Friday, August 28, 2009

On The Road From Mont Pelerin

I have been reading The Road from Mont Pelerin: The Making of the Neoliberal Thought Collective, a collection edited by Philip Mirowski and Dieter Plehwe (Harvard University Press, 2009). One theme I find emergent in this book is the influence of funders (e.g., Harold Luhnow, Jasper Crane) on the redirection of economic thought, without any corresponding empirical evidence.

But I'm not yet ready to offer too many thoughts on this book. Instead I'm interested in the cover photo, reproduced as Figure 1.
Figure 1: Cover Photo
I cannot find photo credits in the book. Presumably, this photo is of attendees at a Mont Pelerin society meeting, maybe the first. Can anybody identify these people? Figure 2 letters them to facilitate referring.
  • F. Ludwig Von Mises
  • G. Friedrich Hayek
Figure 2: Cover Photo with Annotations

Monday, August 24, 2009

Some Issues In Joint Production

1.0 Introduction
Sraffa's work on single product systems is sufficient for demonstrating the incorrectness of neoclassical economics, at least in applications in which equilibrium prices supposedly are ultimately, in some sense, scarcity indices. Sraffa's work on joint production is important in justifying a claim that Sraffa has rediscovered the logic behind the Classical theory of value. An interesting question is whether Sraffa's treatment of joint production holds up to a rigorous theoretical analysis. Christian Bidard, Heinz Kurz & Neri Salvadori, and Bertram Schefold are some economists who have gone into this question in some detail.

An example developed by J. E. Woods (1990: pp. 281-285) illustrates some questions raised by joint production. Unfortunately, I am not sure Woods is correct in his analysis; he constrains all goods to have positive prices in his example. I do not impose this constraint in my treatment of his example.

2.0 Technology
Consider an economy in which two goods, iron and coal, are produced. The managers of firms each know of three Constant-Returns-to-Scale processes for producing these goods (Figure 1). In each process, the inputs need to be available at the start of the year. The inputs are totally used up in these production processes, and the outputs become available at the end of the year. Since each process produces both iron and corn, this is an example of a model of joint production.
TABLE 1: Processes Exhibiting Joint Production
INPUTSProcess IProcess IIaProcess IIb
Labor5 Person-Yrs10 Person-Yrs10 Person-Yrs
Iron18 Tons12 Tons
Coal10 Cwt
Iron48 Tons12 Tons12 Tons
Coal10 Cwt30 Cwt30 Cwt

3.0 Quantity Flows
Suppose the final demand in this economy is for a composite good consisting of an equal amount of iron and coal. Four techniques can be formed from the technology to produce such a commodity. Two processes are used in each of the first two techniques. The Alpha technique consists of Process I and Process IIa operated in the proportions shown in Table 2. Notice that after the outputs are used to replace the inputs, the net output consists of one ton iron and one Cwt. coal, as required.
TABLE 2: Quantity Flows in Alpha Technique
INPUTSProcess IProcess IIa
Labor1/6 Person-Yr2/9 Person-Yr
Iron9/15 Ton4/15 Ton
Iron1 9/15 Tons4/15 Ton
Coal1/3 Cwt2/3 Cwt

The Beta technique consists of Process I and Process IIb used in the proportions shown in Table 2. Here too the net output is one ton iron and one Cwt. coal.
TABLE 3: Quantity Flows in Beta Technique
INPUTSProcess IProcess IIb
Labor1/360 Person-Yr1/108 Person-Yr
Iron3/10 Ton
Coal5/12 Cwt
Iron4/5 Ton1/2 Ton
Coal1/6 Cwt1 1/4 Cwt

If Process I is operated alone at unit level, the net output of the economy is 30 tons iron and 10 cwt. coal. The requirements for use would be satisfied if 20 tons of iron were thrown away - free disposal is assumed. If this technique is adopted, iron is a free good.

The last technique to be considered is the operation of process IIb alone. In this case more coal would be produced net than is needed. If this technique is cost minimizing, coal is a free good. (Notice than the combination of Process IIa and Process IIb would just produce more of coal, a free good. This is not economical.)

4.0 Prices
Since I want to consider cases where either iron or coal is a free good, neither can be chosen as the numeraire in an analysis of prices. Accordingly, suppose a person-year - in other words, labor commanded - is the numeraire.

