Wednesday, January 01, 2025


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.

Saturday, January 18, 2020

Only The Super-Rich Can Save Us!

Neoliberals are hostile to labor unions and every other institution that would allow the vast majority of the population to have some effect on how we are ruled. And they have been so successful that only the super-rich can save us, as the title of a Ralph Nader novel a few years back had it. A couple of recent examples of journalism are about movements of the super-rich:

I suspect most of the super-rich, however, are vicious, reactionary fools. Apparently, Benjamin Page, Jason Seawright, and Matthew Lacombe provide evidence in their recent book, Billionaires and Stealth Politics. I've read and commented on their previous working paper.

In the United States and elsewhere, we had a progressive movement reacting to the terrible effects and excesses of the "roaring twenties" of a century ago. Of course, there was a fascist movement, too, that resulted in global war.

In the United States, prominent celebrities such as Henry Ford and Charles Lindbergh supported fascism. The super-rich did not step back. The business plot was an attempt by millionaires to stage a coup against Franklin Delano Roosevelt. They tried to get Major General Smedly Butler to act as a figurehead. I know of him for saying, war is a racket. I do not know if this falls in the politics of the super-rich, but I only recently learned about the Christian Front, a fascist organization inspired by the radio demagogue Father Coughlin. In 1940, their office in New York City was raided by the FBI for trying to overthrow the government. Seventeen members was arrested, but their prosecution was unsuccessful. (Caveat: I have not read the books and literature linked to in this paragraph.)

I think we need a better material basis than the well wishes and work of the super-rich to bring about hopeful change.

Saturday, January 11, 2020

Towards the Derivation of the Cambridge Equation with Expanded Reproduction and Markup Pricing

I have a new working paper.

Abstract: Does the Cambridge equation, in which the rate of profits in a steady state is equal to the quotient of the rate of growth and the savings rate out of profits, hold in an economy with widespread non-competitive markets? This article presents a multiple-good model of markup pricing in an attempt to answer this question. A balance equation is derived. Given competitive conditions, this model can be used to derive the Cambridge equation. The Cambridge equation also holds in a special case of markup pricing, with one capital good and many consumption goods being produced. No definite conclusions are reached in the general case.

Tuesday, January 07, 2020

The Factor Price Frontier In The Space Of Factor Rental Prices

Figure 1: Real Factor Price Frontier
1.0 Introduction

Carlo Milana has proposed a new way of visualizing the choice of technique, including in the case of reswitching. This way of describing what he has done is not neccessarily how he thinks of it. In this post, I describe his approach with a reswitching example, in a model of the production of commodities by means of commodities.

2.0 Technology

Table 1 shows the coefficients of production for this example. Coefficients of production specify inputs per unit output. Each process takes a year to complete. Inputs are totally used up in the production of the outputs. (This example is taken from one of my papers.)

Table 1: Coefficients of Production for The Technology
InputSteel IndustryCorn Industry
Labor1275/4641 Person-Yr
Steel1/10113/2322 Tons
Corn1/400(2/5) Bushels

Two techniques of production arise in this example. The Alpha technique consists of the Alpha process for producing steel and the corn-producing process. Both steel and corn are basic commodities, in the sense of Sraffa, for the Alpha technique. The Beta technique consists of the Beta process for producing steel and the corn-producing process. Only steel is a Sraffa-basic commodity for the Beta process. Suppose, however, corn is the only consumption good in this example. Then in the Beta technique, as with the Alpha technique, both steel and corn will be (re)produced for both techniques.

3.0 Prices of Production

If the Alpha technique is in use in a long-period position, prices satisfy the following two equations:

((1/10) pα,1 + (1/40) pα,2)(1 + r) + wα = pα,1
(2 pα,1 + (2/5) pα,2)(1 + r) + wα = pα,2

Prices are spot prices. The services of produced inputs are paid for at the start of the year, while wages are paid out of the surplus at the end of the year.

