Keynes All The Rage

I noticed some articles and posts on Keynes recently. The ones I noticed are somewhat different than those highlighted by the Sandwichman. I think Robert Skidelsky's new book, Keynes: The Return of the Master, is getting more buzz than Paul Davidson's new book, The Keynes Solution: The Path to Global Economic Prosperity. Paul Krugman's review of Skidelsky's book in the Observer contrasts the rejection of Say's law with an emphasis on fundamental uncertainty. Davied Warsh also alludes to the debates over what Keynes really meant. Here is a year old oped by Skidelsky, while here is a more recent article quoting him. Aaron Swartz has been reading The General Theory of Employment, Interest, and Money. He has both a chapter-by-chapter summary and a brief explanation.

I think Keynes book was primary about economic theory and only secondary about advocating policy based on that theory. One can perhaps explain why an economy might deviate from a full employment equilibrium. Workers are constrained to budget based on the income they receive, not on the income they would receive if they were fully employed. This idea could be basis of a dynamic story. But Keynes argued, building on Richard Kahn's multiplier, that it could also explain an equilibrium with involuntary unemployment.

I think that Keynes argued that such an unemployment equilibrium could hold in both the Marshallian short run and the long run. To make sense of Keynes' claim, one must construct a model in which money enters in some essential way. And I would expect money to be non-neutral in all runs. To me, this introduction of money into an economic model is connected with modeling fundamental uncertainty. In short, I see Keynes' rejection of Say's law and his emphasis (e.g., in Chapter 12) on uncertainty as complementary.

(Apropos of none of the above - some might be amused by this cartoon. H/T to Brian Leiter.)

O Brave New World That Has Such Bacteria In It

The BioBricks Foundation (BBF) has Request For Comments (RFCs), just like the Internet Engineering Task Force (IETF). They have a BioBrick language, a graphical language, and are working on an RDF-based framework for a synthetic biology ontology. (The Resource Description Framework (RDF) is a standard for the semantic web.)

BBF is using this this computer science technology and organizational structure to create "standard biological parts" that "encode basic biological functions". The goal is to enable biological engineers to "program living organisms in the same way a computer scientist can program a computer".

(Hat Tip to Michael Specter's New Yorker 28 September 2009 article.)

From Alexander Rosenberg On Cochrane On Krugman

Brian Leiter reports Alexander Rosenberg's thoughts. I'll select one extract:

"Add in [Chicago economists'] ideological attachment to the nonsensical ideas that the marginal productivity of labor or capital measures its causal role, and therefore its moral right to a proportional slice of the profits, and you easily slip from Laissez-faire 'science' to 'trickle down' political philosophy."

(Rosenberg's views remind me of this comment.) The nonsense isn't limited to Chicago. I have seen positive references to Rosenberg's book, Economics: Mathematical Politics or Science of Diminishing Returns, but I have not read it.

Stiglitz Reports

Joseph Stiglitz has been chairing commissions. The draft report of the Commission of Experts of the President of the UN General Assembly on Reform of the International Monetary and Financial System is downloadable from here. The Report of the Commission on the Measurement of Economic Performance and Social Progress is downloadable from here. (Amartya Sen was the Chair Advisor for the latter commission.)

Samir Amin has some criticisms of the former report. Amin thinks the report treats the global financial crisis as a short-term downturn, not as a manifestation of a Fordist accumulation regime that needs to be replaced.

It does seem like a new Bretton Woods, along with a meeting like the Bandung conference in 1955, might be a good thing at this conjuncture.

To Read:

• M. Aglietta (1979) A Theory of Capitalist Regulation: The U.S. Experience, Verso Books.
• Giovanni Arrighi (1994) The Long Twentieth Century, Verso Books.

Piling On

A fool writes:

"Paul's Keynesian economics requires that people make logically inconsistent plans to consume more, invest more, and pay more taxes with the same income... In economics, stimulus spending ran aground on Robert Barro's Ricardian equivalence theorem. This theorem says that debt-financed spending can't have any effect because people, seeing the higher future taxes that must pay off the debt, will simply save more." -- John H. Cochrane, "How did Paul Krugman get it so Wrong?"

On the other hand:

"Ricardian equivalence was another property of rational expectations monetarism. It was tested, in effect, by the Bush administration, which swung the federal budget into large deficit. The increase in the deficit was not compensated by increased private saving. Instead, American households decreased their savings to basically nothing. This violation of Ricardian equivalence suggests that the transversality condition imposed in intertemporal general equilibrium models has no empirical counterpart. Without such a condition consistency of all decisions is no longer guaranteed in intertemporal models. But bubbles and crashes are admitted." -- Axel Leijonhufvud (2009) "Out of the corridor: Keynes and the crisis", Cambridge Journal of Ecnomics, V. 33: pp. 741-757

Special Issues on Global Financial Crisis

Some journals with articles on current problems:

• Cambridge Journal of Economics, V. 33, N. 2 (July 2009).
• Challenge, V. 52, N. 1 (January-February 2009) to V. 52, N. 4 (July-August 2009).
• Real-Word Economics Review, Issue no. 47 (3 October 2008) to Issue no. 50 (8 September 2009). (They've also collected some of their articles in Crash: Why It Happened and What to Do About It, V. 1 Edited by Edward Fullbrook, 2009.)
  
