the literature. As far as I can see, mainstream economists are still mostly trained into ignorance.

P. Garegnani:

"The idea that demand and supply for factors of production determine distribution has become so deeply ingrained in economic thought that it is almost viewed as an immediate reflection of facts, and not as the result of an elaborate theory. For the same reason, it is easily forgotten how comparatively recent that theory is. In the first systematic analysis of value and distribution by the English classical economists up to Ricardo, we would look in vain for the conception that demand and supply for labour and 'capital' achieve 'equilibrium' as the proportions in which those 'factors' are employed in the economy change with the wage and rate of profits. Thus, Ricardo saw no inconsistency between free competition and unemployment of labour. In his view lower wages could eliminate unemployment only by decreasing the growth of population or by favouring accumulation...

...Outputs can influence relative prices ... by affecting the relative scarcity of labour and capital, and thus the wage and rate of interest, given the supply of the two factors and the state of technical knowledge. This link between prices and outputs is one and the same thing as the explanation of distribution by demand and supply of factors of production: and it becomes untenable once that explanation is abandoned.

Thus, the separation of the pure theory of value from the study of the circumstances governing changes in the outputs of commodities, does not seem to meet any essential difficulty. On the contrary, it may open the way for a more satisfactory treatment of the relations between outputs and the technical conditions of production. Moreover, by freeing the theory of value from the assumption of consumers' tastes given from outside the economic system, this separation may favour a better understanding of consumption, and its dependence on the rest of the system.

With this, the theory of value will lose the all-embracing quality it assumed with the marginal method. But what will be lost in scope will certainly be gained in consistency and, we may hope, in fruitfulness." -- P. Garegnani, RES, 1970.

Harvey Gram:

"The intractable problems created by the effort to extend into the unobservable future the terrain over which the forces of supply and demand hold sway are somehow set aside as questions that will ultimately yield to a more sophisticated analysis. Meanwhile, the existence of an alternative framework of thought based on a revival of classical theory is denied. Certainly the critics of neoclassical theory committed a great heresy during the capital theory debate by proving false the analytical basis for the principle of substitution in so far as it affects the demand for capital and labour. Those who would defend neoclassical theory against any attack on its logical structure fail to see the significance of this result. This is because they have given up any causal claims for general equilibrium theory..., thus abandoning the traditional notion of equilibrium as a centre of gravity relative to which prices and quantities fluctuate. The revival of interest in classical theory is, in part, a revival of interest in this old-fashioned idea. It is also a revival of interest in a broadly based theory that does not presume to find the essence of all market phenomena in terms of the single principle of substitution." -- Harvey Gram, 1990.

Heinz Kurz and Neri Salvadori

"However, as was argued in Section 3 with regard to 'perversely' shaped, that is, upward sloping, factor-demand functions, this possibility would question the validity of the entire economic analysis in terms of demand and supply." -- H. D. Kurz and N. Salvadori, Theory of Production: A Long Period Analysis, Cambridge University Press, 1995.

Heinrich Bortis:

"...Specifically, it must be shown that under ideal conditions, i.e. perfect competition and absence of disturbing elements like uncertainty and money, one or more markets do not function properly so that, even in the long run, no tendency towards full employment exists: the problem is not about possible market failures, but about principles.

This task has been accomplished by the capital-theory debate, the main economic implications of which are set out in Garegnani (1970), Kurz (1985) and Pasinetti (1974, pp. 132-42; 1977, pp. 169-77); a comprehensive and easily understandable presentation of the crucial issues is Harcourt (1972).

...As a consequence, no regular (downward-sloping) associations between profit rates, on the one hand, and capital and output per worker and the capital-output ratio, on the other hand, exist. These relationships are, in fact, totally irregular. Since the 'capital market' does not function in the neoclassical sense and since factor markets are supposed to be interrelated, regular long-period relationships between 'factor prices' and 'factor quantities' cannot exist in general, i.e. there are no 'factor markets' at all if the long run is considered. This is the main result of the capital-theory debate...

...The fact that there are no regular relationships between 'factor prices' and 'factor quantities' is extremely damaging for equilibrium theory: the market cannot produce a tendency towards some postulated long-period equilibrium to solve the central economic problems, i.e. value, distribution and employment....

...These references to the history of the capital-theoretic discussion show that it is a discussion about fundamentals. The basic question is whether there are regular relationships between 'factor prices' and 'factor quantities' or not, i.e. normally functioning factor markets. Examining this question seriously will inevitably shape an economist's vision in a decisive way. The capital-theoretic debate is a theoretic watershed dividing two different views of looking at socioeconomic phenomena, i.e. neoclassical equilibrium theory which emphasizes behavior and classical-Keynesian political economy which starts from the functioning of the socioeconomic system, the question being which approach is more appropriate to tackle fundamental socioeconomic problems, such as value, distribution and employment. Therefore, as Geoffrey Harcourt was one of the first to perceive, the Cambridge controversies are 'not merely about the measurement of capital...but about the scientific status of neoclassical (equilibrium) theory' (Dixon 1988, pp. 251-2)...." -- Heinrich Bortis, Institutions, Behavior and Economic Theory: A Contribution to Classical-Keynesian Political Economy, Cambridge University Press, 1997.

