Welcome

I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

The Production Of Commodities And The Structure Of Production

Many of my examples illustrate simple structures of production for models in which commodities are produced with commodities. Economists following the Austrian school often illustrate the structure of production with Hayekian triangles. Accordingly, this post illustrates a Hayekian triangle with a model in which commodities are produced out of commodities. I consider the case in which only circulating capital exists. This post is a rewrite of this one.

The following are taken as given for the technique in use:

• A: The nxn Leontief input-output matrix in physical terms. Assume all commodities are basic and the economy is productive.
• a₀: The n-element row vector of direct labor coefficients.
• d: An n-element column vector that is in the proportions in which commodities are consumed.

Define:

denom = a₀(I - A)^-1d

From the given data, one can find the quantities of labor-time in the first column below.

Distribution of Work in a Given Year

Labor Time	Purpose
a0d/denom	To produce (1/denom) d, a basket of commodities for consumption at the end of the current year.
a0A d/denom	To produce capital goods to be used to produce the (1/denom) d basket of commodities for consumption at the end of the next year.
a0A2 d/denom	To produce capital goods to be used to produce capital goods to produce the (1/denom) d basket of commodities for consumption at the end of two years hence.
...	...

The first column can be summed:

(1/denom) a₀(I + A + A² + ...)d = a₀(I - A)^-1d/denom = 1 person-year

So the above table shows a decomposition, per person-year, of employment in a given year. It is a Hayekian triangle. Because it is constructed from a model of the production of commodities, the elements go on forever. No last year exists in the future for which capital goods are currently being produced.

The capital goods, Aⁿ d, approach the ratios of Sraffa's standard commodity. Consequently, the ratio of labor inputs approaches a constant, related to the maximum rate of profits.

Hayekian triangles are not necessarily set out with a single physical measure of an unproduced input at each stage. The value of capital goods per worker varies because of three effects:

• Composition effect: a different mixture of capital goods is used for different rates of growth.
• Price Wicksell effect: the capital goods are re-evaluated at different prices with a different interest rate.
• Real Wicksell effect: the capital goods vary with the technique, and the cost-minimizing technique varies with the interest rate.

The wage-rate of frontier is useful for visualizing these effects. They do not go away just because one represents the structure of production as a Hayekian triangle. The sort of regularities that Machaj (2017), for example, assumes with variations in the interest rate lack logical foundation.

I want to that the price of the commodities consumed at the end of the year is:

[w(r)/denom] [a₀d + a₀A d (1 + r) + a₀A² d (1 + r)² + ... ]

The terms in the above are useful in representing a Hayekian triangle in price terms.

A model of the production of commodities by means of commodities with general joint production cannot necessarily be represented to a series of inputs of dated labor inputs. I go back and forth on my intution in the case of pure fixed capital.

References

• Renaud Fillieule. 2007. A formal model in Hayekian macroeconomics: the proportional goods-in-process structure of production. Quarterly Journal of Austrian Economics 10: 193-208.
• Harris, Donald J. 1973. Capital, distribution and the aggregate production function. American Economic Review 63(1): 110 - 113.
• Machaj, Mateusz. 2017. Money, Interest, and the Structure of Production: Resolving Some Puzzles in the Theory of Capital. Lanham: Lexington Books.

Maynard Keynes Making Fun Of The Austrian School

This is for my commonplace book.

"It is true that some lengthy or roundabout processes are physically efficient. But so are some short processes. Lengthy processes are not physically efficient because they are long. Some, probably most, lengthy processes would be physically very inefficient, for there are such things as spoiling or wasting with time. With a given labour force there is a definite limit to the quantity of labour embodied in roundabout processes which can be used to advantage. Apart from other considerations, there must be a due proportion between the amount of labour employed in making machines and the amount which will be employed in using them. The ultimate quantity of value will not increase indefinitely, relatively to the quantity of labour employed, as the processes adopted become more and more roundabout, even if their physical efficiency is still increasing. Only if the desire to postpone consumption were strong enough to produce a situation in which full employment required a volume of investment so great as to involve a negative marginal efficiency of capital, would a process become advantageous merely because it was lengthy; in which event we should employ physically inefficient processes, provided they were sufficiently lengthy for the gain from postponement to outweigh their inefficiency. We should in fact have a situation in which short processes would have to be kept sufficiently scarce for their physical efficiency to outweigh the disadvantage of the early delivery of their product. A correct theory, therefore, must be reversible so as to be able to cover the cases of the marginal efficiency of capital corresponding either to a positive or to a negative rate of interest; and it is, I think, only the scarcity theory outlined above which is capable of this.

