Slope Of "Demand Curve" Varying With Numeraire

1.0 Introduction
As I have previously blogged, Ian Steedman has a number of articles explaining price theory. These articles typically explain the implications, for example, for the slopes of certain functions, but often do not contain graphical illustrations. Here then is an opportunity for me to develop blog posts. For instance, this post works through the example in Section 4 of Arrigo Opocher and Ian Steedman's article, "Input price-input quantity relations and the numéraire" (Cambridge Journal of Economics, V. 33, N. 5 (2009): 937-948).

2.0 Technology
Consider a simple economy in which three commodities - iron, steel, and corn - are produced. Corn is the only commodity people consume, and corn is not used as an input in the production of any commodity. The problem considered here is how much of each input into the production of corn will be demanded by the firms in the corn-production industry.

Iron is produced by unassisted labor. The production function for iron is:

q₁ = f₁(l₁, x_1,1, x_2,1, x_3,1) = l₁

where:

• q_i; i = 1, 2, 3; is the quantity of the ith commodity produced in the period under consideration.
• f_i( ); i = 1, 2, 3; is the production function for the ith commodity.
• l_j; j = 1, 2, 3; is the number of person-years hired in the period under consideration to produce the jth commodity.
• x_i,j; i = 1, 2, 3; j = 1, 2, 3; is the quantity of the ith commodity used in the production of the jth commodity in the period under consideration.

Steel is produced by labor from iron. Steel production is modeled by a Cobb-Douglas production function:

q₂ = f₂(l₂, x_1,2, x_2,2, x_3,2) = (l₂)^D (x_1,2)^E/(D^D E^E)

where D and E are positive parameters and D + E = 1.

Corn is produced by labor from inputs of iron and steel. The production function for corn is:

q₃ = f₃(l₃, x_1,3, x_2,3, x_3,3) = (l₃)^d (x_1,3)^e (x_2,3)^f/(d^d e^ef^f)

where d, e, and f are positive parameters and d + e + f = 1.

All production functions exhibit Constant Returns to Scale (CRS). All capital goods are totally used up in production, and all production processes require the same amount of time.

3.0 Cost Functions and Coefficients of Production
Consider competitive firms producing a commodity who want to adopt a cost-minimizing technique. For definitiveness, consider a firm producing steel. Let w be the wage (paid at the beginning of the period) and p_j; j = 1, 2, 3; be the spot price of the jth commodity. The unit cost function, c₂( ), for producing steel is the value of the objective function in the solution to the following mathematical programming problem:

Given w, p₁, p₂, p₃

Choose l₂, x_1,2, x_2,2, x_3,2

To Minimize wl₂ + p₁x_1,2 + p₂x_2,2 + p₃x_3,2

Such that:

f₂(l₂, x_1,2, x_2,2, x_3,2) = 1

l₂ ≥ 0; x_i,2 ≥ 0, i = 1, 2, 3.

Solving this programming problem, one finds the unit cost function for producing steel is:

c₂(w, p₁, p₂, p₃) = (w)^D (p₁)^E

In working out the cost function, I also figured out how much labor and iron a steel-producing firm would hire to produce one ton of steel. Opocher and Steedman pose the problem with given cost functions, not production functions. They derive the coefficients of production by invoking Shephard’s Lemma.

A similar cost-minimizing problem arises for corn-making firms.
The unit cost function, c₃( ), for producing corn is:

c₃(w, p₁, p₂, p₃) = (w)^d(p₁)^e(p₂)^f

The derivatives of the cost functions are summarized by the coefficients of production, a₀ and A, where:

• a₀ is a three-element row vector such that a_0,j; j = 1, 2, 3; is the person-years of labor hired per unit output of the jth industry.
• A is a 3x3 matrix such that a_i,j; i = 1, 2, 3; j = 1, 2, 3; is the quantity of the ith commodity purchased as an input per unit output in the jth industry.

Table 1 displays coefficients of production.

Table 1: The Cost-Minimizing Technique

	Iron Industry	Steel Industry	Corn Industry
Labor	a0,1 = 1	a0,2 = D (p1/w)E	a0,3 = dwd - 1 (p1)e(p2)f
Iron	a1,1 = 0	a1,2 = E (w/p1)D	a1,3 = ewd (p1)e - 1(p2)f
Steel	a2,1 = 0	a2,2 = 0	a2,3 = fwd (p1)e(p2)f - 1
Corn	a3,1 = 0	a3,2 = 0	a3,3 = 0
Output	1 ton iron	1 ton steel	1 bushel corn

4.0 Long Period Price Equations
The above shows the coefficients of production that perfectly competitive firms choose, given prices. Each column in Table 1 has been derived independently of the others. Firms will continue to produce corn, the consumption good, period after period only if some firms also choose to produce iron and steel. Cost-minimizing firms will not make these choices for any configuration of prices. The long-period condition that firm choices be self-sustaining yields the following system of three equations:

a_0,1 w (1 + r) = p₁

[p₁ a_1,2(w, p₁) + w a_0,2(w, p₁)](1 + r) = p₂

[p₁ a_1,3(w, p₁, p₂) + p₂ a_2,3(w, p₁, p₂) + w a_0,3(w, p₁, p₂)](1 + r) = p₃

where r is the rate of profits. Since production takes time, the rate of profits is generally positive. These equations, when solved, define long-period equilibrium prices for produced commodities as functions of the wage and the rate of profits:

p₁ = w(1 + r)

p₂ = w(1 + r)^{1 + E}

p₃ = w(1 + r)^{1 + e + f + (1 + E)f}

5.0 The Numeraire
The above system of price equations has two degrees of freedom. One degree of freedom is removed when the numeraire is specified. Let the numeraire consist of σ₁ units of iron, σ₂ units of steel, and λ person-years:

