Precursors of Piero Sraffa

I want to consider contributions to economics after 1870 that reconsidered classical or Marxist economics, used input-output models and linear algebra, or bear a family resemblance to at least some points in Sraffa's 1960 book.

• Vladimir K. Dmitriev. Used input-output analysis in an interpretation of Ricardo's theory of value.
• Ladislaus Bortkiewicz. Had a simple three-good model, with one basic good, input-output model of prices of production. Sraffa and others argued against aspects of his interpretation of Marx's theory of value.
• Georg von Charasoff. Apparently, around 1909 and 1910, he came up with the concept of "original capital". In a infinite series, much like Sraffa's reduction to dated labor, the capital goods needed more and more indirectly in producing some given net output converge to Sraffa's standard commodity.
• Father Maurice Potron. A fairly conservative Jesuit priest and mathematician, writing in French. I know of him from this collection.
• Wassily Leontief. His empirical work extends from the 1920s. I do not know that those building on his work often cite Sraffa.
• Walter Isard. Applied Leontief input-output analysis to regional or spatial economics in 1951.
• John von Neumann. I am thinking of the 1945-1946 translation of his A Model of General Economic Equilibrium. Kurz and Salvadori read this as a response to Robert Remak.
• Jacob T. Schwartz. A mathematician whose 1961 Lectures on the Mathematical Method in Analytical Economics criticizes neoclassical and Austrian economics. Personally, I found his work not as rigorous as Sraffa's.

I do not know much about many of these authors, but other economists in the post Sraffian tradition have written about them.

Why Does The Labor Theory Of Value Work Empirically As A Theory Of Prices?

Anwar Shaikh On The Transformation Problem

Lots of empirical work shows that prices tend to be proportion to the labor embodied in commodities. My references in this article document this claim. Furthermore, empirical wage-rate of profits curves tend to be close to straight lines. This is not what, say, Sraffa' mathematical economics would lead me to expect. What explains these surprising empirical findings?

Almost 34 minutes in, in the above video, Shaikh makes the above point about the contrast between theory and empirical findings. He concludes with speculation, including with comments on Bertram Schefold's work with input-output matrices formed out of random matrices.

I offer some speculations myself in this post. I do not have much theory to back these suggestions up.

The Leontief matrices obtained from National Income and Product Accounts (NIPAs) are still highly aggregated. The empirical results on the LTV are obtained with matrices that have on the order of, say, 100 industries. One of these industries, if disaggregated, might contain commodities that are produced with a high Organic Composition of Capital (OCC) and a low OCC. Their prices of production would deviate more from labor values than an average combining them both. The extremes would be cancelled out in forming an average.

In my examples of pattern analysis, I also suggest that Sraffa effects could be difficult to see, in that they arise in a transition from one very long run position to another. But I concoct those examples to make a point about possibilities. I do not want to insist on any empirical point here.

Technical progress, despite how I usually model it, is endogenous. If in process of production adopted in some industry, some input is noticeably more expensive than others, managers of firms will seek out and research processes in which that input is reduced or some other cheaper input is substituted for it. Perhaps after a couple of centuries of rapid technical change under these incentives, empirical Leontief input-output matrices will have the properties Schefold highlights for random matrices. I suppose one could confirm this by showing wage-rate of profits curves are closer to affine functions for more highly developed economies. I have done some empirical work along these lines.

Aside: Here is another YouTube video with Anwar Shaikh. He sounds a lot like he accepts Milgate and Eatwell's critique of "imperfectionism". Actually existing capitalism is to be analyzed by a theory that accepts empirical reality, not by deviations from a neoclassical utopia that could never exist in any conceivable world.

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:

• Sheelah Kolhatkar writes, in the New Yorker, about Patriotic Millionaires.
• Theodore Schleifer writes, in Vox, about Resource Generation.

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.

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.

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

Input	Steel Industry		Corn Industry
	Alpha	Beta
Labor	1	275/464	1 Person-Yr
Steel	1/10	113/232	2 Tons
Corn	1/40	0	(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) p_α,1 + (1/40) p_α,2)(1 + r) + w_α = p_α,1

(2 p_α,1 + (2/5) p_α,2)(1 + r) + w_α = p_α,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) p_β,1)(1 + r) + (275/464) w_β = p_β,1

(2 p_β,1 + (2/5) p_β,2)(1 + r) + w_β = p_β,2

At this point, I take a bushel corn as the numeraire. One can solve the Alpha system of equations, for example, to find (w_α/p_α,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:

w_α,L = w_α/p_α,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:

w_α,Steel = p_α,1(1 + r)/p_α,1

Likewise, the rental or factor price of corn is:

w_α,Corn = p_α,2(1 + r)/p_α,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) w_α,Steel + (1/40) w_α,Corn + w_α,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) w_β,Steel + (275/464) w_α,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.

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.