Syed Ahmad:

"The issue was settled in favour of Cambridge University when Samuelson wrote (1976) that wherever 'informed economic theory is taught', the 'paradoxes' are accepted, and their consequences for the concept of capital known. It is another matter that, on the basis of this criterion, many seats of learning in North America, as perhaps also elsewhere, do not teach informed economic theory." -- Syed Ahmad (1998)

Edward Nell:

"After Sraffa's book in 1960 the next decades saw major battles in the journals, battles which resulted in conclusions widely held today: to wit, the technical errors are conceded, but their significance is contested. This has a practical meaning: open any major journal at random today, and there will be marginal products... - with no hint that any technical error is involved. The critique is simply ignored. It can't be answered, but it is held to be unimportant." -- Edward Nell (1998)

Ian Steedman:

"Both classical and marginalist economists provided accounts of the long-period (uniform rate of profit) theory of value and distribution, but whereas a classical economist could take the real wage as a datum for the purpose of such analysis (whatever the implicit 'background' theory of wages might be), the marginalist economist had to 'close the system' in some other manner. In effect, since 'resource supplies' were often taken as given, this meant that 'the supply of capital' had to be taken as given, in one way or another. Just how the given supply of capital was to be represented was an issue that led to considerable heterogenity amongst even those marginalist economists who shared the long-period method of analysis with the classical economists and with each other. That heterogenity cannot be entered into here (see Kurz and Salvadori, 1995: 427-43) but it is now widely recognized that each version of such traditional long-period marginalist theory of value and distribution encountered insoluble problems (ibid.: 443-48)." -- Ian Steedman (1998)

Michael Mandler:

"But, as economic theory has learned since the 1930s, the pattern of activities adopted in the face of long-run factor-price changes can be complicated and counterintuitive. Consequently, the long-run demand for factors can be badly behaved functions of factor prices... The principle of variation works as an argument for long-run determinancy insofar as the set of zero-profit activities shift in response to factor price changes; it is not necessary that newly adopted activities use cheaper factors more intensively..." -- Michael Mandler (1999)

Luigi L. Pasinetti:

"But something even more interesting and intriguing has happened. After only a few years, even the admissions initially made no longer found any mention... The typical economics student entering university from the 1980s onwards has heard nothing of the re-switching difficulties involved in the neoclassical theory of capital and income distribution." -- Luigi L. Pasinetti (200?).

James Galbraith:

"The critique of Robinson and Sraffa is more than forty years old. Yet for psychological and political reasons, rather than for logical and mathematical ones, the capital critique has not penetrated mainstream economics. It likely never will. Today only a handful of economists seem aware of it... Ostensible liberals are not exempt; their arguments for higher public infrastructure investment (based on its alleged marginal productivity) are precisely of this type, as are arguments for increased investment in education based on the higher marginal productivity of human skill." -- James Galbraith (2001).

Steve Keen:

"Of course, the average economist would never tell you that economic theory has suffered such a devasting blow. This is because the average YOUNG economist doesn't even know that this intellectual bout took place - the concepts in this debate don't make it onto the curriculum for either undergraduate or postgraduate students. Older economists cannot avoid some knowledge of the war, but they erroneously believe that their camp won, or they dismiss the issue completely.

Today economic theory continues to use exactly the same concepts which Sraffa's critique showed to be completely invalid...

There is no better sign of the intellectual bankruptcy of economics than this." -- Steve Keen (2001)

Neri Salvadori:

"Reswitching debate is relevant for...theories which determine income distribution on the basis of demand and supply of all factors including labour and 'capital'."

Fabio Petri:

"The arguments necessary to surmount these confusions started becoming available in English only with Garegnani (1976), which was quickly followed by a number of other papers and books among which Petri (1978, 1991, 1998, 1999), Garegnani (1978-9, 1989, 1990, 2000), Eatwell (1979, 1982), Milgate (1979, 1982), Eatwell and Milgate (1983), Schefold (1985, 1997), Kurz (1987). This wave of contributions finally started clarifying the difference between long-period and neo-Walrasian versions of the marginalist/neoclassical approach, as well as the different roles of the conception of capital as a single factor, roles some of which were argued to be present even in the neo-Walrasian versions... The neoclassical reaction was striking: no reply at all. Some of the neoclassical assessments of the Cambridge controversies (e.g. Blaug, 1974; Stiglitz, 1974; Bliss, 1975b) antedate the writings of this second critical wave, but other ones do not (e.g. Dougherty, 1980; Burmeister, 1980, 1991; Hahn, 1982) and yet contain no reference to any of the post-1975 critical writings just mentioned. One possible interpretation ... is that no reply came forth because a satisfactory reply was not easy to find. Be that as it may, the fact is that up to now (end 2002) none of the post-1975 critical writings just remembered is mentioned in any of the writings of Hahn or Solow or F. M. Fisher or Burmeister even when they return on the themes of the Cambridge controversy. No wonder that considerable misunderstandings persist, which is what prompted me to write the present essay." -- Fabio Petri

Thursday, April 11, 2019

Gramsci Should Be Difficult To Understand

Fact: If you use the word "carceral" instead of "prison" your argument immediately becomes more persuasive.

Good praxis is to use words like "praxis" that nobody understands. -- Matthew Yglesias (5 April 2019, on Twitter)

A large academic literature exists around Antonio Gramsci's Prison Notebooks. Topics discussed include the relationship of civil society to the state, hegemony, the contrast between consent and coercion, class alliances in political parties, Fordism, the contrast between a "war of position" and a "war of movement", the contrast between organic intellectuals and traditional intellectuals, and the concept of a passive revolution.

When writing his notebooks, Gramsci had to be concerned with Fascists guards reading them and tearing them up in displeasure. Thus, he wrote in a kind of code. The communist party becomes the "modern prince". Machiavelli wrote to advise the ruler of Florence how to obtain rule over Italy; Gramsci was thinking about how communists could rule with the consent of the governed. Marxism or Marxist-Leninism becomes "the philosophy of praxis." As I understand it, praxis is practice informed by theory or theory embodied in practice, in some sense. Gramsci is referring to the last of Marx's Theses on Feuerbach:

The philosophers have only interpreted the world, in various ways; the point is to change it. -- Karl Marx

As you can see, these code words are not a mechanical substitution. To understand Gramsci, one would want to think about these choices.

Gramsci never thought of his notebooks as complete. You can find him often writing about what a study on some topic should contain. I saw this in the selection titled, "The Modern Prince", for example. Gramsci could order books. Piero Sraffa provided an unlimited account at some bookstore. Nevertheless, he hoped to complete his work, which was to be "for forever", sometime in the future. Given the circumstances of their writing, the Notebooks were not required to be internally consistent.