σ₁p₁ + σ₂p₂ + λw = 1

Prices of the commodities comprising the numeraire are then:

w = 1/[σ₁(1 + r) + σ₂(1 + r)^{1 + E} + λ]

p₁ = (1 + r)/[σ₁(1 + r) + σ₂(1 + r)^{1 + E} + λ]

p₂ = (1 + r)^{1 + E}/[σ₁(1 + r) + σ₂(1 + r)^{1 + E} + λ]

Figure 1 shows the relationship between the wage and the rate of profits. This relationship is known as the wage-rate of profits frontier. In this example, coefficients of production vary continuously along the frontier.

Figure 1: Wage-Rate Of Profits Frontier

6.0 Quantity Demanded for Inputs
The above derivations allow one to draw various graphs for specific parameter values. I set the parameters for the production functions as follows: D = 3/4; E = 1/4; d = 2/3; e = 1/6; and f = 1/6. And I considered two numeraires. For the first numeriare, σ₁ = 1/3; σ₂ = 1/3; and λ = 1/3. For the second numeriare, σ₁ = 1/3; σ₂ = 1/2; and λ = 1/6.

For each numeraire, the wage and other prices in a long-period position are defined as functions of the rate of profits. And the cost-minimizing coefficients of production are functions of these prices, that is, ultimately of the rate of profits. Figure 2 shows a locus constructed out of these functions. Curves at the top of the figure plot the price of iron against the quantity of iron demanded by the (non-vertically integrated) corn-producing industry. In drawing this figure, the quantity of corn produced is constrained to be unity. The curves are analogous to conditional demand curves in neoclassical economic theory. And one can see that, for certain regions, whether the slope of such a curve is positive or negative depends on the numeraire. But is not a main point of neoclassical economics to argue that demand curves are downward-sloping (for arbitrary numeraires)?

Figure 2: A Locus for Firms in Long Period Equilibrium

7.0 Conclusion
So much for explaining the price of a capital good by well-behaved supply and demand curves in the market for that commodity.

Book Series

Any number of publishers have published series of books over the last couple of decades of interest to heterodox economists. Some are, I think, targeted for reference libraries - who else can afford them¹? Some collect papers for specific themes or schools of thought. And various publishers specialize in such.

But here I want to focus on the Modern Cambridge Economics Series. These books seem to be targeted for the more introductory student. They consist of, as far as I can tell:

• A. Asimakopulos (1991) Keynes's General Theory and Accumulation²
• Amiya Kumar Bagchi (1982) The Political Economy of Underdevelopment
• John Cornwall and Wendy Cornwall (2007) Capitalist Development in the Twentieth Century
• Phyllis Deane(1978) The Evolution of Economic Ideas²
• Michael Ellman (1989) Socialist Planning
• Eprime Eshag (1984) Fiscal and Monetary Policies and Problems in Developing Countries
• Frederick S. Lee (2006) Post Keynesian Price Theory
• Joan Robinson (1979) Aspects of Development and Underdevelopment
• Colin Rogers (1989) Money, Interest and Capital: A Study in the Foundations of Monetary Theory²

Phyllis Deane and Joan Robinson were the original editors. Phyllis Deane, Geoffrey Harcourt, and Jan Kregel were the editors after a later relaunch.

¹Edward Elgar has a series on Schools of Thought in Economics, another series called The Elgar Companion to ..., and The International Library of Critical Writings in Economics. Palgrave Macmillan had themed extracts from the New Palgrave (with some original entries) and is currently publishing their Great Thinkers in Economics series. (This last series is more introductory and affordable by some students.) Routledge has their multi-volume Critical Assessments of Leading Economists collections and, for the Austrian school, the Foundations of the Market Economy Series. Back in the 1970s, Penguin had the Penguin Modern Economic Readings collections. (Links are to information about random books in a series.)

² I have read and enjoyed these.

Cyril Hédoin On The Failure Of Macroeconomics

Some time ago, I noted James Galbraith's article, "Who Are These Economists, Anyway?" Galbraith suggests that it might be worthwhile to on the work of those economists who were researching "the nature and causes of financial collapse" before the present crisis and had presciently warned of potential problem areas. These empirically successful economists happen to be non-orthodox economists.

The other day, I stumbled upon a somewhat old response to Galbraith,
"Vers un changement de paradigme en économie" (English version), from Cyril Hédoin. As I understand it, he thinks neoclassical economics is collapsing and - what with behavioral economics, evolutionary game theory, complexity economics, etc. - mainstream economics is pluralist. Given these changes, he thinks economists have no need to look among traditionally heterodox economists for good ideas. Hédoin cites articles I like by David Colander, Richard Holt, & Barkley Rosser and by John B. Davis.

Galbraith replies in the comments. He unequivocally rejects the idea that his recommended alternative is on the periphery of economics. He says he cites the economists he does because he thinks their work is good.

Mainstream economists certainly have a problem in explaining - especially to outsiders - why one should not cite certain past presidents of the American Economic Society, various Harvard-trained economists or professors in the Harvard economics department, articles published in certain economics journals associated with the University of Cambridge, some "Nobel Prize" winners, and so on. (For any Austrian-school economists who may be reading this - certain economists trained at New York University don't count either.)