Moreover there are all sorts of reasons why various kinds of services and facilities are scarce and therefore expensive relatively to the quantity of labour involved. For example, smelly processes command a higher reward, because people will not undertake them otherwise. So do risky processes. But we do not devise a productivity theory of smelly or risky processes as such. In short, not all labour is accomplished in equally agreeable attendant circumstances; and conditions of equilibrium require that articles produced in less agreeable attendant circumstances (characterised by smelliness, risk or the lapse of time) must be kept sufficiently scarce to command a higher price. But if the lapse of time becomes an agreeable attendant circumstance, which is a quite possible case and already holds for many individuals, then, as I have said above, it is the short processes which must be kept sufficiently scarce." -- John Maynard Keynes, The General Theory of Employment, Interest and Money, Chapter 16.

Before this quotation, Keynes notes that when people save, they do not put in future orders for specific capital goods. Savers want general power over wealth. Keynes is correct about this. Nevertheless, I can see how some might say capital theory has something to do intertemporal coordination of plans. Yet the Austrian school is mistaken about how they associate greater capital with more lengthy investments, in some sense.

Francis Spufford On Commodity Fetishism As A Dance

I have expressed an appreciation before of the section in Capital on commodity fetishism. Perhaps this section stands up to a critique of Marx's theory of value.

"But Marx had drawn a nightmare picture of what happened to human life under capitalism, when everything was produced only in order to be exchanged; when true qualities and uses dropped away, and the human power of making and doing itself became only an object to be traded. Then the makers and the things made turned alike into commodities, and the motion of society turned into a kind of zombie dance, a grim cavorting whirl in which objects and people blurred together till the objects were half-alive and the people were half-dead. Stock-market prices acted back upon the world as if they were independent powers, requiring factories to be opened or closed, real human beings to work or rest, hurry or dawdle; and they, having given the transfusion that made the stock prices come alive, felt their flesh go cold and impersonal on them, mere mechanisms for chunking out the man-hours. Living money and dying humans, metal as tender as skin and skin as hard a metal, taking hands, and dancing round, and round, and round, with no way ever of stopping: the quickened and the deadened, whirling on. That was Marx's description, anyway. And what would be the alternative? A dance of another nature, Emil presumed. A dance to the music of use, where every step fulfilled some real need, did some tangible good, and no matter how fast the dancers spun, they moved easily, because they moved to a human measure, intelligible to all, chosen by all. Emil gave a hop and shuffle in the dust." -- Francis Spufford, Red Plenty, Graywolf Press, 2010: 66-67.

I may write a short review of this novel. If I do, I think I will not first review the seminar at Crooked Timber on it.

A Derivation Of Prices Of Production With Linear Programming

1.0 Introduction

This post illustrates a derivation of prices of production, based on certain properties of duality theory as applied to linear programming. I strive to be more concise and elementary than previous expositions. This exposition is based on John Roemer's Reproducible Solution (Analytical Foundations of Marxian Economic Theory, Cambridge University Press, 1981).

You will find no utility maximization or supply and demand functions below. I have no need for such hypotheses. Nevertheless, one can read this derivation as consistent with marginalism.

2.0 Technology and Endowments

Two commodities, iron and corn, are produced in this example. Managers of firms know a technology consisting of the processes defined in Table 1. Each column shows the inputs and outputs for a process operated at a unit level. All processes take a year to complete and provide their output at the end of the year. Each process exhibits constant returns to scale (CRS). For convenience, assume all coefficients of production defined in the table are positive. The inputs to production are totally used up by operating these processes.

Table 1: The Technology

INPUTS	Processes
	Iron Industry		Corn Industry
	a	b	c	d
Labor	a0,1(a)	a0,1(b)	a0,2(c)	a0,2(d)
Iron	a1,1(a)	a1,1(b)	a1,2(c)	a1,2(d)
Corn	a2,1(a)	a2,1(b)	a2,2(c)	a2,2(d)
OUTPUT	1 ton iron	1 ton iron	1 bushel corn	1 bushel corn

The endowments of iron and corn in the firm's inventory at the start of the year are also given parameters. Table 2 lists the remaining variables in this post. Presumably, the endowments are from production during the previous year. They are unlikely to be in the proportions needed to continue production. For example, if the managers of a firm decide to specialize in producing corn, they will have no endowments of iron.