Despite the abstractions used by Gramsci, his writing is often quite concrete. But to appreciate it, one would need to know about Italian intellectuals before he entered prison. Myself, I am no expert on Amadeo Bordiga, Benedetto Croce, Giovanni Gentile, Antonio Labriola, or Achille Loria. Nor can I easily check claims about arguments on how to standardize Italian, whether focused on the dialect in Florence or also allowing for influence of other dialects. I suppose to understand Gramsci, one should also know about Giuseppe Garibaldi, Sardina and the southern question, and lots more about Italian history.

For me, there is a language issue. I rely on Quentin Hoare and Geoffrey Nowell Smith's Selections from the Prison Notebooks, not Joseph Buttigieg's comprehensive translation. The literature on Gramsci also contains attempts to translate his concepts to times and places, other than the Italy of Gramsci's day.

Friday, April 05, 2019

The FAA Process For Certifying Flightworthy Software

1.0 Introduction

This post is on current events. The plane crashes of the Boeing 737 Max 8 airplane is arguably about more than a software bug. I point out in this post that you can read about how the United States' Federal Aviation Administration (FAA) is supposed to certify software and electronic hardware in airplanes yourself. In some sense, this post is not about software bugs, but rather about software engineering certification processes that fit into a larger systems engineering perspective.

2.0 FAA Resources

The FAA provides lots of resources associated with DO-278C, Software Considerations in Airborne Systems and Equipment Certification, the primary document of interest in this context.

  • You can find an overview of the FAA Airplane Certification Service here.
  • Position papers from the Certification Authorities Software Team (CAST) are available here.
  • I was particularly interested in some of these Research Reports.
3.0 Conclusion of Recent FAA Research on Software Reliability Models

For historical reasons, I am interested in software reliability models. These models address an important problem. One could mandate that software be developed by rigourous processes, by some defined model or another. And one could require that developers produce certification arguments along with delivered software. But how does the variability of rigor relate to quantitative measures of software reliability and availability, as needed for system reliability? A recent report looks at software reliability and, as I understand, concludes the technology is not mature enough yet:

"the current position is that methods for estimating probabilities of software errors have not yet provided a level of confidence acceptable for software assurance purposes. Since the publication of the report and DO-178C document, work on software reliability has improved the level of confidence. However, the multiplicity of available models and absence of quantified performance objectives contribute to the confidence issue remaining open and added the issue of guidelines on selecting an adequate reliability method." Final Report for Software Service History and Airborne Electronic Hardware Service Experience in Airborne Systems (DOT/FAA/TC-16/18, Section 7.5.4, p. 102)

I don't know that I disagree with this conclusion. One important issue is not mentioned in that summary statement. If enough catastrophic or hazardous failures exist for estimating model parameters, the software is unlikely to ever meet reliability goals. One might apply the models to less severe failures, though. I do not think the range of models is quite as diverse as suggested. For example, the Goel-Okumoto model is a continuous version of the Jelinski-Moranda model. But no sign exists of settling down on a single model. I think there are a number of quantified performance objectives for these models: the LaPlace test for a decreasing failure rate, measures of the stability of parameter estimates, and Bev Littlewood's U and S tests of goodness of fit. Of course, one would have to agree to adopt some convention for confidence intervals or some such.

4.0 Further Thoughts

It is my impression that the FAA takes certification very seriously. Cost pressures and the evolution of technology lead to developers continually wanting to introduce new technology. And FAA-sponsored research has looked at the desirability of such introductions. For example, does the possibility of model checking make formal verification more practical? How should code coverage metrics be applied in testing object-oriented software? How should software developed with Model-Based Design be certified? Do MBD tools need to be certified and accredited, perhaps as installed on specific platforms? Should both the inputs and generated software be assessed?

Some of these considerations and developments in software technology are not all that new. The FAA should be conservative in what they will allow. For example, I like Java, but do not think it should be used for mission-critical software, with hard real-time and performance requirements. It might be used on an airplane for delivering consumer services, like music and movies to passengers, but in isolation from flight software.

At any rate, certification and accreditation by the FAA requires insight into engineering processes and cooperation with certification teams within developer organizations and their subcontractors. Even in an ideal world, decisions about who does what must be made here. Software technology is an important driver here, orthogonal to the need to align incentives.

But it does not matter how thoroughly certification and accreditation are defined if the FAA does not have the resources to provide oversight. And certification authorities must be willing to refuse to allow a plane to fly, with both commercial and government entities accepting such a decision. This is not a responsibility that I would want to have.

Saturday, March 23, 2019

Elsewhere

  • Arindrajit Dube writes an obituary for Alan Krueger, in Slate.
  • Maria Cristina Marcuzzo, at INET, highlights Krishna Bharadwaj's contributions to economics.
  • Longtime commentator Emil Bakkum's web page, collecting a variety of resources, is here.
  • An advocate of Modern Monetary Theory, Brian Romanchuk is apparently writing a book about models supposedly of Dynamic Stochastic General Equilibrium. Some recent posts include:
    • Questions about time scales in DSGE models. Anticipations have a time scale and so does calendar time as it passes.
    • A tutorial introduction to the limitations of linear models of business cycles. Basically, they either explode or decay, with possibly sinusoidal variation. Persistent cycles can only exist because of driving noise.
    • A long summary of problems with DSGE. Some of Romanchuk's objections, like that DSGE models are not put forth with standard mathematics, I find it hard to credit. On the other hand, I find it difficult to make sense of them too. (Romanchuk should probably read Athreya's book.)

Friday, March 15, 2019

Arguing Against "Libertarianism"

1.0 Introduction

By "libertarianism", I mean propertarianism, a right-wing doctrine. In this post, I want to outline some ways of arguing against this set of ideas. (On this topic, Mike Huben has much more extensive resources than I can allude to.)

2.0 On Individual Details

I like to use certain policy ideas as a springboard for arguments that they have no coherent justification in economic theory. Unsurprisingly, the outdated nonsense market fundamentalists push does not have empirical support either. I provide some bits and pieces here.