Nozick's Anarchy, State, and Utopia

1.0 Overview
Propertarianism, misleadingly called "libertarianism" by its fans, is a political philosophy. Do any supposedly rigorous arguments exist for this philosophy? Some cite Robert Nozick's 1974 tome, Anarchy, State, and Utopia as a demonstration that this question can be answered in the affirmative.

The book has three main parts. In the first part, Nozick argues that a state can emerge from an anarchistic state of nature without violating anybody's rights. The state, according to Nozick, evolves from a private protection agency; its clients become citizens. In the second part, Nozick argues that a state that tries be to more than a minimal state will violate somebody's rights, especially their right to property. For the distribution of property to be just, according to Nozick, three conditions must be met:

• The original acquisition of property must not have violated anybody's rights.
• The transfer of holdings must be likewise just.
• Whatever injustices may nevertheless have arisen in original acquisition or transfer must be rectified justly.

In the last part, Nozick provides a recipe for cookbooks of the future. He describe an association of voluntary communities, where people are free to join whichever commune they like. Only some of these communities may initially be propertarian.

This obvious decomposition of the book explains the three-word title. Despite Nozick's pretense to be presenting an analytic argument, I did not find nearly as much structure at a lower level. The first part seems to beg how people in an original anarchy would behave. Nozick postulates bourgeois contract-making; I think feudalism would more likely result. He continually brings up objections and needed refinements, pursues the argument to an arbitrary level, and then declares the resolution of these details beyond his scope since he is not writing a work of psychology or epistemology or whatever. So I find it difficult to summarize much more of the book.

2.0 Popular Bits
I think Nozick originated many sayings now popular among propertarians. Maybe some he reformulated or re-emphasized.

Nozick's calls his version of Descartes' demon "The Experience Machine". His story is a science fiction story with technology, tanks to float in, and computers. It raises the question, "What else can matter to us, other than how our lives feel from the inside?"

Nozick comes fairly close to saying that there is no such thing as society:

"But there is no social entity with a good that undergoes some sacrifice for its own good. There are only individual people, different individual people, with their own individual lives."

Nozick formulates a non-aggression principle, now called the No-Initiation-of-Force principle in propertarian polemics:

"An underlying notion sufficiently powerful to support moral side constraints against the powerful intuitive force of the end-state maximizing view will suffice to derive a libertarian constraint on aggression against another."

Nozick creates a well-known example with Wilt Chamberlain. Wilt Chamberlain's contract with a basketball team gives him a share of the gate. People "cheerfully attend his team's game". Nozick's imagines that when they buy their tickets, part of the price is that each person "drops" 25 cents "of their admission price into a special box with Chamberlain's name on it." What can be wrong with all of these voluntary transactions making Chamberlin rich? In the course of this exposition, he comes up with a clever turn of phrase:

"The socialist society would have to forbid capitalist acts between consenting adults." (my emphasis)

3.0 Some Absurdities
Nozick's book is a work of political philosophy containing much economic reasoning. But Nozick makes many mistakes in economics, and ignores what seems to me some major problems in political philosophy.

For example, I think a major question in political philosophy is how people with different ideas of good and evil can live together. Nozick acknowledges he doesn't address this question:

"I have proceeded in this essay (as much as possible) without questioning or focusing upon the assumption common to much utopian and anarchist theorizing, that there is some set of principles obvious enough to be accepted by all men of good will, precise enough to give unambiguous guidance on particular situations, clear enough so that all will realize its dictates, and complete enough to cover all problems that actually will arise. To have rested the case for the state on the denial of such an assumption would have left the hope that the future progress of humanity (and moral philosophy) might yield such agreement, and so might undercut the rationale for the state.

... the day seem[s] distant when all men of good will shall agree to libertarian principles... People who prefer peace to the enforcement of their view of right will unite together in one state."

In contrast to my opinion, Nozick thinks Marxian exploitation is a normative idea¹:

"One traditional socialist view is that workers are entitled to the product and full fruits of their labor; they have earned it; a distribution is unjust if it does not give the workers what they are entitled to."

Nozick doesn't understand marginal productivity. He incorrectly thinks that it is a theory of distribution:

"Almost every suggested principle of distributive justice is patterned: to each according to his moral merit, or needs, or marginal product, or how hard he tries, or..."

I could cite many more instances in which Nozick makes this mistake.

Nozick erroneously ignores the possibilities of multiple equilibria and of path dependence:

"Let us suppose that we know from economic theory that under the standard assumptions defining a competitive market economy, income and wealth will be distributed in an efficient way, and that the particular efficient distribution which results in any period of time is determined by the initial distribution of assets, that is, by the initial distribution of income and wealth, and of natural talents and abilities. With each initial distribution, a definite efficient outcome is arrived at."

Also, Nozick begs the question of the definition of property rights, of how a society determines what can be a commodity and what cannot. I could cite even more examples of Nozick getting economics wrong.

Nozick has a definite view on the always burning question of whether or not slavery is compatible with propertarianism. He thinks it is:

"Perhaps no persons completely sell themselves into slavery... Since this very extensive domination of some persons by others arises by a series of legimate steps, via voluntary exchanges, from an initial situation that is not unjust, it itself is not unjust."

And again:

"The comparable question about an individual is whether a free system will allow him to sell himself into slavery. I believe that it would."

4.0 Conclusion
I do not find Nozick's book convincing². You might want to read it to understand some context for certain debates in political philosophy. Nozick treats Rawls in the second part of his book. Before having read Nozick, I already knew about some of the popular bits from having read Alan Haworth. Nozick tends to be cited by many soi-disant libertarians - I suspect by more than have actually read him.