4.1 The Alpha Technique
The price equations for the Alpha technique show the same rate of profits being obtained in the processes comprising the technique:
18 pI(1 + r) + 5 = 48 pI + 10 pC
12 pI(1 + r) + 10 = 12 pI + 30 pC
where pI is the price of iron in units of person-years per ton, pC is the price of coal in units of person-years per Cwt., and r is the rate of profits. By assumption, workers are paid at the end of the year. If the rate of profits as taken as given, the above system consists of two equations in two unknowns. The solution is:
pI = 5/[6 (15 - 7 r)]
pC = (5 - 2 r)/(15 - 7 r)
An economic restriction is that both prices be non-negative. Thus, the solution only obtains in the following interval for the rate of profits:
0 ≤ r ≤ 15/7

4.2 The Beta Technique
The price system for the Beta technique is:
18 pI(1 + r) + 5 = 48 pI + 10 pC
10 pC(1 + r) + 10 = 12 pI + 30 pC
Its solution is:
pI = -5 r/[6 (r - 1)(3 r - 8)]
pC = (4 - 3 r)/[(r - 1)(3 r - 8)]
Both prices are nonnegative if:
(4/3) ≤ r ≤ (8/3)

4.3 Choice of Technique
First, suppose Process I were operated alone. Since iron would be in excess supply, its price would be zero person-years per ton. Revenues would be equated to costs in Process I if pC were 1/2 person-years per Cwt. But revenues would exceed costs in Process IIa by five person-years when operated at the unit level. Thus, firms would want to adopt Process IIa. Thus, operating Process I alone could not be cost-minimizing. (Since Process IIa alone cannot satisfy final demand, Process IIa could also not be operated alone.)

Second, suppose Process IIb were operated alone. In this case, coal would be a free good, and the price of iron would be 5/6 person-years per ton. For any non-negative rate of profits, revenues would never cover costs in Process IIa. On the other hand, for any rate of profits below approximately 133%, Process I would earn pure economic profits (Figure 1). That is, for rates of profits below this level, Process IIb would never be operated alone.
Figure 1: Profitability of Process I (Process IIb Prices)

Third, suppose prices corresponding to the Alpha technique were ruling. Figure 2 shows the difference in revenues and costs for Process IIb, the one process not in the Alpha technique. As usual in this analysis, costs include interest charges on the value of advanced capital. The Alpha technique is cost-minimizing only for rates of profits between zero and 200%, inclusive.
Figure 2: Profitability of Process IIb (Prices for Alpha Technique)

Last, suppose prices solved the price system for the Beta technique. Figure 3 shows the resulting difference in revenues and costs for process IIa, which lies outside the Beta technique. The Beta technique is cost-minimizing for rates of profits between 133 1/3 percent and 200%.
Figure 3: Profitability of Process IIa (Prices for Beta Technique)

5.0 Conclusions
The above analysis demonstrates that, for rates of profits between 0% and approximately 133%, the Alpha technique is cost-minimizing. For rates of profits above approximately 133%, Process IIb is operated alone and coal is free.

In a comparison of the Alpha and Beta techniques alone (without considering the possibility of operating a single process alone):
  • The Alpha technique would be cost minimizing if the rate of profits were between 0% and 200% and the prices associated with the Alpha technique were ruling.
  • The Beta technique would also be cost minimizing if the rate of profits were between approximately 133% and 200% and the prices associated with the Beta technique were ruling.
  • The Beta technique would be cost minimizing if the rate of profits were between 200% and approximately 214% and the prices associated with the Alpha technique were ruling.
  • The Alpha technique would be cost minimizing if the rate of profits were between 200% and approximately 267% and the prices associated with the Beta technique were ruling.
In short, the cost-minimizing technique would not be unique between the rate of profits of approximately 133% and 200%, if it were not for the possibility of operating Process IIb alone. The cost-minimizing technique would not exist between the rate of profits of 200% and approximately 267%, once again if it were not for the possibility of operating process IIb alone.

This example raises a question: Can examples arise with these sorts of non-uniqueness and non-existence problems, even allowing for the possibility of free goods? This is a theme in some of Christian Bidard's and Bertram Schefold's work. (Bidard amusingly names one of his articles "Is von Neumann Square?") I do not recall their conclusions. I think Bidard comes down negatively on Sraffa, based, I guess, partly on his analysis of joint production.