Consider the reduction or elimination of minimum wages. More generally, consider advocacy of labor market flexibility. I like to provide numerical examples in which firms, given a level and composition of net output, want to employ more workers at higher wages. Lots of empirical work suggests wages and employment are not and cannot be determined by supply and demand.

Lately, I have been developing examples of international trade. (I think these examples need work when produced means of production can be traded.) In these numerical examples, the firms in each country specialize as in the theory of comparative advantage. That is, they produce those commodities that are relatively cheaper to produce domestically. I explicitly show processes for producing capital goods and assume that capitalists obtain accounting profits. Numeric examples demonstrate that a country can be worse off with trade than under autarky. Their production possibilities frontier (PPF) is moved inward. So much for the usual opposition to tariffs.

Some like to talk about the marginal productivity theory of distribution. But no such valid entity exists. I suppose one could read empirical data on the distribution of income and wealth and mobility as support for this, although others might talk about monopsony and market power.

No natural rate of interest exists. So some sort of market rate would not be an attractor, if it wasn't for the meddling of Jerome Powell and the Federal Reserve. As I understand it, this conclusion also has empirical support.

A whole host of examples arises in modeling preferences. I do not think I have previously mentioned, for example, Sen's demonstration of The Impossibility of a Paretian Liberal.

One can point out sources of market failure from a mainstream perspective. I think of issues arising from externalities, information asymmetries, principal agent problems, and so on. As I understand it, John Quiggin is popularizing such arguments in his upcoming Economics in Two Lessons.

3.0 Arguments From Legitimate Authority

I like to cite literature propertarians claim as their own. One set of arguments is of their experts advocating policies on the other side. For example, in The Road to Serfdom, Hayek advocates a basic income and social security. He says his disagreement with Keynes is a technical argument about whether fiscal or monetary policy can stabilize the economy and prevent business cycles, not a matter of the fundamental principles he is arguing about in the book. Adam Smith argues for workers and against businessmen, projectors, and speculators. He doesn't expect rational behavior, as economists define such. Among scholars, those building on Marx could with more right wear Smith ties than Chicago-school economists.

A second set of arguments from authority provide a reductio ad absurdum. One points out that propertarian authorities seem to end up praising authoritarians and fascists or adopting racists as allies. I think of Von Mises praising Mussolini, Friedman's advice to Pinochet, and Hayek's support for the same. The entanglement between propertarianism and racists in the USA has been self-evident at least since Barry Goldwater's run for president. I might also mention Ron Paul's newsletters.

4.0 Hermeneutics of Suspicion

Instead of arguing about the validity of certain supposed propositions, one might argue about why some come to hold them. Why do so many argue against their concrete material interests and for the whims of malefactors of great wealth? In social psychology, one can point to research on the need for system justification and on the just world fallacy. Marxists can draw on Lukács' analysis of reification or Gramsci's understanding of civil society and hegemony.

I also like how doubt is cast on the doctrines just by noting their arguments are easily classified as falling into a couple of categories. Propertarians can be seen as hopping back and forth from, on one foot, justifying their ideas on consequential, utilitarian, or efficiency grounds to, on the other foot, justifying it based on supposed deductions from first principles. So when you attack one argument, they can revert to the other, without ever admitting defeat. (Am I stealing from John Holbo here? From Cosma Shalizi?)

Albert Hirschman classified arguments into three categories: perversity, futility, and jeopardy. One could always say, "I agree with your noble goals", but:

  • Your implementation will lead to the opposite.
  • What you are attempting is to change something that is so fundamental (e.g., human nature) that it cannot succeed.
  • Your attempt risks losing something else we value (e.g., self-reliance, innovation, liberty etc.)

If the arguments are always so simply classified, they cannot be about empirical reality, one might think.

5.0 Conclusion

None of the above addresses issues of political philosophy that propertarians may think central to their views. I do not talk about what roles of the state are legitimate, the source of authority in law, the false dichotomy of state versus markets, negative liberties and positive liberties, or the exertion of private power by means of the ownership of property. In short, this approach is probably irritating to propertarians. I'm good with that.

Thursday, March 07, 2019

Should Liberals Want A Coalition With Conservatives Or Labor?

This is current events, but this post is about current events in Britain in 1920. Lenin comments on reports of a dispute between Lloyd George and H. H. Asquith, both leaders of the Liberal party:

[In] the speech delivered by Prime Minister Lloyd George on March 18, 1920... Lloyd George entered into a polemic with Asquith (who had been especially invited to this meeting but declined to attend) and with those Liberals who want, not a coalition with the Conservatives, but closer relations with the Labour Party. (In the above-quoted letter, Comrade Gallacher also points to the fact that Liberals are joining the Independent Labour Party.) Lloyd George argued that a coalition — and a close coalition at that — between the Liberals and the Conservatives was essential, otherwise there might be a victory for the Labour Party, which Lloyd George prefers to call "Socialist" and which is working for the "common ownership" of the means of production. "It is . . . known as communism in France," the leader of the British bourgeoisie said, putting it popularly for his audience, Liberal M.P.s who probably never knew it before. In Germany it was called socialism, and in Russia it is called Bolshevism, he went on to say. To Liberals this is unacceptable on principle, Lloyd George explained, because they stand in principle for private property. "Civilisation is in jeopardy," the speaker declared, and consequently Liberals and Conservatives must unite. . . . -- Lenin (1920).

We see here centrists justifying an alliance with the right by calling those to their left "socialists" and "communists". Lenin, of course, was to the left of the British Labour party and did not consider them communists or Bolsheviks. Rather, he grouped their leaders with those like Karl Kautsky, who could not be counted on to stand up for the workers when World War II started. Or maybe Lenin considered the British soft left as worse, for Kautsky, according to Lenin, had previous achievements, including in theoretical works.