Footnotes
¹Nozick does foreshadow John Roemer's game-theoretic definition of exploitation:

"An individual benefits from the wider system of extensive cooperation between the better and the worse endowed to the extent of his incremental gain from this wider cooperation; namely, the amount by which his share under a scheme of general cooperation is greater than it would be under one of limited intra-group (but not cross-group) cooperation."

Nozick formulates "a condition of stable associations" much like this in the third part of his book.

²This is probably not surprising, given my preconceptions.

Robert Lucas On The Impossibility Of Involuntary Employment

As I understand it, so-called Dynamic Stochastic General Equilibrium (DSGE) models are central to contemporary mainstream macroeconomics. Some may want to criticize DSGE on the grounds that they failed to predict the recent global financial crisis. I think a stronger criticism would be that they led their users to believe in the impossibility of current circumstances arising.

I think of DSGE models as having evolved out of trends in macroeconomics started by Robert Lucas. Here is Lucas being sarcastic:

"The first sentence in Malinvaud, The Theory of Unemployment Reconsidered, is 'The term involuntary unemployment makes it obvious from the start that the labor market is one in which supply exceeds demand.' Thus we acquire factual information about labor markets from the terminology earlier theorists have used to describe them!" -- Robert E. Lucas, Jr. Models of Business Cycles. Basil Blackwell (1987).

And here is more:

"A theory that does deal successfully with unemployment needs to address two quite distinct problems. One is the fact that job separations tend to take the form of unilateral decisions - a worker quits, or is laid off or fired - in which negotiations over wage rates play no explicit role. The second is that workers who lose jobs, for whatever reason, typically pass through a period of unemployment instead of taking temporary work on the 'spot' labor market jobs that are readily available in any economy. Of these, the second seems to me much the more important: it does not 'explain' why someone is unemployed to explain why he does not have a job with company X. After all, most employed people do not have jobs with company X either. To explain why people allocate time to a particular activity - like unemployment - we need to know why they prefer it to all other available activities: to say that I am allergic to strawberries does not 'explain' why I drink coffee. Neither of these puzzles is easy to understand within a Walrasian framework, and it would be good to understand both of them better, but I suggest we begin by focusing on the second of the two." -- Robert E. Lucas, Jr. Models of Business Cycles. Basil Blackwell (1987).

Joe Stiglitz As Cambridge Economist?

Joseph Stiglitz has an article, "Of the 1%, By the 1%, For the 1%", in next month's Vanity Fair. In analyzing America's increasingly ridiculous unequal society, he writes:

"Economists long ago tried to justify the vast inequalities that seemed so troubling in the mid-19th century—inequalities that are but a pale shadow of what we are seeing in America today. The justification they came up with was called 'marginal-productivity theory.' In a nutshell, this theory associated higher incomes with higher productivity and a greater contribution to society. It is a theory that has always been cherished by the rich. Evidence for its validity, however, remains thin. The corporate executives who helped bring on the recession of the past three years—whose contribution to our society, and to their own companies, has been massively negative—went on to receive large bonuses. In some cases, companies were so embarrassed about calling such rewards 'performance bonuses' that they felt compelled to change the name to 'retention bonuses' (even if the only thing being retained was bad performance). Those who have contributed great positive innovations to our society, from the pioneers of genetic understanding to the pioneers of the Information Age, have received a pittance compared with those responsible for the financial innovations that brought our global economy to the brink of ruin."

Stiglitz had negative reviews in 1974 and 1975 of books by Harcourt and Pasinetti. Nevertheless, the idea that marginalism was formulated to justify those with high income echoes certain ideas from Sraffa and others. Likewise, finding marginal productivity theory to be "all bosh" is a long-standing Cambridge idea.

I can think of three ways to attack a theory

• To claim, as above, that the premises and conclusions of the theory are empirically false.
• To argue that, even given all the premises of the theory, the conclusions do not follow.
• To argue that the premises of the theory are mutally inconsistent.

I guess it is a matter of taste which approach you think is strongest. I have a preference for the second.

Brouhaha Over Krugman On Endogenous Money

I recently posted about the theory that the money supply is endogenous and under the control of a country's central bank, such as the Federal Reserve. Paul Krugman dismisses the theory.

Proponents of Modern Monetary Theory, in the comments and elsewhere, have taken issue with Krugman. I have in mind, for example, Dean Baker, Peter Cooper, Scott Fullwiler, Greg Hannsgen (of the Levy Institute), Bill Mitchell, Warren Mosler, Cullen Roche, and Pavlina Tcherneva (cross-posted). James Galbraith appears in various comments, for example, in this one, in which he says, "I was a student of Godley (and even more so, of Kaldor) many years ago and a close observer of monetary policy during my years on Capitol Hill, so this material came easily to me."

Elsewhere

• Steve Keen, in the Australian newspaper The Business Spectator simultaneously praises Paul Krugman for building on Hyman Minsky's work, while criticizing him for "embod[ying] everything that is bad in neoclassical economics."
• Bill Mitchell argues, in last week's Nation, that government responses to the global economic crisis have been based on a series of economic myths. (Will the winning cruciverbalist for the Nation be paid in the "high two figures"?)
• John T. Harvey also warns, but in Forbes, against cutting the deficit.
• Branko Milanovic, in a guest post for D. M. Nuti, explains the connection between rising income equality and the global economic crisis.

H/T: Peter Cooper for the links to the second and third links.