Table 2: Parameters and Variables

Additional Parameters
ω1	Endowment of iron (in tons) for the firm.
ω2	Endowment of corn (in bushels) for the firm.
Parameters taken as given by managers of the firm
p	Price of iron (in bushels per ton).
w	The wage (in bushels per person-year).
Decision Variables
q1(a)	Quantity of iron (in tons) produced by the first process.
q1(b)	Quantity of iron (in tons) produced by the second process.
q2(c)	Quantity of corn (in bushels) produced by the third process.
q2(d)	Quantity of corn (in bushels) produced by the fourth process.
r	The rate of profits.

3.0 The Primal Linear Program

Managers of firms choose the quantities to produce with each process to maximize the increment z in value, subject to the constraint that they can buy the needed inputs at the start of the year out of the revenue obtained by selling their endowment. The objective function for the primal linear program is:

z = {p - [p a_1,1(a) + a_2,1(a) + w a_0,1(a)]} q₁(a)

+ {p - [p a_1,1(b) + a_2,1(b) + w a_0,1(b)]} q₁(b)

+ {1 - [p a_1,2(c) + a_2,2(c) + w a_0,2(c)]} q₂(c)

+ {1 - [p a_1,2(d) + a_2,2(d) + w a_0,2(d)]} q₂(d)

The quantities in the square brackets above are the costs of operating each process at a unit level. A bushel corn is taken as numeraire. The quantities in the squiggly brackets are the net revenues (also known as accounting profits) of operating each process at a unit level. Scaling these net revenues by the level of operation for each process results in the total accounting profit for the firm.

The constraints are:

[p a_1,1(a) + a_2,1(a)] q₁(a)

+ [p a_1,1(b) + a_2,1(b)] q₁(b)

+ [p a_1,2(c) + a_2,2(c)] q₂(c)

+ [p a_1,2(d) + a_2,2(d)] q₂(d) ≤ p ω₁ + ω₂

q₁(a) ≥ 0, q₁(b) ≥ 0, q₂(c) ≥ 0, q₂(d) ≥ 0

The statement of the constraints is based on the assumption that wages are paid at the end of the year, not advanced at the start.

4.0 The Dual Linear Program

The above linear program has a dual. In the dual, the rate of profits r is chosen to minimize the charge y on endowments:

y = (p ω₁ + ω₂) r

Such that:

[p a_1,1(a) + a_2,1(a)](1 + r) + w a_0,1(a) ≥ p

[p a_1,1(b) + a_2,1(b)](1 + r) + w a_0,1(b) ≥ p

[p a_1,2(c) + a_2,2(c)](1 + r) + w a_0,2(c) ≥ 1

[p a_1,2(d) + a_2,2(d)](1 + r) + w a_0,2(d) ≥ 1

r ≥ 0

Each constraint in the dual specifies that the revenues obtained from operating a process at the unit level do not exceed the costs, where costs include a charge for the going rate of profits. In other words, no super-normal profits can be obtained.

5.0 Some Observations About Duality

The value of the objective functions are equal in the solutions to the primal and dual LPs. In other words, the increment in value obtained by the decisions of the manager of a firm is charged to the value of the endowment.

Suppose the solution of the primal LP results in some process being operated at a positive level. Then the corresponding constraint in the dual LP is met with equality in its solution. Likewise, if a constraint in the dual is met with inequality, then that process will not be operated in the dual.

If the rate of profits in the solution to the dual is positive, then the constraint in the primal LP will be met with equality. That is, the whole value of the endowment will be used for further production.

6.0 Prices of Production

I introduce a final assumption. The solution to these LPs must be such that the economy can continue. In the context of this exposition, some firms must produce iron, and some must produce corn. Thus, one of the first two constraints in the dual LP must be met with equality. One of next two constraints must also be met with equality.

Consider the case when only one of the processes for producing iron is operated, and the same is true of the processes for producing corn. The dual LP yields a system of two equations in three variables: the price of iron, the wage, and the rate of profits. This system specifies prices of production.

This formulation solves for the choice of the technique, as well as prices of production. It can be generalized to allow for the production of many more commodities and many more processes for producing each commodity. A generalization can allow for heterogeneous labor. Another generalization allows for the production and use of fixed capital, that is, machines that last for many years. For a given wage, prices and the rate of profits drop out of the equations for prices of production for the chosen technique. These prices do not support the parables often told in introductory economics classes with supply and demand. For example, unemployment cannot necessarily be eliminated by lowering the wage and encouraging firms to thereby hire more labor.

7.0 Conclusion

The above illustrates some elements of a theory of value. This is neither a labor theory of value, nor Marx's theory of value. The theory is focused on production and has implications about how labor is allocated among industries, a central concern of Karl Marx.