  • Christian Bidard (2004) Prices, Reproduction, Scarcity, Cambridge University Press
  • Heinz D. Kurz and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis, Cambridge University Press
  • Bertram Schefold (1989) Mr. Sraffa on Joint Production and Other Essays, Unwin-Hyman
  • Bertram Schefold (1997) Normal Prices, Technical Change and Accumulation, Macmillan
  • J. E. Woods (1990) The Production of Commodities: An Introduction to Sraffa, Humanities Press International

Friday, August 14, 2009

Good Timing, Paul

Compare and contrast this:
"Some of us were skeptical. A couple of months after Mr. Obama gave that speech, I warned that his vision of a 'different kind of politics' was a vain hope, that any Democratic who made it to the White House would face 'an unending procession of wild charges and fake scandals, dutifully given credence by major media organizations that somehow can't bring themselves to declare the accusations unequivocally false.'" -- Paul Krugman, "Republican Death Trip", New York Times, 14 August 2009, p. A19 (Emphasis added)
to this:
"The stubborn yet false rumor that President Obama's health care proposal would create government-sponsored 'death panels' to decide which patients were worthy of living seemed to arise from nowhere in recent weeks.

Advanced even this week by Republican stalwarts including ... Sarah Palin and Charles Grssley ..., the nature of the assertion nonetheless seemed reminiscent of the modern-day viral Internet campaigns that dogged Mr. Obama last year, falsely calling him a Muslim and questioning his nationality." -- Jim Rutenberg and Jackie Calmes, "Getting to the Source of the 'Death Panel' Rumor", New York Times, 14 August 2009, Page A1 (Emphasis added)

Tuesday, August 11, 2009

More On Economic Reasoning

All ten of the letters in the 8-14 August issue of The Economist are responses to the critique of academic economics in the 18-24 July issue. My favorite is from Meghnad Desai:
"SIR - When I was a student we studied business cycles, but the topic disappeared with the rise of mathematical equilibrium theorising. The idea that capitalism is an equilibrium system is common among Keynesian and neoclassical economists; they only differ as to whether the equilibrium is at full employment or under employment. The grand synthesis being taught makes the equilibrium stochastic and dynamic, but that is all.

Capitalism is, however, a disequilibrium dynamic stochastic system as Marx, Wicksell, Schumpeter and Hayek have told us over the past two centuries. Richard Goodwin tried his best to present a mathematical theory of such a disequilibrium system. After the crisis we need to revive that tradition if we are not to be surprised by another crisis."
The on-line Lucas Roundtable at The Economist doesn't have any invited contributions from left-leaning non-mainstream economists.

Tuesday, August 04, 2009

Still A Man Hears What He Wants To Hear And Disregards The Rest

Mark Blaug has another paper criticizing Sraffianism. Here's one quotation from it:
"One of the striking features of the Sraffian side of the debate, the victorious side, was their categorical refusal to throw light on the debate by empirical research, insisting along with Sraffa himself that an anomaly such as reswitching is a theoretical flaw, which can only be repaired by discarding the theory in which it occurs. This is a position that has been steadfastly maintained through a half century and has only recently been broken by two Sraffians, namely, Lynn Mainwaring and Ian Steedman (2000)... Despite diligent combing through the literature, I have been unable to find more than one or two pieces of empirical work inspired by the theoretical ideals of Sraffian economics." -- Mark Blaug, "The Trade-Off between Rigor and Relevance: Sraffian Economics as a Case in Point, History of Political Economy, V. 41, N. 2 (2009): 219-247
I still don't see how empirical work is necessary to demonstrate a logical error. But confining myself to work before Mainwaring and Steedman (2000) and work in English, I find more than two: Albin (1975), Prince and Rosser (1985), and Ozanne (1996). Asheim (2008) is based on work written up long ago.

Those works, though, are looking for empirical evidence of Sraffa effects. But a plethora of empirical work is somewhat consistent with Sraffianism. I refer to work following in Leontief's wake. Blaug even acknowledges the relevance of this tradition:
"I have inadverently slipped into the language of Leontief's input-output analysis, which of course is rooted in physiocracy and classical economics, but was later adapted by Leontief himself to the mode of analysis of G[eneral] E[quilibrium] T[heory]" -- Mark Blaug, ibid
I find tendentious the assignment of Leontief to General Equilibrium Theory.