The corresponding equations for prices for the Beta technique are:

((113/232) pβ,1)(1 + r) + (275/464) wβ = pβ,1
(2 pβ,1 + (2/5) pβ,2)(1 + r) + wβ = pβ,2

At this point, I take a bushel corn as the numeraire. One can solve the Alpha system of equations, for example, to find (wα/pα,1) as a function of the interest rate. This is the wage curve for the Alpha technique and is shown below. The wage curve for the Beta technique is also graphed. The outer envelope of these curves, called the wage frontier, shows which technique is cost-minimizing at any given interest rate. Both techniques are cost-minimizing at the switch points, which arise for interest rates of 20 percent and 80 percent. Between the switch points, the Alpha technique is cost-minimizing. Outside the switch points, the Beta technique is cost minimizing.

Figure 2: Wage Curves and the Wage Frontier

4.0 Rental Prices for Factor Inputs

In marginalism, the choice of technique is often analyzed in terms of rental prices for factors of production. One can think of the example in terms of three factors: labor, steel, and corn. Steel and corn are capital goods.

Since a choice of production processes arises in the steel industry, I here take steel as numeraire. The rental price, also known as the factor price, for labor is the real wage:

wα,L = wα/pα,1

The rental or factor price for steel is the cost of a the services of a ton of steel when paid at the end of the year:

wα,Steel = pα,1(1 + r)/pα,1

Likewise, the rental or factor price of corn is:

wα,Corn = pα,2(1 + r)/pα,1

Using these definitions, the condition that, when in use, no extra profits are made and no extra costs are in incurred in producing steel with the Alpha process yields the following equation:

(1/10) wα,Steel + (1/40) wα,Corn + wα,L = 1

Notice that this is a linear equation in three variables. It is illustrated by the blue plane in Figure 1. The factor prices for the Beta process yield another linear equation:

((113/232) wβ,Steel + (275/464) wα,L = 1

The plane for Beta is shown in red in Figure 1.

At a switch point, both the Alpha and the Beta processes are eligible for adoption by cost-minimizing managers of firms. Accordingly, switch points must lie on the intersection of the two planes described above. The intersection, although difficult to see, is shown in black in the figure.

In discussing rental or factor prices, I have yet to take into account that corn must also be produced. If one substitutes, on the right-hand side in the three equations defining rental prices, the solution of the Alpha system of equations in Section 3, one obtains factor prices as a parametric function of the interest rate. This is the real factor price curve for the Alpha technique and is shown in blue above. The real factor price curve for the Beta technique, in red, is easier to see. (Each real factor price curve lies within the plane of the same color.) For each curve, when it lies on the real factor price frontier is indicated. And the switch points do indeed lie on the intersections of the real factor price curves.

5.0 Conclusion

Does the real factor price frontier in Figure 1 provide a mechanism for analyzing the choice of technique? Is the factor price curve for the cost-minimizing technique always furtherest from the origin?

The wage frontier, where applicable, can be drawn in a two-dimensional diagram for examples with any number produced of produced commodities. If n commodities are produced, Milana's diagram illustrates, roughly, the intersections of hyperplanes of dimension (n - 1). And those intersections will be themselves hyperplanes of dimension (n - 2). Switch points, if any, lie in those intersections. The factor price curves will still be one-dimensional curves, as I understand it, in the appropriate hyperplanes.

Obviously, this cannot be visualized in higher dimensions. Nevertheless, the mathematics still works out. Different valid approaches to finding the cost-minimizing technique in a long-period position, given an exogenous specification of the distribution of income, in some sense, will all yield the same answer. That is the case for the reswitching example presented here.