The context of this argument was Lenin arguing with those to his left. I think he is talking about anarchists and anarcho-syndicalists. He was criticizing them for arguing that, as a matter of principle, communists should not participate in such compromised institutions as parliaments and labor unions. Lenin asserts that this rules out the tactical flexibility the Bolsheviks exhibited in Russia through the 1905, February 1917, and October 1917 revolutions and so on. Lenin thinks British communists should support Labour, although he does say this support should be like the noose supports the hanged man. He continues the Marxist view that anarchism is a petty bourgeois tendency.

Lenin always wanted to agitate everywhere and on everything, including in labor unions, in parliaments, on economic questions, on land redistribution, on non-economic issues. The working class, according to him, need an external vanguard to elevate their consciousness from just trying to get more under capitalism, instead of throwing over capitalism. This approach worked for Lenin. But perhaps his attempt to generalize from Russia to Western Europe exhibited the need for the development of Antonio Gramsci's ideas.

References

Saturday, March 02, 2019

Scholars on Neoliberalism

The literature on neoliberalism is large. Here are some scholarly books on this subject or on related matters:

I think this literature has some common themes:

  • Neoliberalism was always a global project. (Is there a whole literature on Latin America I am missing?)
  • Markets are not natural, but a society organized around such must be created by a system of laws, along with instilling a "common sense" in the population so governed.
  • Neoliberalism must be accompanied by control on or limitations of democracy.
  • The development of neoliberalism was funded by extremely wealthy individuals around the world, who sought to prevent their project from receiving public scrutiny.
  • Those academics funded to develop apologetics and guidance were always interdisciplinary, including those specializing in law and international relations, as well as in economics.

The literature also contains disagreements, including what institutions, groups, and individuals to emphasize in telling the story of the project of imposing neoliberalism on the world.

Tuesday, February 26, 2019

"The Microeconomic Foundations of Aggregate Production Functions"

Figure 1: A Production Network

I here comment on Baqaee and Farhi (2018). I am still trying to absorb it. I suppose that it is nice that an economist at Harvard is revisiting the Cambridge Capital Controversy (CCC). (Where is Michael Mandler these days?)

My major criticism is they do not do what their title claims. That is, their supposed microeconomic foundations are still up in the air.

In many CCC examples, technology is specified in terms of fixed-coefficient production processes. Sometimes, more than one process is available for producing a specified commodity. This structure gives rise to a choice of technique. If one wanted, one could formulate a programming problem, in each sector, whose solution is a production function for that sector. This production function would not be differentiable everywhere.

Baqaee and Farhi, on the other hand, assume the existence of continuously-differentiable microeconomic production functions in each sector. In this paper, these production functions are specifically Constant Elasticity of Scale (CES) production functions. (As should be the case, their inputs and outputs are specified in physical units, not in price terms.)

I am willing to be convinced that this difference in starting points is a technical matter. Or that Baqaee and Farhi are making some progress towards a more complete framework that will include models of the production of commodities by means of commodities. I have some challenges, however.

There is a theorem whose status I am not sure of. It states that, given a continuously differentiable production function for a commodity that is basic, in the sense of Sraffa, for all techniques, reswitching is not possible. (Stephen Marglin was not the first to offer a proof of this theorem.) Thus, Baqaee and Farhi rule out, by assumption, many (most?) of the reswitching examples and much of the structure in the literature on the CCC. As they note, their assumptions do include an example from Paul Samuelson, in his 1966 "Summing Up" article. That example, had a flow-input, point-output structure, with no commodity basic in any technique.

Second, I gather Baqaee and Farhi think of themselves as starting with microeconomic data that is in principle empirically observable. These would be elasticities of substitution at points on factor demand curves that are chosen at an instance of time. Part of the point of the CCC is to question the existence of factor demand curves, including for intermediate inputs. In a comparison of long period positions, it is an incoherent thought experiment to vary one price at a time. On the other hand, as Han and Schefold have shown, empirical work can be based on given fixed coefficients processes. I think if Baqaee and Farhi were to take this point, they would have to rewrite a lot of their paper, including sections talking about the bias of technical change and macroeconomic elasticities of substitution between factors.

Baqaee and Farhi do have an interesting suggestion for visualizing a production network in logical time. (I've previously presented a less detailed approach from Bidard.) My diagram above is an attempt to expand on Baqaee and Farhi's approach. For each time period, four processes (a, b, c, and d) exist for producing one of two commodities from inputs of labor and those two commodities. The first two processes have the first good as output, and the second two processes produce the second good. The second commodity can be used for consumption, as well as a capital good in the production of either good. This is basically the technology for the examples in Vienneau (2005). The diagram could be simplified by not explicitly showing the demultiplexers and the summations.

References
  • David Rezza Baqaee and Emmanuel Farhi (2018). The Microeconomic Foundations of Aggregate Production Functions. 26 November.
  • Robert L. Vienneau (2005). On Labour Demand and Equilibria of the Firm. Manchester School 73(5): 612-619.

Thursday, February 14, 2019

Some Contradictions Of Capitalism

I tend to be doubtful, albeit sometimes amused, by comments drawing on Hegel. But I thought I would adopt some of that sort of language for a post.

Capitalism constantly revolutionizes production, leading to a fantastic increase in productivity. An ever more diverse set of commodities is produced, including for consumption. Machines for making, controlling, and communicating with other machines, are constantly being introduced, reducing the labor time needed to produce any commodity.

For the diversity in commodities to be sold, workers, who constitute the most part of consumers, must develop their abilities to appreciate as much as possible. Likewise, they must developers their capabilities to be able to change the industry in which they work:

But if, on the one hand, variation of work at present imposes itself after the manner of an overpowering natural law, ... modern industry, on the other hand, through its catastrophes imposes the necessity of recognising ... variation of work, consequently fitness of the labourer for varied work, consequently the greatest possible development of his varied aptitudes... Modern Industry, indeed, compels society ... to replace the detail-worker of to-day, grappled by life-long repetition of one and the same trivial operation, ... by the fully developed individual, fit for a variety of labours, ready to face any change of production, and to whom the different social functions he performs, are but so many modes of giving free scope to his own natural and acquired powers. -- Karl Marx, Capital, Chapter 15, Section 9.