Nancy Kress On Global Inequality And Poverty

I picked up the novel that the following quotation is from because I think I recall Kress participating in conversations on Usenet years ago. This novel ended up more a political argument than I expected. It is for Genetically Modified Organisms (GMOs), done right. We should rather strive for plants for food resistant to insects, not resistant to pesticides, for example. I assume that Kress agrees with her heroine.

"He had spent the two-week winter vacation from school, which somehow got extended to nearly another week, with Jake in Los Angeles...

He left an eleven-year old nerd, dress in Levi's, a tee that said CHESS PLAYERS HAVE GREAT MOVES, and a baseball cap. He returned looking like a thirty-two-year-old investment banker trying to be cool, dressed in a $300 Ferragamo zip-front polo, designer jeans, and sockless shoes that cost more than my weekly salary. He carried a state-of-the-art laptop that could probably have moved satellites in orbit. Jake had invested in an independent production company that had struck movie gold with two wildly popular films about aliens who battled Earth. Jake was rich.

'Wow, look at you,' I said, not approvingly.

Ian could always read me. 'You don't like it. Dad said you wouldn't. But just because some of the world isn't blessed doesn't mean that we shouldn't enjoy the facts that through our own efforts, we are.'

I stared at him. No way that was Ian talking, or even Jake. I asked, 'Who is she?'

'Who's who?' But he shifted from one foot to the other as we faced each other at the SeaTac arrival gate. Passengers streamed past.

'Your dad's new girlfriend. It's okay, Ian, he's an adult. So am I.'

He turned sulky. 'Sage Scott.'

I blinked. She was a huge international star with more beauty than talent. 'Well,' I said heartily, 'that's fine. But -'

'Mom,' Ian blurted out, 'don't hassle me because I like money, okay.'

'Money is useful,' I said, and hugged him again.

But it wasn't that easy. With almost-teenagers, it never is. There were times during the next week when I wanted to apologize to my lone-dead parents for my own teen years.

Ian was disdainful of his old school and wanted to transfer to one that had a good lacrosse team.

Ian was disdainful of his old clothes.

Ian refused to go with me to the soup kitchen where once a week for years now, we'd helped feed the homeless.

When Ian said, 'People can always feed themselves if they just try, just like the rest of the world could if it got its act together. All you have to do is grow food,' I'd had enough. Arguments weren't going to do it here. He needed immersion learning.

'Pack up your designed duds,' I said. 'We're taking a field trip.'

'Where?'

'Overseas.'

'I don't want to. Mom, I missed enough school already.'

'Like you really mind that. And we'll only be gone for a long weekend, so pack up.'

He was eleven, and eleven-year-olds don't have household veto. Not in my house. Ian went with me. Sulky, barricaded during the long flight behind laptop and earbuds and resentment, he went.

Chennai was a huge, prosperous commercial and cultural center in southern India. A tourist draw, it had the gorgeous Kapaleeswarar Templd, museums, parks, a British fort dating from the Raj, the Tamil film industry. That was not the Chennai I took Ian to.

I'd arranged for a guide who, along with an armed bodyguard, took us to outlying slums, to coastal villages flooded by the rising sea, to fields so ravaged by inland drought or coastal salt water that they could grow nothing. Ian saw ragged, starving children living in tin boxes, beggars whose bones stuck out sharp as chisels, a fight over food on an aid truck that left two people lying bloody in the road. Each night I brought him back to Chennai to eat rich food in expensive restaurants. I spent the money from my divorce freely, and I didn't have to say a word.

Sweating in the heat, Ian said, 'Sage was wrong. Those people - they can't grow enought food.'

'No. Each year, childhood deaths from malnutrition rise sharply, and it's only going to get worse. The need for food is projected to rise 70 percent over the next thirty years. And as to poverty - well, a handful of super-rich people have as much money as the whole bottom half of the world's population put together.'

'That can't be right.'

'It's not right.'

'I mean, that can't be correct.'

'It is.'

He said nothing more, staring at a child digging through a stinking garbage dump for something to eat. Back at the hotel, after a shower, I saw him checking statistics on his laptop. At dinner he stared at the exquisitely cooked food on his plate.

'Mom, what can we do?'

'Donate. Understand the situation. Care.'

He picked up his fork, put it down again, scowled. But not, this time at me. I thought I saw down beginning on his upper lip - could that be true? So soon?

'I can sell a lot of my stuff,' Ian said, 'and donate the money.'

'That's your choice, honey,' I said. 'But keep what you really need. The trick is to decide what that is.'" -- Nancy Kress, Sea Change, Tachyon Publications, 2020.

Where Do Prices Come From In Marginalist Economics?