Some British Nineteenth Century Controversies In Monetary Theory

Britain suspended convertibility during the Napoleonic wars. During that period, until 1821, money in England was paper, unbacked by gold. The restoration of convertibility was followed by a stagnant period in British development, with a crisis in 1825 and a reform in 1844 called the Bank Charter Act.

This post recalls some debates in monetary theory among British political economists while these events were occurring. (I don't consider myself expert on monetary theory during the Classical period.) Table 1 shows some schools of thought in monetary theory. The term schools is traditional with respect to the currency and banking schools, but should not be interpreted too strongly for any groups in the table. These schools, unlike, say, the Physiocrats, do not have a recognized leader, followers, popularizers, etc. Rather, they are more like the Mercantilists, a diverse set of pamphleteers and politicians grouped together by later writers.

Table 1: Some "Schools" and Example Members

Years	Contending Schools
1797-1821	Bullionists Henry Thornton David Ricardo	Anti-Bullionists Robert Torrens Robert Malthus
1825-1844	Currency School Robert Torrens Samuel Jones Lloyd Mountifort Longfield	Banking School Thomas Tooke John Stuart Mill
2nd Half of the 20th Century	Quantity Theory Milton Friedman	Endogenous Money Nicholas Kaldor

In each period shown in the table, I have listed two schools. Economists in the first school in each row argued that the money supply was exogenous and that the price level varied with amount of money issued by central bank. Economists in the second school in each row argued that the money supply was endogenous, that is was not capable of being controlled by the central bank, and that it varied with demand for it. The details of these arguments varied among these and other economists.

The last row suggests that these arguments are still current. In fact, advocates of Modern Monetary Theory currently argue that the money supply is endogenous.

Card And Krueger's Research On Minimum Wages Superceded

I think of David Card and Alan Krueger's empirical demonstration that increased minimum wages do not reduce employment as having two main components:

• Natural experiments, especially one comparing and contrasting New Jersey and Pennsylvania.
• A meta-analysis of previous published research on minimum wages.

Recent researchers have replicated Card and Krueger's results for both components. And this recent research is more comprehensive and rigorous. (Since Card and Krueger's work, many economists have adopted the methods of natural experiments and meta-analysis, aside from the specific application to labor "markets".)

For natural experiments, I look to a paper by Dube and others. Here's their abstract:

"We use policy discontinuities at state borders to identify the effects of minimum wages on earnings and employment in restaurants and other low-wage sectors. Our approach generalizes the case study method by considering all local differences in minimum wage policies between 1990 and 2006. We compare all contiguous county pairs in the U.S. that straddle a state border and find no adverse employment effects. We show that traditional approaches that do not account for local economic conditions tend to produce spurious negative effects due to spatial heterogeneities in employment trends that are unrelated to minimum wage policies. Our findings are robust to allowing for long term effects of minimum wage changes." -- Andrajit Dube, T. William Lester, and Michael Reich. "Minimum Wage Effects Across State Borders: Estimates Using Contiguous Counties". Review of Economics and Statistics, V. 92, N. 4 (Nov. 2010): 945-964.

For meta-analysis, I look to some studies by Doucouliagos and others. Here's the abstract of an accessible working paper:

"Card and Krueger’s (1995a) meta-analysis of the employment effects of minimum wages challenged existing theory. Unfortunately, their meta-analysis confused publication selection with the absence of a genuine empirical effect. We apply recently developed meta-analysis methods to 64 US minimum wage studies and corroborate that Card and Krueger’s findings were nevertheless correct. The minimum wage effects literature is contaminated by publication selection bias, which we estimate to be slightly larger than the average reported minimum-wage effect. Once this publication selection is corrected, little or no evidence of a negative association between minimum wages and employment remains. --Hristos Doucouliagos and T. D. Stanley (2008). "Publication Selection Bias in Minimum-Wage Research? A Meta-Regression Analysis". Deakin University, Australia.

I don't expect orthodox economists to absorb any time soon my unoriginal point that economic theory gives no foundation for the belief that minimum wages must lead to disemployment, even when one abstracts from less than perfect competition, principal agent problems, information asymmetries, etc. After all, mainstream economists are trained in mumpsimus.

Three Routes To The Choice Of Technique

1.0 Introduction
I think the analysis of the choice of technique in a steady state is a settled question. (The meaning of Sraffa's equations in wider contexts can be debated.) One strength of the analysis of the choice of technique is the existence of several methods of analysis, all reaching the same conclusion. If one wanted to overthrow this analysis, one would need to show that one is not attacking just one such method, but all of them - or at least as many as possible. This post illustrates this strength of the analysis by presenting three such methods.

2.0 Example Technology
I need an example technology (Table 1) to use in stepping through different methods for analyzing the choice of technique. Each process requires the inputs shown to be purchased at the start of the production period (a year) for each unit of output produced and available at the end of the year. Two processes are known for producing steel, and two other processes are likewise known for producing corn. The coefficients are fairly arbitrary. In this example, to produce any net output in a steady state, all commodities - that is, both steel and corn - must be produced.

Table 1: Constant-Returns-to-Scale (CRS) Production Processes

Inputs	Industry Sector
	Steel Industry		Corn Industry
	First Steel-Producing Process	Second Steel-Producing Process	First Corn-Producing Process	Second Corn-Producing Process
Labor (Person-Yrs)	3220/3321	13930/63099	3115/3321	1
Steel (Tons)	0	0	1/2	9/20
Corn (Bushels)	1/18	2752/7011	0	0
Output	1 Ton	1 Ton	1 Bushel	1 Bushel

The analysis of the choice of technique calculates which production process would be adopted for each combination of prices and interest rates. For this technology to be compatible with a steady state, at least one process for producing steel and one process for producing corn must be adopted. A "technique" consists of one process from each of the industries in this example. Table 2 defines the four techniques, each named with a greek letter. (I think this convention of using greek letters in this context may have been introduced by Joan Robinson.)