• Review of Radical Political Economics, V. 41, N. 3 (September 2009).

Economists With Ethics

The Association for Integrity and Responsible Leadership in Economics and Associated Professions (AIRLEAP) is "deeply concerned about the issues of integrity and responsible leadership in economics as they relate to economic discourse, economic decision making, and the career development of economists and related professionals."

One Math, Three Applications

I previously pointed out that the same math that can formalize classical economics is used by Google to find page ranks. Now Stefano Allesina and Mercedes Pascual have found that the Perron-Frobenius theorem also supports the detection of critical species in ecosystems.

Only Mainstream Macroeconomists Exist For Krugman

Many have already written about Paul Krugman's article, "How Did Economists Get It So Wrong?" in the September 6 issue of the New York Times Magazine. Krugman himself followed up with blog comments. Brad DeLong has prepublication and postpublication comments, as well as comments on other commentators. I like Colin Danby's take, in comments, on the intolerance of the orthodoxy. Mark Thoma has a comment on Sean Carroll's take. Some commentators, such as Ramanan get it.

In Krugman's article, all macroeconomists are either freshwater or saltwater. Post Keynesian criticisms that apply to both types are not mentioned. Although I am not too familiar with mainstream macro, I can think of three:

• Both situate their models in logical, not historical time
• Both assume a representative agent
• Both assume a single good that functions as both a capital and a consumption good.

These limitations rule out a priori the possibility of some interesting dynamics and perhaps make it difficult to see why agents in the model would want to hold money or even trade with one another.

References

• Paul Davidson (1982-83) "Rational Expectations: A Fallacious Foundation for Studying Crucial Decision-Making Processes", Journal of Post Keynesian Economics, V. V, N. 2 (Winter): pp. 182-198
• Alan P. Kirman (1992) "Whom or What Does the Representative Individual Represent" Journal of Economic Perspectives, V. 6, N. 2 (Spring): pp. 117-136
• Graham White (2004) "Capital, Distribution and Macroeconomics: 'Core' Beliefs and Theoretical Foundations", Cambridge Journal of Economics, V. 28, N. 4: pp. 527-547

Samuelson’s Revealed Preference: A Failed Research Program

Wong (1978, 2006) grew out of what may have been the last doctorate thesis Joan Robinson supervised. As it is, Wong did not complete his thesis under Robinson's supervision. Luigi Pasinetti and then Geoffrey Harcourt later became Wong's supervisor.

Wong’s study is centered around three publications by Paul Samuelson, in 1938, 1948, and 1950. Samuelson, in 1938, according to Wong, attempted to construct a new theory without any reliance on utility theory or any concept that relies on non-observational phenomena. This theory was intended to be a replacement, not a complement for utility theory.

Samuelson, in 1940, according to Wong, attempted to construct indifference maps from observed consumer choices in a space of price and quantity observations. "The whole theory of consumer's behavior can thus be based upon operationally meaningful foundations in terms of revealed preference." -- Samuelson (1948)

Samuelson, in 1950, according to Wong, was responding to work primarily by Hendrik Houthakker, who showed that ordinal utility theory and revealed preference theory were logically equivalent. Thus, utility theory has the same empirical implications and operational foundations.

Wong interprets the observational equivalence of utility and revealed preference as a defeat for Samuelson's 1938 program. Samuelson, however, asserted this finding was the completion of a victorious research program. And mainstream economists have let him get away with this claim, without ever subjecting it to a critical inquiry.

"I soon realized that [the weak axiom of revealed preference] could carry us almost all the way along the path of providing new foundations for utility theory. But not quite all the way. The problem of integrability, it soon became obvious, could not yield to this weak axiom alone." -- P. A. Samuelson (1950)

References

• Paul A. Samuelson (1938) “A Note on the Pure Theory of Consumer’s Behaviour”, Economica, v. 5: pp. 61-71.
• Paul A. Samuelson (1948) “Consumption Theory in Terms of Revealed Preference”, Economica, v. 15: pp. 243-253.
• Paul A. Samuelson (1950) “The Problem of Integrability in Utility Theory”, Economica, v. 17: pp. 355-385.
• Stanley Wong (1978, 2006) Foundations of Paul Samuelson’s Revealed Preference Theory: A Study by the Method of Rational Reconstruction, Revised Edition, Routledge.