In this chapter, Marx also quotes from the Communist Manifesto, "All that is solid melts into air..."

But, yet, the time in which the worker is enjoying himself is time that he is not generating surplus value for the capitalist. And it is an accidental distinction that some goods can be marketed and some cannot. Furthermore, higher wages is a threat to maintaining the rate of profits. So the evolution of capitalism puts some constraints on what and how the workers can develop their selves. Furthermore, the development of flexibility in production capabilities is accompanied with anxiety at being made redundant in one's job, of recurrent unemployment, and the continual recreation of the army of the unemployed.

(Fans of Pierre-Joseph Proudhon might be interested that, around where the above passage appears, Marx talks about the "good side" and the "bad side" of these contradictions in the development of capitalism, in quite a different tone than in The Poverty of Philosophy.)

Saturday, February 09, 2019

Catalog Of Neoclassical Responses To The Cambridge Capital Controversy

This is merely a list and, as usual, off the top of my head.

  • Paul A. Samuelson (1966). A summing up. Quarterly Journal of Economics 80: 568-583.
  • Mark Blaug (1975). The Cambridge revolution: Success of failure? A critical analysis of Cambridge theories of value and distribution. Institute of Economic Affairs.
  • Joseph E. Stiglitz (1974). The Cambridge-Cambridge controversy on the theory of capital: A view from New Haven.
  • Christopher J. Bliss (1975). Capital Theory and the Distribution of Income. Elsevier North-Holland.
  • Avinash Dixit (1977). The accumulation of capital theory. Oxford Economic Papers 29: 1-29.
  • Edwin Burmeister (1980). Capital Theory and Dynamics, Cambridge University Press.
  • Frank Hahn (1982). The neo-Ricardians. Cambridge Journal of Economics 6: 353-374.
  • Andreu Mas Colell (1989). Capital theory paradoxes: Anything goes. In Joan Robinson and Modern Economic Theory (ed. by G. R. Feiwel), Macmillan.
  • Mario Ferretti (2004). The neo-Ricardian critique: An anniversary assessment.
  • Gaetano Bloise and Pietro Reichlin (2005). An obtrusive remark on capital and comparative statics.
  • Michael Mandler (). Sraffian economics (new developments). In New Palgrave, 2nd edition.

I could have cited many more references from Burmeister, Mandler, or Samuelson. I do not know if the last two were published as anything more than working papers. As far as I am concerned, most mainstream economists also ignore the neoclassical side of the CCC.

Thursday, February 07, 2019

Women In Economics

Here is a list of female economists I have learned from or would like to know more about:

  • Jane Marcet
  • Harriet Martineau
  • Charlotte Perkins Gilman
  • Rosa Luxemburg
  • Edith Penrose
  • Joan Robinson
  • Krishna Bharadwaj
  • Anne Mayhew
  • Phyliss Deane
  • Victoria Chick
  • Ingrid Rima
  • Nancy Folbre

Obviously, this list reflects my interests and biases. This list is off the top of my head.

Friday, January 25, 2019

Donald J. Harris

Don Harris is a Stanford economist. Apparently, this post is on current events. His daughter, Kamala Harris is the junior senator from California and has announced that she is running for President of the United States. I gather Don and his wife divorced when Kamala was quite young, and that his ex-wife raised her.

I do not know much about Harris' personal history. I did not even know that he was Jamaican. Did he give Michael Manley any advice? (This is a great movie.) It is his more theoretical work that I am aware of. It is decades since I have read his AER article and book, and I do not recall much about them. I find that I happen to have handy the other five items in the reference below, including Harris' foreword to a reprint of the Bukahrin book.

If I do remember anything about the AER article, my impressions is that it is an overview of the Cambridge capital controversy, closer to Sraffa than Joan Robinson's emphasis on historical time. For purposes of this article, I'll talk about, rather, the article in Nell's 1980 collection.

Harris (1980) starts out by describing the aggregate neoclassical theory, including growth theory. He refers to Samuelson calling it a parable or fairy tale. He presents this theory in the context of a response to Harrod. Substitution of capital for labor allows for the existence of a stable steady state growth path. Of course the Cambridge capital controversy showed this parable does not apply once one allows for the production of more than one commodity. I like to put it that, in a comparison of steady states, a higher wage, all else equal, is not necessarily associated with the adoption of a technique requiring less labor to be employed per unit output. Harris suggests the existence of such non-monotonic relationships between inputs and prices has wider repercussions in the neoclassical theory of general equilibrium. Asserting that the price of each input is equal to the value of its marginal product doesn't get you very far.

Harris then moves on to considering an alternate theory, with labor being exploited, as in Marx. He has an independent investment function. He considers three possible regimes. I am reminded of some work of Joan Robinson in the 1960s and her "banana" diagram. Or looking ahead, to a Bhaduri and Marglin paper.

Harris, I guess, is closer to Marx than some Post Keynesians. It make sense that once one has seen that most of academic mainstream economics is nonsense, in many ways, that one would turn to a sociological explanation of why this balderdash persists. The leisure class, in Bukharin's terminology, consists of those, generally very rich, who obtain income from property, without having to do a lick of work. They need it to be commonsense that their exploitation be acceptable. Academics, particularly neoclassical economics, fill this need. Bukharin focuses specifically on Austrian economics.

I should probably reread Bhaduri and Harris (1987). It is the sort of article that needs an illustration or two. Such an illustration is easy to generate with the information technology we now have available.

(Gramsci's Political Thought (Brill, 2012), by Carlos Nelson Coutinho, is another book on my shelf. The foreword is by Joseph A. Buttigieg. His son, Pete, is mayor of South Bend, Indiana and just announced that he is running for President.)