Table 2: Techniques and Production Processes

Technique	Steel-Producing Process	Corn-Producing Process
Alpha	First	First
Beta	First	Second
Gamma	Second	First
Delta	Second	Second

A technique, in this case, is expressed by a 2-element row vector of direct labor coefficients and a square Leontief Input-Output matrix. For example, the labor coefficients, a₀^α, for the first technique are:

a₀^α = [(3220/3321) (3115/3321)]

The Leontief Input-Output matrix, A^α, for the first technique can be expressed as two columns a_.1^α and a_.2^α:

A^α = [ a_.1^α a_.2^α]

The first labor coefficient and the first column in the Leontief Input-Output matrix come from the specified production process from the steel industry for that technique:

a_.1^α = a_.1^β = [0, (1/18)]^T

The second labor coefficient and the second column in the Leontief Input-Output matrix come from the specified production process from the corn industry for that technique:

a_.2^α = a_.2^γ = [(1/2), 0]^T

I leave to the reader how to completely specify a₀^β, A^β, a₀^γ, A^γ, a₀^δ, and A^δ.

3.0 Direct Method
Heinz D. Kurz and Neri Salvadori refer to this method for analyzing the choice of technique I describe here as the "Direct Method". Before proceeding, I need to introduce some notation. Let p be a two-element row vector of prices:

p = [p₁, p₂]

where p₁ is the price of a ton steel and p₂ is price of a bushel corn. Let w be the wage, assumed to be paid at the end of the year for each person-year of labor expended during the year. Let r be the rate of interest, also called the rate of profits.

I need to introduce a column vector to represent the numeraire. Let e₂ be the second column of the 2x2 identity matrix:

e₂ = [0, 1]^T

The assumption that e₂ is the numeraire implies the following equation:

p e₂ = 1

This specification of the numeraite implies that, p₂, the price of a bushel corn is unity.

The problem is to find a pair (p, w), given the interest rate r, such that

• No process can be operated with costs less than revenues.
• For any process that is operated, the costs do not exceed the revenues.

The first condition implies the following four inequalities must hold:

p a_.1^α(1 + r) + a₀₁^α w ≥ p₁

p a_.1^γ(1 + r) + a₀₁^γ w ≥ p₁

p a_.2^α(1 + r) + a₀₂^α w ≥ p₂

p a_.2^β(1 + r) + a₀₂^β w ≥ p₂

The conjunction of the requirement that steel be produced with the second condition implies that one of the first two inequalities must be met with a strict equality. The analogous requirement for corn production implies that at least one of the last two inequalities must be met with equality.

These specifications are easily graphed (Figure 1). Given the interest rate, the first two inequalities yield upward-sloping lines in the the figure. The last two inequalities yield the downward-sloping lines. The first condition implies the solution must lie on or above all of the lines in the figure. The second condition implies that the solution must lie on

• At least one of the upward-sloping lines
• At least one of the downward-sloping lines.

The only point that satisfies these conditions is graphed. It lies on the upward-sloping line corresponding to the first steel-producing process and the downward-sloping line corresponding to the second corn-producing process. Thus, this analysis shows that the beta technique is cost-minimizing at an interest rate of 100%. The solution wage and price of steel can be read off the figure.

Figure 1: Direct Method Illustrated At r = 100%

The direct method is easily generalized to any finite number of techniques. Each additional production process results in an additional line in the figure, upward-sloping for the steel industry and downward-sloping for the corn industry. The method also generalizes for any finite number of commodities. Each additional commodity results in the introduction of another dimension to the figure. Although the figure quickly becomes unvisualizable, the mathematics generalizes.

4.0 Indirect Method
The indirect method generalizes to cases in which an uncountably infinite number of techniques are available. It is based on constructing the wage-rate of profits frontier as the outer envelope of the wage-rate of profits curve for each technique (Figure 2). I illustrate how to construct the wage-rate of profits curve for the Alpha technique.

Figure 2: Indirect Method Illustrated

The condition that the same rate of profits be earned for each process comprising a technique yields a system of two equations:

p A^α(1 + r) + a₀^α w = p

One also has the equation setting the price of the numeraire to unity:

p e₂ = 1

For a given interest rate r, the above is a linear system of three equations for three variables (p₁, p₂, and w). One can solve the system to express each of these three variables as a function of the interest rate. The wage, for example, can be found as:

w = 1/(a₀^α [ I - (1 + r)A^α]^-1e₂)

One knows, from a theorem due to Perron and Frobenius, that the inverse exists between an interest rate of zero and some maximum interest rate.

Figure 2 shows the wage-rate of profits curves for each of the four techniques. The cost-minimizing technique at each rate of interest is the one with the highest wage. Points at which the rate-rate of profits curves for two or more techniques interesect on the outer frontier are known as switch points. The two switch points are shown in the example. The Gamma technique is cost-minimizing for a very low interest rate. For a somewhat larger interest rate, the Delta technique is cost-minimizing. Finally, the Beta technique is cost minimizing for larger interest rates. My exposition illustrates that the direct and indirect methods give the same conclusion. For example, the wage-rate of profits frontier shows that the Beta technique is cost-minimizing for an interest rate of 100%.

5.0 Cost Minimization Algorithm
This method I take from J. E. Woods. He provides an algorithm for finding the cost-minimizing technique(s), given the interest rate.