Thursday, January 02, 2020

Some People Who Have Shaped Economics

"The University [of Chicago] is the best investment I ever made in my life." -- John D. Rockefeller

Consider the following people and selected activities:

  • Lewis Brown founded the American Enterprise Institute, in 1938.
  • Jasper Crane cofounded the Foundation for Economic Education, in 1946.
  • Leonard Read cofounded the Foundation for Economic Education, in 1946.
  • Harold Luhnow, even before 1947, directed spending for the Volker Fund.
  • Sir Antony Fisher funded the Institute for Economic Affairs, around 1956.
  • Lord Ralph Harris, first general director of the Institute for Economic Affairs.
  • Arthur Seldon, first editorial director of the Institute for Economic Affairs.
  • F. A. Harper founded the Institute for Humane Studies, in 1961.
  • Charles Koch funded the development of the Virginia school, notably including James Buchanan's work.
  • Edwin Feuler, founded the Heritage Foundation, in 1973.
  • Edward H. Crane founded the Cato Institute, in 1977.
  • Eamonn Butler cofounded the Adam Smith Institute, in 1978.
  • Madsen Pirie cofounded the Adam Smith Institute, in 1978.

I've written on the influence of fundings sources on the development of economics before. A developing body of scholarly literature explores the impact of the above list of people. The above list is not complete. For example, John Blundell seems to be an important fellow in the world hinted at above.

I think funding sources have been concentrated on the right. I suppose you can try to make a list not so concentrated on the right. George Soros and the Institute for New Economic Thinking, John Reed of Citicorp and Santa Fe Institute, John Podesta and theCenter for American Progress (CAP) would all be in the list. I do not know where funding for the Economic Policy Institute comes from. It seems to me a distinction exists between investigating ideas and trying to publicize conclusions you already believe.

Thursday, December 26, 2019

2019 Nobel Prize Celebrating The Triumph Of Institutionalism?

Elizabeth Warren Echoing A View Institutionalists Understand

This year, the "Nobel prize" in economics went to Abhijit Banerjee, Esther Duflo, and Michael Kremer. They champion empirical economics over theory. Previously, institutionalist economics was described as 'theory without measurement' (Koopmans 1947). Does institutionalist economics parallel the supposed mainstream empirical turn?

Although institutionalists, as far as I know, did not have the resources to create randomized control trials (RCTs), they did collect and analyze statistical data. I think especially of Wesley Clair Mitchell and the National Bureau of Economic Research (NBER).

Institutionalists was not atheoretical, I think. They developed qualitative analytical concepts. I think of C. E. Ayres extension, for example, of the Veblenian dichotomy. Sometime, I intend to read John R. Commons' 1924 book to see how he breaks up a transaction. John Kenneth Galbraith's concept of the technostructure and Alfred Eichner's idea of the megacorp are other examples here. Institutionalists contributed to the development of Industrial Organization. John Maurice Clark had, at least, a verbal description of the business cycle that combined the multiplier and the accelerator.

Institutionalist economics is not a strictly American school of thought. I include Geoffrey M. Hodgson and Gunnar Myrdal as institutionalists. I suppose I should read the Journal of Economic Issues or the Journal of Institutional Economics more frequently. The Association for Evolutionary Economics (AFEE) puts out the JEI.

  • John R. Commons. 1924. Legal Foundations of Capitalism Macmillan.
  • John S. Gambs. 1946. Beyond Supply and Demand: A Reappraisal of Institutional Economics. Columbia University Press.
  • Tjalling C. Koopmans. 1947. Measurement without theory. Review of Economics and Statistics 29(3): 161-172.

Saturday, December 14, 2019

A Fake Switch Point in an Example With Circulating Capital

Figure 1: A Switch Point and a Fake Switch Point on Wage Curves
1.0 Introduction

In the analysis of the choice of technique, I typically consider examples of technology with a finite number of techniques. For each technique, I find the wage as a function of the rate of profits. The outer envelope of these curves shows the cost-minimizing technique at each rate of profits (or each level of the wage). Points on more than one wage curve are switch points.

This approach is valid when, for example, all techniques produce the same set of commodities, and each commodity is basic, in the sense of Sraffa. That is, all commodities enter directly or indirectly into the production of all commodities.

But another requirement is that prices of all commodities in common between two techniques be identical at a switch point. Points of intersection on wage curves without this property of identical prices are known as fake switch points. I have previously considered fake switch points in (an extension of) an example from Christian Bidard. In this post, I present an example of a fake switch point in an example with single production (or circulating capital) only. It is critical to this example that a non-basic commodity is the numeraire and that the techniques vary in the process used to produce a non-basic commodity.