References
  • Amit Bhaduri and Donald J. Harris (1987). The Complex Dynamics of the Simple Ricardian System. Quarterly Journal of Economics. (Reprinted in: Unconventional Economic Essays: Selected Papers of Amit Bhaduri (1993). Oxford University Press.)
  • Nikolai Bukharin. (1927). Economic Theory of the Leisure Class.
  • Donald J. Harris (1973). Capital, distribution, and the aggregate production function, American Economic Review 63 (1): 100-113. (reprinted? in Sraffian Economics, 2 volumes, (ed. by Ian Steedman) Edgar Elgar (1989)).
  • Donald J. Harris (1978). Capital Accumulation and Income Distribution. Stanford University Press.
  • Donald J. Harris (1980). A postmortem on the neoclassical 'parable'. In Growth, Profits, and Property: Essays in the Revival of Political Economy (ed. by E. J. Nell). Cambridge University Press
  • Donald J. Harris (1990). Comment (on Pasinetti). In Essays on Piero Sraffa: Critical Perspectives on the Revival of Classical Theory (ed. by K. Bharadwaj and B. Schefold). Routledge
  • Donald J.Harris (2005). Robinson on 'History versus equilibirum'. In Joan Robinson's Economics: A Centennial Celebration (ed. by B. Gibson). Edward Elgar.

Saturday, January 19, 2019

Elsewhere: Popular Writing On Modern Monetary Theory

Some articles:

I do not assert that all points in these articles are well-taken.

I think of MMT as descriptive. It combines endogenous money, functional finance, and chartalism. Much of its empirical evidence consists of qualitative descriptions of how financial institutions and central banks operate. One can imagine a policy regime where unemployment and inflation are addressed by changes in the level of taxes and government spending, with monetary policy is a more passive attempt to keep interest rates permanently low. This would contrast with one where central banks are more responsible, through interest rate policy, with addressing unemployment and inflation. An analysis of the implications of such treatments need not be normative.

(Some asides: As a contrast, Josh Barro could have brought up his father, Robert's, treatment of Ricardian equivalence, which Ricardo rejected. Doesn't Marx, in chapter 1, volume 1 of Capital have an incorrect theory in which barter precedes money?)

Saturday, January 12, 2019

What Is Pure Capitalism?

1.0 Introduction

This post is fairly stream of consciousness. It is a bit more about how many find me odd.

I have previously mentioned, as an aside, Kozo Uno and his reading of Marx's Capital as a theory of pure capitalism. I like this idea, although it needs to be noted Marx had a lot to say in Volume I about concrete practices in his day and the historical development of capitalism. The theory and history are entwined. But Marx certainly presents the capitalist, not as a person, but as an embodiment of capital, in some sense.

I often bring a book with me when I go out to eat by myself. Sometimes people ask me what I am reading. For example, I have lately been re-reading the first volume of Capital; Marx's Value, Price, and Profit; and Böhm-Bawerk's Karl Marx and the Close of his System.

2.0 Small Businessmen Do Not Exist in Pure Capitalism

Many I run into are small businessmen, that is, petty bourgeois, in Marxist phraseology. I think of restaurant owners, general handymen, providers of mowing and plowing services, owners of auto repair shops, landscaping artists, and even one movie producer, musicians, consultants on Information Technology and Information Assurance, and so on. They do not obtain income solely from returns to capital, but, rather, from some combination of labor and capital. Their labor includes general scut work, managerial direction, and strategic planning. (Which of these tasks comprises the labor of superintendence?) Some have partners with finance capital invested in the business, often family members. Some sometimes have a few employees, and some have many more.

Maybe this is politeness, but I often say that Marx is not writing about you. I do not want to try to explain that capitalism restricts even your agency. I think many are conscious of trade-offs in staffing too much or too little on any given day, on the level of service provided, and on ensuring that staff do not quit. I bet many might agree that some staff that fall into the category of so-called unskilled labor, such as bartenders, baristas, waiters, bussers really know a lot about their tasks, do them well, and would take much time to train replacements. When they bid on jobs, they are conscious of socially necessary labor time and are worried about whether, for some reason not necessarily within the control of the worker, a job might take longer than assumed in the calculations which a bid was based on. Yet they feel that, with competition as it is, they cannot include a reserve time or even fully charge their own time. (Come to think of it, I am not including here those I know who make their income from profit on alienation, by buying collectibles low and selling high.)

I am more likely to explain to workers that the business owners' income comes from value added by their labor but not paid out in their wages. I also say that my income from Apple also comes from the exploitation of workers, and that this would be so even if Foxconn was not treating their workers so badly that they had to line their dorms with nets at ground level. And, of course, I am a consumer of commodities produced under capitalism. I am amused to attempt to explain that the labor theory of value can be seen not to work, as a theory of price, because of the existence of such products as wine and whiskey.

If you think about it, small businessmen do not fit in with the abstraction of pure capitalism since their earnings do not come solely from capital. Self-employed artisans and those close to such are, for Marx, survivors from a period of time before capitalism was fully developed. With John Kenneth Galbraith, I think this sector, however, will always exist, aside with the large corporate sector, in which many are somewhat sheltered, for a time, from the gales of competition.

3.0 Workers with Savings Do Not Exist in Pure Capitalism

Many skilled workers in the United States have savings, often in the form of mutual funds. They might not be able to access this wealth immediately, without a penalty, if it is in a 401K or Individual Retirement Account (IRA). (Defined-benefit pensions are now rare.) My casual empiricism is consistent with the observation that a tiny fraction of the population owns most of the wealth in the United States.

Here is another class of people whose income consists of returns to both labor and ownership of capital. And they have deferred not only the day-to-day management of the firms they indirectly have ownership shares in, but even decisions about investing and disinvesting in such firms to paid professionals. Does it matter to how the system works whether these savings are managed by financial experts on Wall Street or specialists more closely connected to labor unions? How should analyze executives corporate suites whose income is often classified as salaries, but anyways seems to have something to do with being in a class with control, but not ownership of the means of production? (I have not actually read that book or the one linked above by Drucker.)

4.0 Conclusion

So what kind of society is Marx describing abstractly? I think that in pure capitalism, some capitalists should be making investment decisions, but not being paid for labor power. Perhaps we want to think of the mid-nineteenth century when industrialists like John D. Rockefeller, Andrew Carnegie, or Karl Wittgenstein were starting out, but before they had obtained oligopolistic power.