1. Pick an initial technique. (For illustration, I start with the Beta technique in the example.)
2. Solve the equations specifying the wage-rate of profits curve for the selected technique. So you now have a price vector p and the wage w.
3. Using p and w, calculate the cost of producing a ton steel with each of the known production processes (Figure 3).
4. If the steel-producing process in the selected technique is cheapest, go to Step 6. Otherwise go to Step 5. (In the example, one would go to Step 5 for low interest rates and to Step 5 for higher interest rates.
5. Replace the steel-producing process in the technique analysed in Step 2 with the cheapest steel-producing process identified in Step 4. Solve the equations specifying the wage-rate of profits curve for the newly selected technique. Use the resulting p and w in Step 6. (In the example, one would calculate the wage-rate of profits curve for the Delta technique for a sufficiently low interest rate.)
6. Using the specified p and w, calculate the cost of producing a bushel corn with each of the known production processes (Figure 4).
7. If cost of producing corn could be found in Step 6 for the technique selected in Step 2 and the corn-producing process in that technique is cheapest, then stop. You have identified the cost-minimizing technique. Otherwise, replace the corn-producing process in the technique analyzed in Step 6 with the cheapest corn-producing process identified in Step 6. (In the example, the algorithm would terminate in one-pass for a sufficiently high interest rate, with the Beta technique identified as the cost-minimizing technique.)
8. Go to Step 2.

Figure 3: Costs of Producing Steel with Prices for the Beta Technique

Figure 4: Costs of Producing Corn with Prices for the Beta Technique

Figures 3 and 4 suggest that for a sufficiently low interest rate, the technique consisting of the second steel-producing process and the first corn-producing process, that is, the Gamma technique, is cost-minimizing. For a somewhat higher interest rate, the technique consisting of the second steel-producing process and the second corn-producing process, that is, the Delta technique, seems to be cost-minimizing. And, as noted above, the algorithm terminates with the Beta technique identified as the cost-minimizing technique at an even higher interest rate. In other words, the graphs suggest that the above algorithm converges to the same solution as the indirect method.

6.0 Conclusions
I have not exhausted the methods available for analyzing the choice of technique. For example, I have not formulated any Linear Programs above. Nor have I presented the diagram in my 2005 Manchester School paper. Furthermore, I have glossed over many interesting mathematical questions, such as proving the existence of solutions and proving that all methods give the same result. But this post is already too long.

References

• Heinz D. Kurz and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis. Cambridge University Press.
• J. E. Woods (1990) The Production of Commodities: An Introduction to Sraffa, Humanities Press.

Great Female Economists

This is a selection. I always exempt those alive in making such judgements.

• Jane Marcet
• Harriet Martineau
• Rosa Luxemburg
• Mary Paley Marshall
• Beatrice Webb
• Charlotte Perkins Gilman
• Elizabeth Boody Schumpeter
• Joan Robinson
• Krishna Bharadwaj

Lost Knowledge In Economics

Economists' concerns can be expected to change as the world changes. In a serious scholarly discipline, however, such changes in emphasis should be theorized and argued. They should not be just a matter of fads and the following of changes in the political environment. I am not sure economics meets this standard. Anyways, here are examples I came up with today for exploring this question:

• Managerial theories of the firm (as developed by, e.g., Robin Marris)
• Markup pricing
• Sidney Chapman's theory of the length of the working day (as opposed to the textbook analysis of tradeoffs between leisure and commodities) (Derobert (2001), (Spencer 2003), and (Walker 2007)).
• Co-operatives (Kalmi 2007).
• Sidney and Beatrice Webb's analysis of labor markets (Kaufman 2008).

References

• L. Derobert. "On the Genesis of the Canonical Labor Supply Model". Journal of the History of Economic Thought, V. 23, N. 2 (2001): 197-215.
• Panu Kalmi. "The Disappearance of Cooperatives from Economics Textbooks". Cambridge Journal of Economics, V. 31 (2007): 625-647.
• Bruce Kaufman. "How a Minimum Wage Can Improve Efficiency Even in Competitive Labor Markets: The Webbs and the Social Cost of Labor". Andrew Young School of Policy Studies Research Paper Series, Working Paper 08-16 (July 2008).
• D. A. Spencer. "The Labor-Less Labor Supply Model in the Era Before Philip Wicksteed". Journal of the History of Economic Thought, V. 25, N. 4 (2003): 505-513.
• Tom Walker. "Why Economists Dislike a Lump of Labor". Review of Social Economy, V. 65, N. 3 (2007).

Coase Theorem Not About Markets

Mainstream economists tend to think of the "laws of demand and supply", for example, as applying to all of human history and independent of institutional structure¹. Geoffrey Hodgson has noted the difficulty of finding a definition of "markets" in mainstream economics.

To me, a market must allow for repetitive purchases and sales of a commodity where participants have information on, for example, prices from previous purchases and sales. A contract drawn up between two organizations to last for several years is a bilateral negotiation, not a market transaction, when neither organization is simultaneous to draw up parallel contracts with competing organizations².

One application of this idea is to labor unions. Maybe the difficulties mainstream economists have with defining "markets" is connected with their backward notions on labor unions, backward notions that others have recently pointed out³.