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

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

INPUTS	Process I	Process IIa	Process IIb
Labor	5 Person-Yrs	10 Person-Yrs	10 Person-Yrs
Iron	18 Tons	12 Tons
Coal			10 Cwt
OUTPUTS
Iron	48 Tons	12 Tons	12 Tons
Coal	10 Cwt	30 Cwt	30 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

INPUTS	Process I	Process IIa
Labor	1/6 Person-Yr	2/9 Person-Yr
Iron	9/15 Ton	4/15 Ton
Coal
OUTPUTS
Iron	1 9/15 Tons	4/15 Ton
Coal	1/3 Cwt	2/3 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

INPUTS	Process I	Process IIb
Labor	1/360 Person-Yr	1/108 Person-Yr
Iron	3/10 Ton
Coal		5/12 Cwt
OUTPUTS
Iron	4/5 Ton	1/2 Ton
Coal	1/6 Cwt	1 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 p_I(1 + r) + 5 = 48 p_I + 10 p_C

12 p_I(1 + r) + 10 = 12 p_I + 30 p_C

where p_I is the price of iron in units of person-years per ton, p_C 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:

p_I = 5/[6 (15 - 7 r)]

p_C = (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 p_I(1 + r) + 5 = 48 p_I + 10 p_C

10 p_C(1 + r) + 10 = 12 p_I + 30 p_C

Its solution is:

p_I = -5 r/[6 (r - 1)(3 r - 8)]

p_C = (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 p_C 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.

References

• 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

"The Most Notable Critic of Austrian Economics"

Apparently, that is me.

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)

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.

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.

Marc Lavoie - Quite Fierce

I think I downloaded Marc Lavoie's paper, "Neoclassical Empirical Evidence: On Employment and Production Laws as Artefact" from some conference proceedings. It's downloadable from his site, but I'm not sure for which recent conference it was presented.

Lavoie summarizes the orthodox response to the Cambridge Capital Controversy and the counterexamples:

• "Neoclassical authors minimize the capital paradoxes, making an analogy with Giffen goods in microeconomics, which do not question the entire neoclassical edifice;
• They look for the mathematical conditions that would be required to keep production functions as 'well-behaved', or they claim that this is a simple aggregation problem that can be resolved;
• They claim that Walrasian general equilibrium theory is impervious to the critique;
• They claim that they have the faith, or they plead ignorance;
• Empiricism (It works, therefore it exists)."

And he also mentions how some react to the arguments of such economists as Franklin Fisher and Anwar Shaikh:

"I have discussed some of these issues with a few of my neoclassical colleagues - those that I thought would be most open to dialogue. Amazingly, their response has been to fake that they did not understand the implications of the Shaikh or McCombie papers that I emailed them. The most genuine answers have been that without these elasticity estimates they could not say anything anymore. But they would rather continue making policy proposals based on false information than make no proposition at all. In other words, they would rather be precisely wrong than approximately right."

Unsent Letter

Others have already commented on the three articles on the breakdown of macroeconomics and financial economics in the July 18-24 issue of The Economist.

SIR - You write:

"[Macroeconomists'] framework reflected an uneasy truce between the intellectual heirs of Keynes, who accept that economies can fall short of their potential, and purists who hold that supply must always equal demand. The models the epitomise this synthesis ... incorporate imperfections in labour markets ('sticky' wages, for instance, which allow unemployment to rise)..."

But the idea that persistent unemployment is the result of wages sticky downward is a pre-Keynesian idea. Keynes explicitly rejected this explanation of the cause of unemployment:

"...the Classical Theory has been accustomed to rest the supposedly self-adjusting character of the economic system on an assumed fluidity of money-wages; and, when there is rigidity, to lay on this rigidity the blame of maladjustment... My difference from this theory is primarily a difference of analysis." (John Maynard Keynes, The General Theory of Employment, Interest and Money, "Chapter 19. Changes in Money Wages"

Apparently neither saltwater nor freshwater macroeconomists follow Keynes.

Woodstock Thirtieth Anniversary

They did not hold the 30th anniversary concert at Woodstock. They held it in my backyard.

Crowd for Dave Matthews. Dave Did "Watchtower"

Naked Man and Photographer

The man in the purple shirt is Ken Kesey's business partner.

Salesman

What With The Arson, That Didn't Work Out So Well, Did It?

Now, Judge, I Had Debts No Honest Man Could Pay/The Bank Was Holding My Mortage And They Were Gonna Take My House Away

1.0 Introduction
This example illustrates one aspect of how Sraffa analyzed natural resources. In this case, natural resources consist of land of various qualities or grades. The quantity of each grade is given; more land cannot be produced. Land is not destroyed either. Appropriate production processes yield as much land as a joint output as given as input. So this sort of model does not incorporate a natural resource like oil that is used up in production.