One can build on this model to describe historic capitalism. You might think my account of small businesses shows something about a system organized around the production of commodities by means of commodities. Others have developed analyses of monopoly and finance capitalism. In the Post Keynesian tradition, Richard Kahn, Nicholas Kaldor, Luigi Pasinetti, and Joan Robinson had developed a model in which workers save, but investment decisions are driven by another class. Maybe a different model is more appropriate for the neoliberal era after the end of Bretton Woods, and in which workers do not seem to find their wages growing with productivity.

Friday, January 04, 2019

Linear Programming, M-C-M, and C-M

1.0 Introduction

Consider typical Linear Programs (LPs) for formulating the theory of firm in classical and neoclassical economics. I claim that the classical theory can be formulated as M-C...P...C-M, and that the neoclassical theory of production is something like C...P...C-M.

The notation is from Marx. For Marx, simple commodity circulation is represented as C-M-C. A commodity is sold for money, and then that money is used to buy another commodity. An owner of a use value trades it for a more desired use value. The formula M-C-M characterizes capitalism. A capitalist buys commodities so as to later sell commodities to somehow obtain more money. The goal is the accumulation of capital, not the acquisition of commodities.

2.0 Classical Theory of Production

For the classical theory, I had a recent presentation here. This is the price-side of John Roemer's Reproducible Solution (RS). The question is what must prices be such that firms can be willing to choose to produce commodities such that capital goods are reproduced (perhaps on an expanded scale), so that the economy will continue.

For ease of exposition, I might as will assume all commodities are basic commodities (in Sraffa's sense) and that there is no choice of technique. I define the following variables:

  • ω: A N-element column vector of commodities in existence at the start of the year.
  • a0: A N-element row vector of labor coefficients for each industry.
  • A: A N x N Leontief matrix, with each column listing the coefficients of production for each industry.
  • w: The wage.
  • p: A N-element row vector of prices for each produced commodity.
  • q: Decision variables. A N-element column vector of the quantity of each commodity to produce.
  • r: Decision variable. The rate of profits.

Each firm begins with an inventory of produced commodities, after having sold those needed for consumption last year. A firm chooses quantities to produce, q, to:

Maximize {p - [p A + a0 w]} q

such that

p A qp ω
qi ≥ 0, i = 1, 2, ..., N

The dual LP is to choose the rate of profits, r, to:

Minimize p ω r

such that:

p A(1 + r) + a0 wp
r ≥ 0

Some theorems from duality theorem are useful here. If a decision variable is positive in an optimal solution to the primal LP, the corresponding constraint is met with equality in the dual LP. In this simple presentation, where all commodities must be produced for the economy to be smoothly reproduced, all decision variables in the primal LP must be positive. Consequently, all constraints must be met with equality in the dual LP. That is, the dual LP provides a system of N equations in N + 2 price variables. An introduction of a choice of technique yields a justification of Kurz and Salvadori's direct method.

Commodities appear on the right-hand side of the constraint in the primal LP. And the decision variables are the commodities to be produced. But the constraint is that the value of the capital goods advanced be less than the value of the given inventory. Likewise, the capitalists are trying to maximize the increment of value. Realization problems are abstracted from here. One assumes that markets exist where one can trade inventory for more appropriate commodities for production plans, and likewise produced commodities can be sold. So the LP can be characterized as M-C-M'. It describes the wealth of society as "an immense accumulation of commodities."

3.0 Neoclassical Theory of Production

For the neoclassical theory, you can look at an appendix in Pasinetti (1977). Neoclassical theory is about the allocation of given resources. I define the following variables:

  • b: A M-element column vector of (unproduced?) factors of production available at the start of the year.
  • A: A M x N Leontief matrix, with each column listing the coefficients of production for each process.
  • p: A N-element row vector of prices for each produced commodity, with repeated prices for commodities with more than process for producing them.
  • q: Decision variables. A N-element column vector of quantities to produce with each process.
  • w: Decision variables. A M-element column vector of shadow prices.

The factors of production need have no relation to produced commodities. Don't think of seed corn and harvested corn. Think rather of various kinds of land, ores, and such-like for factors; and of consumer goods for produced goods. The managers of firms, in neoclassical theory, choose the levels, q, of operation of each process to:

Maximize p q

such that

A qb
qi ≥ 0; i = 1, 2, ..., N

The dual LP is to choose shadow prices w

Minimize bT w

such that

AT wpT
wj ≥ 0; j = 1, 2, ..., M

If a process is not operated in the solution to the primal LP, its cost, at shadow prices, exceeds the price of its outputs. If a given resource has a positive shadow price in the solution to the dual LP, it will fully used in the primal LP. Or, if it is not fully used (its constraint in the primal LP is met with inequality) then its shadow price will be zero.

The neoclassical theory ends up with C-M as a description of produced commodities being sold on markets. Its starts with use-values, though. So I guess it can be represented at, a high-level, as C-M alone.

4.0 Conclusion

I have previously contrasted post-Sraffian price theory and the neoclassical theory of value. The former is about an analysis of what needs to be the case for the reproduction of society. The latter is about the allocation of scarce resources. This post has introduced another contrast. Post-Sraffian price theory applies to a capitalist society, in which the accumulation of monetary value is an end of itself. I am not sure what kind of society, if any, can be described by the neoclassical theory of production. I guess neoclassical economics makes a bit more sense when it is used to described a series of temporary equilibria strung together.

References
  • Robert Dorfman, Paul A. Samuelson, and Robert M. Solow. 1958. Linear Programming and Economic Analysis
  • Heinz Kurz and Neri Salvadori. 1995. The Theory of Production: A Long-Period Analysis.
  • Luigi L. Pasinetti. 1977. Lectures on the Theory of Production
  • John Roemer. 1979. Analytical Foundations of Marxian Economic Theory
  • Robert L. Vienneau. 2005. On labour demand and equilibria of the firm. Manchester School: 73: 612-619.