The necessity to consider prices in the analysis of the choice of technique is, as I understand it, a critical point from Milana. I think he extends this point, though, to examples in which it cannot be used to criticize Sraffians.

2.0 Technology

Table 1 shows the coefficients of production for this example. Coefficients of production specify inputs per unit output. Each process takes a year to complete. Inputs are totally used up in the production of the outputs.

Table 1: Coefficients of Production for The Technology
InputCorn IndustrySilk Industry
Labor112 Person-Yrs
Corn1/53(38/15) Bushels
Silk000 Square-Yds

The first produced commodity, corn, enters directly into the production of both commodities. It is a basic commodity, in the sense of Sraffa. Silk is a non-basic commodity. It does not enter, either directly or indirectly, into the production of corn.

3.0 Price Equations

I take a square yard of silk as the numeraire. The same rate of profits is assumed to be made in both industries when prices of production prevail. Labor is advanced, and wages are paid out of the net product at the end of the year.

3.1 The Alpha Technique

The following two equations specify prices of production for the Alpha technique:

(1/5) p1, α (1 + r) + wα = p1, α
3 p1, α (1 + r) + wα = 1

The variables are:

  • r: The rate of profits.
  • wα: The wage, for the Alpha technique.
  • p1, α: The price of corn, for the Alpha technique.
The solution, in terms of the rate of profits, is:

wα(r) = (4 - r)/(19 + 14 r)
p1, α(r) = 5/(19 + 14 r)

3.2 The Beta Technique

The price equations for the Beta technique are:

(1/5) p1, β (1 + r) + wβ = p1, β
(38/15) p1, β (1 + r) + 2 wβ = 1

The solution is:

wβ(r) = 3(4 - r)/[2( 31 + 16 r)]
p1, β(r) = 15/[2( 31 + 16 r)]

4.0 Switch Points

Suppose, at the given rate of profits, the Alpha technique is in use and prices of production for the Alpha technique prevail. Figure 2 shows the cost of producing silk, for each process, at these prices. The advances, at the beginning of the year, for produced inputs are costed up at the going rate of profits. The cost of producing silk with the process in the Alpha technique, under these assumptions, is unity for any feasible rate of profits. Extra costs are not incurred in the Alpha technique. Neither are supernormal profits available.

Figure 2: Cost of Producing Silk at Alpha Prices

But supernormal profits are available for the silk-producing process in the Beta technique if the rate of profits is feasible and exceeds the rate of profits at the switch point. The Beta technique is cost-minimizing here, while the Alpha technique is only cost-minimizing at lower rates of profits. The same conclusion about when each technique is cost-minimizing would be drawn if one started with prices of production for the Beta technique.

The switch point occurs at a rate of profits of 50 percent. The wage is (7/52) square yards per person-years, and the price of corn is (5/26) square yards per bushel at the switch point. Prices of production are the same, at the switch point, whichever technique is used.

5.0 A Fake Switch Point

Figure 1, at the top of this post, graphs the wage curves for the two techniques. Consider rates of profits that equate wages:

wα(r*) = wβ(r*)

The wage curves have two intersections. One is at the switch points, at a rate of profits of 50%. At the maximum rate of profits of 400 percent, the wage is zero. In the Alpha system, the price of corn is (1/15) square yards per bushel, while it is (3/38) square yards per bushel in the Beta system. Since, prices of production vary among techniques at the maximum rate of profits, it is not a switch point. Rather, it is a fake switch point.

6.0 Conclusions

I would like to find another example of a fake switch point in a circulating capital example with a choice of processes for producing a non-basic commodity. I want a fake switch point not at an extreme, with a wage of zero. The example in Stamatis (2001) seems not to work; maybe there is a misprint in the coefficients of production. Both techniques, however, have the structure of Sraffa's "beans".

  • Carlo Milana. 27 Nov. 2019. Solving the Reswitching Paradox in the Sraffian Theory of Capital
  • Georg Stamatis. 2001. Why the comparison and ordering of techniques is impossible. Political Economy 9: 5-44.