This example demonstrates that owners of less efficient (productive) natural resources can receive a greater rent.

By the way, Sraffa introduces a distinction between basic and non-basic commodities. Lands with positive rent are non-basic, and therefore their rent is a candidate for taxation.

2.0 Technology
This is a simple economy in which only corn is produced. Table 1 shows the available processes that have corn as an output. Each process requires the use of one grade of land, and no more than one process is known for each grade of land. (This is an example of a model of extensive rent.) Suppose this economy has available 150 acres of land of grade I, 162 acres of grade II land, and 210 acres of grade III land.

Table 1: Technology

Inputs	Process
	Alpha	Beta	Gamma
Labor (Person-Years)	2/5	1	2/7
Grade I Land (Acres)	1	0	0
Grade II Land (Acres)	0	3/2	0
Grade III Land (Acres)	0	0	1
Corn (Bushels)	2/5	1/6	4/7
Output (Bushels)	1	1	1

3.0 Prices
The question to be addressed is what prices and distribution of income are compatible with a long-period position, given the technology. The amount of corn required for net output is a parameter that must be known to answer this question.

3.1 When Only One Grade Of Land Is Cultivated
Suppose the requirements for use for corn in this economy can be satisfied by cultivating any one of the three grades of land. Two grades, and maybe some of the third grade, can lie fallow. So at most 90 bushels are produced each year, after replacinging up the seed corn.

And suppose that the wage is 1/2 bushels per person-year. The wage is paid out at the end of the year. These assumptions are enough to derive the factor-price curves shown in Figure 1. These curves are drawn under the assumption that all grades of land paid no rent.

Figure 2: Factor Price Curves

Since the beta factor-price curve is rightmost (on the outer frontier) at the given wage, all corn is produced on land of the second grade, and this land pays no rent. The wage and the rate of profits must satisfy the following equation:

(1/6)(1 + r) + w = 1

where a bushel corn is the numeraire. For a wage of 1/2 bushels per person-year, the rate of profits is 200%.

Under the given assumptions, the cost of producing a bushel corn on the first grade of land, even if that land were to pay no rent, is 7/5 bushels. Since this cost exceeds the revenues from selling a bushel of land, no capitalist would want to produce on the first grade of land. The reader can check that the cost of producing a bushel corn on the third grade of land also exceeds unity.

3.2 When Two Grades Of Land Are Cultivated
Now suppose the requirements for use are such that two grades of land must be cultivated. The net output of this economy is between 90 and 180 bushels corn. The wage remains 1/2 bushels per person-year. In this case, the first and second grades are cultivated, with the second grade paying rent. The price equations are:

(2/5)(1 + r) + (2/5)w + ρ₁ = 1

(1/6)(1 + r) + w + (3/2)ρ₂ = 1

ρ₁ ρ₂ = 0

ρ₁, ρ₂ ≥ 0

The equations specify that no land can have a negative rent and that at least one grade of land must have a rent of zero. The rate of profits is 100%, when the wage is 1/2 bushels per person-year. Land of grade I pays no rent, and the rent on land of grade II is 1/9 bushels per acre.

The cost of producing a bushel corn on the third grade of land, accounting just for outlays of seed corn and labor, is 9/7 bushels. Capitalists will not want to cultivate the third grade of land, even if it is free.

3.3 When Three Grades Of Land Are Cultivated
Finally, suppose the requirements for use for use require all three grades of land to be cultivated. The price equations are:

(2/5)(1 + r) + (2/5)w + ρ₁ = 1

(1/6)(1 + r) + w + (3/2)ρ₂ = 1

(4/7)(1 + r) + (2/7)w + ρ₃ = 1

ρ₁ ρ₂, ρ₃ = 0

ρ₁, ρ₂, ρ₃ ≥ 0

The rate of profits is 50%, when the wage is 1/2 bushels per person-year. The rent on land of grade I is 1/5 bushels per acre. The rent on grade II land is 1/6 bushels per acre

3.4 Orders Of Efficiency And Rentability
The above analysis has identified a definite order in which different grades of land will be cultivated as greater quantities of output are required to be produced. This is the order of efficiency. In this example, the order of efficiency, from most efficient to least efficient, is: Grade II, Grade I, Grade III.

One can also rank the grades of land from high rent to low rent, when all three grades of land are cultivated and the wage is 1/2 bushels per person-year. The order of rentability, from highest rent to zero rent, is: Grade I, Grade II, Grade III.

The orders of rentability and efficiency differ. It is possible for a less productive, that is, the less efficient, resource to provide its owner with a greater rent than the more efficient resource.

This example is not driven by the existence of switch points.

Reference

• Alberto Quadrio-Curzio, "Rent, Income Distribution, and Orders of Efficiency and Rentability", in Essays on the Theory of Joint Production (Edited by L. L. Pasinetti), Columbia University Press, 1980.