Wednesday, January 01, 2020


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.

Wednesday, November 06, 2019

An Example Of The Labor Theory Of Value

Figure 1: Variation of Prices of Production with Wages and Markups
1.0 Introduction

This post documents an example in my working paper, The Labor Theory of Value and Sraffa's Standard Commodity with Markup Pricing.

2.0 Technology

Consider a simple economy in which corn and ale are each produced from inputs of labor, corn, and ale. Inputs for unit outputs are shown in the columns in Table 1. Obviously, the units of measure should not be taken serious. Inputs are totally used up in the production of outputs. I abstract from the existence of fixed capital, land, and joint production.

Table 1: The Technology
Labor1 Person Year1 Person-Year
Corn(1/8) Bushels(3/8) Bushels
Ale(1/16) Pints(1/16) Pints

The standard net product consists of (9/16) bushels corn and (3/16) pints ale. The Perron-Frobenius root of the Leontief input-output matrix is 1/4. (The other eigenvalue is (-1/16). The maximum rate of profits is 300 per cent. Labor values are (64/51) person years per bushel corn and (80/51) person-years per pint ale.

3.0 Price Equations

Equations for prices of production are:

[(1/8) pcorn + (1/16) pale]( 1 + r̂) + w = pcorn

[(3/8) pcorn + (1/16) pale]( 1 + s2 r̂) + w = pale

(9/16) pcorn + (3/16) pale = 1

I have taken the standard commodity as the numeraire. This allows one to freely move back and forth, when evaluating aggregates, from labor values to monetary units.

The rate of profits in producing corn is 100 r̂ percent, while it is s2 r̂ percent in producing ale. I am assuming there are persistent barriers to entry or some reason why the rate of profits persistently varies between industries. Some economists talk about dual markets. I can also point to John Kenneth Galbraith's The New Industrial State for a contrast of corporations in the planning system and more traditional firms. Anyways, the solution of these equations is:

pcorn = 16 [16 + (1 - s2) r̂]/[204 + (3 + 9 s2) r̂]

pale = 32 [10 - (1 - 3 s2) r̂]/[204 + (3 + 9 s2) r̂]

w = 4 [51 - (9 + 5 s2) r̂ - s22]/[204 + (3 + 9 s2) r̂]

These equations show that prices of production vary from labor values when the rate of profits is positive. Furthermore, these are not straight lines, although the curvature is not visually impressive in the figure at the top of this post.

Anyways, here is a question. Suppose labor coefficients happen to be a left-hand eigenvector of the Leontief input-output matrix, a very special case. When prices of production are defined with equal rates of profits across all industries, prices of production are labor values in this special case. (The specification of the numeraire does not matter.) Does this property still hold under the sort of markup pricing which I am assuming?

Update (8 Nov 2019): A supporter in email points out a special case. Let s1 = 5/13 and let s2 = 5/29. Then prices of production are labor values. The scale factor for the rate of profits is: r̂ = 3 (1 - w). That is, the scale factor is the rate of profits. Presumably, with these relative markups, relative prices are relative labor values, whatever the numeraire.

Friday, November 01, 2019

Keen's Debunking Economics Most Popular Among Popular Critiques

Table 1: Selected Critiques
Moshe AdlerEconomics for the Rest of Us214
Rod Hill & Tony MyattThe Economics Anti-Textbook134
Steve KeenDebunking Economics, 1st edition253 to 4
Debunking Economics, 2nd edition564 to 5
Paul OrmerodThe Death of Economics103 to 4
John QuigginEconomics in Two Lessons24
John WeeksEconomics of the 1%134 to 5

Steve Keen seems to be the most popular of those writing internal critiques of economics directed towards the common reader. I selected the above books and looked at rankings on Amazon's United States website. You can spend lots of time reading the comments.

I am not sure about how to characterize this genre. I am more focused on theory than offering political programs. Would Robert Reich's Saving Capitalism be excluded? But what about memoirs, such as John Perkins' Confessions of an Economic Hit Man, Stiglitz' Globalism and its Discontents, Thaler's Misbehaving, or Kahneman's Thinking Fast and Slow? These books seem to have much more ratings than the ones I list in the above table.

Why is Keen's book more popular than the other ones in the table? Keen often overstates his case. One reviewer said he confuses necessary conditions with sufficient ones. I'm covered here; I suggested to him, before publication of the first edition, that well-behaved aggregate excess demand curves might exist in special, numeric, cases even if all consumers did not have identical and homothetic preferences. But those who know of Alan Kirman's work, with others, in the 1970s know Keen has a point. You cannot find any other condition than Gorman form that is sufficient to have well-behaved aggregate excess demand curves. And this is true of many other of Keen's points. I had not realized before reading Keen that the standard textbook presentation of perfect competition assumes managers of firms are systematically mistaken in their understanding of the demand curves they face.

Anyways, neoclassical economics is mostly wrong or useless for internal, logical reasons.