1.0 Introduction

Where do prices come from in mainstream economics? As far as I know, some hard questions were raised half a century ago. They still have not been answered, I gather.

2.0 No Agent Makes Prices

Consider competitive markets, as defined in marginalist economics for most of the twentieth century. This implies that agents in the market take prices as given.

From Steve Keen, I know that if only a countable infinity of consumers and firms exist, the agents are systematically mistaken. Despite their beliefs, they are not atomic, and their actions in varying quantities bought or sold affect prices. For agents not to be systematically mistaken, an uncountable infinity of consumers and firms must exist.

I have noted Emmanuelle Benicourt making similar points before.

Classical political economy provides another concept of competitive markets. This concept is that no barriers to entry or exit exist. This concept has been taken into mainstream economics under the rubric of contestable markets.

If all agents take prices as given, who makes prices?

"How can equilibrium be established? ... Do individuals speculate on the equilibrium process? If they do, can the disequilibrium be regarded as, in some sense, a higher-order market process? Since no one has market power, no one sets prices; yet they are set and changed. There are no good answers to these questions." -- Kenneth Arrow (1987)

Franklin Fisher did some work here which he agrees is not a fully satisfactory answer. In his investigation of disequilibrium, convergence to an equilibria requires the ad-hoc assumption of 'No favourable suprise'. Furthermore, the equilibrium that is found will generally not correspond to the initial data. The disequilibrium process changes the data, for example, the initial distribution of endowments.

3.0 Equilibrium Paths?

Suppose one wants to model production. Many economists turned away from long run theory, towards analyzing intertemporal equilibrium paths. Even though I have done work in signal processing, I do not not feel comfortable with optimal control theory.

Some general objections can be raised to this whole approach. For example, initial endowments are among the givens. If some were previously produced, a failure to fulfill expectations is possible. But an equilibrium position is one in which all expectations are fulfilled in the future.

As I understand it, markets always clear at all moments in time along an equilibrium path. For given initial conditions, typically an uncountable infinity of such paths exist. Some of these paths result in the economy eventually reaching a point in which capital goods needed to keep the economy going are just not produced. Other paths approach a path for steady-state growth, from which they will eventually diverge. Frank Hahn argued that, given multiple capital goods, an infinite number of steady-state growth paths exist. How one of these paths is picked out is the 'Hahn problem'. Some paths neither lead to the economy collapsing or a steady state. Instead, they lead to cycles.

I am not clear what is typically assumed about expectations. I guess myopic expectations are needed, in some sense, for the existence of equilibrium paths that end up with the economy crashing.

Reswitching appears in this literature. Michael Bruno has a paper in Shell (1967) that has equilibrium paths just skipping over a reswitching regime. Rosser identifies this possibility with a cusp catastrophe. Maybe an issue arises here with how an equilibrium path can approach a steady state. Is this what Hahn refers to in the closing paragraphs of Hahn (1982).

I guess economists typically assume that the economy will not follow a path in which the economy cannot continue to be sustained. And initial prices are such that one unique path is picked out. Typically this path converges to a steady state growth path which has the stability of a saddle poing.

4.0 Conclusion

My references are not recent. Maybe I want to read something by William Brock. As far as I know, marginalist economic theory still has these problems. I guess mainstream economists just assume transversality conditions, with no theory of how equilibrium is reached or why the equilibrium path that is found does not lead to collapse.

References

• Kenneth J. Arrow. 1987. Economic theory and the hypothesis of rationality, The New Pagrave: A Dictionary of Economics.
• Robert Aumann. 1964. Markets with a continuum of traders. Econometrica, 32 (1-2): 39-50.
• Emmanuelle Benicourt. 2016. Is the core e-Book a possible solution to our problems?, Real-World Economics Review, 75: 135-142
• Robert Dorfman, Paul Samuelson, and Robert Solow. 1958. Linear Programming and Economic Analysis.
• Franklin M. Fisher. 1983. Disequilibrium Foundations of Equilibrium Economics, Cambridge University Press.
• Harvey Gram and G. C. Harcourt. 2017. Joan Robinson and MIT, History of Political Economy 49(3): 437-450.
• Frank Hahn. 1982. The neo-Ricardians, Cambridge Journal of Economics 6(4): 353-374.
• Frank Hahn. 1987. 'Hahn problem', The New Pagrave: A Dictionary of Economics.
• J. Barkley Rosser Jr. 1983. Reswitching as a cusp catastrophe, Journal of Economic Theory 31(1): 182 - 193.
• Karl Shell (ed.). 1967. Essays on the Theory of Economic Growth, MIT Press.