Wednesday, October 23, 2019

The Labor Theory of Value and Sraffa's Standard Commodity with Markup Pricing

I have uploaded a working paper with the post title.

Abstract: This article demonstrates relationships that are transparent in Sraffa's standard system hold even when relative rates of profit vary persistently among industries. Even with such variations, total constant capital, total variable capital, total surplus value, and the rate of profits are unaltered by evaluation at labor values and at prices of production in Sraffa’s standard system. These results buttress those who see in the standard commodity a solution for Marx’s so-called transformation problem.

Saturday, October 19, 2019

Actually Existing Socialism In A Capitalist Setting?

Elements of a post capitalist society are and have been developing in actually existing capitalism. This post points out a couple of examples.

The Green Bay Packers is a community-owned (non-proper) football team in the National Football League (NFL). One can find some arguing that they are socialist. And some are concerned to refute this claim.

Decades ago, some universities in the United States set up research and development organizations that then became independent, not-for-profit companies. For example, here is the web site for SRC, formerly Syracuse Research Corporation. This means, apparently, that they re-invest what they make. IRS Publication 557 explains how to apply for status as a 501(c) organization.

A quick Google search gets me to the National Center for Employee Ownership. They explain how a Employee Stock Ownership Plan (ESOP) works.

The cooperative movement is of interest in this context. I gather the Mondragon Corporation, in Spain, is the most well-known example. But I want to turn to producer cooperatives in dairy. The Lowville Producers Dairy Cooperative is one near me. Apparently, the National Milk Producers Federation is a federation of such cooperatives. The United States Department of Agriculture (USDA) provides background. I see that they confirm what I know anecdotally, that not all dairy farmers are members of a coop.

I guess some theory is needed to make sense of any claim that, say, producer coops are an example of socialism or to obtain a general understanding of such organizations. I have only read Hodgson (1998) and Jossa (2005) in the list of references below. From Hodgson, as I recall, I learned that an issue with cooperatives is start-up finance. It may be that producer cooperatives are more efficient than capitalist firms and still be smaller than one would hope. Jossa (2005) argues that cooperatives are consistent with Marx's vision. He draws on Vanek's distinction between worker-managed firms (WMFs) and labor-managed firms (LMFs). In WMFs, workers provide the finance, while in a LMF, the firm borrows. Anyways, here is some literature to explore.

  • Geoffrey M. Hodgson (1998). Economics and Utopia: Why the Learning Economy is not the End of History. Routledge.
  • Bruno Jossa (2019). The Political Economy of Cooperatives and Socialism, Routledge.
  • Bruno Jossa (2005). Marx, Marxism and the cooperative movement. Cambridge Journal of Economics 29: 3-18.
  • Jaroslav Vanek (1970). The General Theory of Labor-Managed Market Economies. NCOL.
  • Jaroslav Vanek (1971). The Participatory Economy: An Evolutionary Hypothesis and a Strategy for Development. Cornell University Press.
  • Jaroslav Vanek (1977). The Labor-Managed Economy: Essays. Cornell University Press.

Thursday, October 10, 2019

Structural Economic Dynamics and Fake Switch Points

Figure 1: A Pattern Diagram with Joint Production
1.0 Introduction

This post completes an example. I analyzed bits of this example here and here. This post may make no sense if you have not read a long series of previous posts or, maybe, the papers highlighted here and here. I am interested in how and if my approach to analyzing and visualizing variations in the choice of technique with technical progress extends to joint production. The example suggests fake switch points do not pose an insurmountable obstacle for such an extension.

2.0 Technology

I repeat the specification of technology.

I postulate an economy in which two commodities, corn and linen, can be produced from inputs of corn, linen, and labor. Managers of firms know of three processes (Tables 1 and 2) to produce corn and linen. Each process produces net outputs of corn and linen as a joint product. Inputs and outputs are specified in physical units (say, bushels and square meters) per unit level of operation of the given process. Inputs are acquired at the start of the year, and outputs are available for sale at the end of the year.

Table 1: Inputs for The Technology
Laboreσ0,1(1 - t)eσ0,2(1 - t)eσ0,3(1 - t)

Table 2: Outputs for The Technology

I assume that requirements for use are such that two processes must be operated to satisfy those requirements. I need to investigate the implications of this assumption further. Apparently, for this example, it implies that the economy is not on a golden rule steady state growth path, with the rate of profits equal to the rate of growth. Anyway, with this assumption, three techniques - Alpha, Beta, and Gamma - can be operated. Table 3 specifies which processes are operated for each technique.

Table 3: Techniques
Alphaa, b
Betaa, c
Gammab, c

The technology, as I have defined it, is parameterized. I consider the following specification for the rate of decrease in labor coefficients.

σ0,1 = 2
σ0,2 = σ0,3 = 5/2

Bidard & Klimovsky's example arises when t is unity.

3.0 Prices and the Choice of Technique

A system of two price equations arises, for each technique. I assume the labor coefficient is treated as a constant over the period of production - say, a year. With linen as numeraire, these equations for the Alpha technique are:

(20 p1 + 20)(1 + r) + [eσ0,1(1 - t)] w = 21 p1 + 27
(20 p1 + 20)(1 + r) + [eσ0,2(1 - t)] w = 23 p1 + 25

One can these equations for two variables in terms of, say, the rate of profits. For each technique, its wage curve shows the wage as a function of the rate of profits. One cannot generally base the choice of technique, under joint production, on figuring out which technique contributes to the outer frontier at a given rate of profits.

Instead, one can calculate profits and losses, with the given rate of profits and a technique's price system for the processes not in the technique. This exercise only makes sense when the rate of profits, the wage, and prices are non-negative for the starting technique. The technique is cost-minimizing only if no extra profits can be made with processes outside the technique.

I deliberately frame this as a combinatorial argument. Bidard likes what he calls a market algorithm, where, when one identifies a process earning extra profits, one introduces the process into the technique. In the case of joint production, it is not clear which process should be dropped. Furthermore, examples exist in which a cost-minimizing technique exists but cannot be reached from certain starting points with the market algorithm.

4.0 Patterns

I have constructed the figure at the top of the post to illustrate how the choice of technique varies with technical progress in this example. The dashed lines highlight features of the example that do not bear on the choice of technique. The light vertical solid lines divide time into numbered regions. Table 3 lists the cost-minimizing techniques, in order of an increasing rate of profits in each region.

Table 3: Regions
1Gamma, No Production, Alpha
2Gamma, No Production, Alpha
3Gamma, Alpha & Gamma, Alpha
4Alpha & Gamma, Alpha
5Beta, Alpha & Gamma, Alpha

I could say a lot more about the example. I will note that in region 1, the wage increases with the rate of profits, for the Alpha technique, in the interval for the rate of profits where both wages and the price of corn are positive. In region 2, the wage decreases with the rate of profits, for the Alpha technique. The division between regions 2 and 3 is associated with that interval for the rate of profits for Alpha transitioning to have a non-empty intersection with the similar interval for the Gamma technique. for

5.0 Conclusion

This post has illustrated that one type of my types of pattern diagrams can apply to joint production. This type illustrates how the relationship between the choice of technique and distribution varies with technical progress. It can be constructed even in cases, such as joint production, where the choice of technique cannot necessarily be based on wage-rate of profits curves and their outer frontier.

If fake switch points are not shown, this type of pattern diagram does not depend on the specification of the numeraire. If the ordinate in Figure 1 were the wage, instead of the rate of profits, it would be upside down, in some sense. A different numeraire would rescale the wage. When corn is numeraire, only one fake switch point exists. It, too, would be a horizontal line segment. But fake switch points are fake precisely because they do not impact the choice of technique. They can be left off the diagram.

The example also illustrates new types of patterns for dividing adjacent regions. Under joint production, a technique can be associated with non-negative prices and a wage for an interval of the rate of profits that does not include a rate of profits of zero. Both the Alpha and the Beta technique exhibit this possibility in the example. And we can divide regions based on when the range of rate of profits in which such a technique becomes cost-minimizing comes to include zero or begins to interact with the range in which another technique is cost-minimizing

This example also illustrates that the cost-minimizing technique may not be unique in a range of rates of profits. I think this non-uniqueness is qualitatively different than how non-uniqueness can arise in models with only circulating capital. In circulating capital models, non-uniqueness is associated with two techniques having identical wage curves. Not so here.

I do not intend to write this example up any more extensively. I have no so-called paradoxical behavior here, such as reswitching, reverse capital-deepening, or the reverse substitution of labor. I may go on to explore where techniques are described by rectangular matrices, with more produced commodities than processes, and there is a dependence on the requirements for use.

  • Bidard, Christian and Edith Klimovsky (2004). Switches and fake switches in methods of production. Cambridge Journal of Economics. 28 (1): 89-97.

Saturday, October 05, 2019


  • Here is a post from a blog devoted to cybercommunism. The blogger is glowing about Paul Cockshoot's work on refuting Hayek's supposed refutation of the possibility of a post-capitalist society.
  • William Milberg writes about how it is becoming more common to use the word "capitalism", a word mainstream economists had mostly stopped using.
  • Herbert Giants and Rakesh Khurana write about the corrupting effects of neoclassical economics on what is taught in business school and then practiced by corporate elites.
  • Osita Nwanevu writes, in The New Republic, about the enthusiasts that showed up at last weekend's Third MMT Conference.
  • Lisa Schweitzer studies urban environments. In a blog post, she expresses irritation at Paul Romer's arrogance, admittedly filtered through a glowing New York Times article.
  • A long time ago, Connie Bruck profiled George Soros in the New Yorker. Soros consciously thinks of himself as building on Karl Popper's The Open Society and its Enemies.