I was inspired to write this post by Hahnel and Sheeran's article. An train engine with tracks through a farmer's field is an example of application of the Coase Theorem. If vegetation isn't kept a certain distance from the rails, supposedly sparks from the train wheels are likely to start a fire and burn the crops. Do the farmers have a well-defined property right not to have sparks ejected on their fields? Or do trains have a well-defined right to emit sparks? Depending on the answers to these questions, the legal liability for maintaining the track and paying for any resulting fires is different. But, according to the Coase "theorem", if property rights are well-defined and no transaction costs exist, the farmer and the railroad will negotiate an efficient price for allowing the trains to emit sparks. Some conclude that it is government's job to ensure property rights are well-defined and perhaps lower transaction costs. Then the market will come to an efficient solution to the problem of externalities, however property rights are allocated.

Among other criticisms, Hahnel and Sheenan point out that the conclusion is a non-sequitur. This is not an example of a market. I think their treatment of information asymmetries is a formalization of a point I first read from Michael Albert. The Coase set-up will encourage those with property rights to act as bullies, to threaten obnoxious behavior they wouldn't otherwise do, so as to extort payments from their victims.

¹ An interesting experiment would be to count the number of occurrences of the word "capitalism" in, say, the American Economic Review or the Journal of Political Economy in the last decade and contrast those counts with the same counts in, say, the Cambridge Journal of Economics, the Review of Political Economy, or the Review of Radical Political Economics.

² Even if you object to this usage of "market", you should see that the game theoretic models appropriate for a bilateral negotiation under various assumptions about available information is not the typical model of demand and supply schedules.

³ Haven't the criticized economists heard of the theory of the second best? I thought that the case of a large employer and a labor union was a canonical example.

References

• Michael Albert. "Nobel Nerve", Z Magazine (Nov. 1991).
• Robin Hahnel and Kristen A. Sheeran. "Misinterpreting the Coase Theorem" Journal of Economic Issues. V 43, N. 1 (March 2009): 215-238.
• Geoffrey M. Hodgson Economics and Institutions: A Manifesto for a Modern Institutionalist Economists, Basil Blackwell (1989).
• R. G. Lipsey and Kevin Lancaster. "The General Theory of the Second Best", Review of Economic Studies, V. 24, N. 1 (1956-1957): 11-32.

Geoff Harcourt In Audio And Video Formats

As I understand it, Geoff Harcourt is now living in Australia, after having recently moved home from Cambridge, England. While in Cambridge, he wrote The Structure of Post-Keynesian Economics: The Core Contributions of the Pioneers and, especially, Joan Robinson, the latter with Prue Kerr.

While there, Harcourt contributed his time to a few interviews and lectures. I have previously mentioned his November 2009 lecture to the Post Keynesian Study Group on the legacy of Joan Robinson. He also gave a May 2010 lecture, to the same forum, on the crisis in mainstream economics. Finally, one can find a two-interview on YouTube.

Figure 1: First Part of Geoff Harcourt Interview

Figure 2: Second Part of Geoff Harcourt Interview

H/T Daniel Kuehn for links to the You Tube video.

Letter To The Editor

Mike Cushman, the secretary of the London School of Economics University and Colleges Union (LSE UCU) writes to the Guardian:

"Philip Inman (Scene of the crime, G2, 18 February) describes the complicity of economics academics in the crash. They were responsible for providing an intellectual gloss for reckless and maybe criminal behaviour. ...They circulated their legitimising patina in the house journals of their club: the leading economics journals beloved of the US and UK business schools.

These journals, a key part of the conspiracy, continue to cast their shadow. It is almost impossible for economists to get employed or promoted in leading economics and management departments like LSE without publishing in these "A-grade" journals. ...It is the same self-referential circulation of authority that underpinned the collateralised debt obligations and other key instruments of the credit bubble. Essential research income is allocated through the Research Excellence Framework by reference to success in those same publications and adjudicated by those who edit and publish in those journals.

Scholars who will not act as shills for the banks and reinforce the Panglossian orthodoxies, and instead promote critical analyses, are rarely welcome in these journals and thus increasingly not welcome in universities... The REF (Research Exalting Finance) is a dangerous, flawed mechanism, at least in economics and management: an ideological straitjacket disguised as a fair and unbiased assessment." -- Mike Cushman

Mr. Cushman's claims are backed up by academic research on the history and sociology of economics. If I recall correctly, Geoffrey M. Hodgson and Harry Rothman¹, for example, demonstrate the self-referential and closed nature of the supposedly "leading" journals in economics.Frederick Lee² adds to the documentation of the unwillingness of mainstream economists to cite non-mainstream economists with empirically validated analyses of the British Research Excellence Framework (REF). In my reading of Lee, the REF is leading to less excellence in British economics, at least if your measure is an ability to understand actually existing capitalist economies.

¹ Geoffrey M. Hodgson and Harry Rothman. "The Editors and Authors of Economics Journals: A Case of Institutional Oligopoly?". Economic Journal, V. 109, Iss. 453 (Feb. 1999): pp. 165-186.

² Frederic Lee. A History of Heterodox Economics: Challenging the Mainstream in the Twentieth Century.

People I've Never Heard Of, Am Barely Aware Of, And Thought I Knew

News coverage of the Egyptian revolution introduced me to Gene Sharp, who I have never heard of before. Apparently he is at the Albert Einstein Institution, and protesters are taking recipes from his book, From Dictatorship to Democracy.

Nonviolent revolutions these days are somewhat anarchist¹. I am not well read on contemporary anarchists. I found out existence of Colin Ward when he died. I am vaguely aware of Murray Bookchin. I have had a copy of Bill Devall and George Sessions' book, Deep Ecology: Living as if Nature Mattered on my bookshelf for a decade. Going back further, I like Hannah Arendt's On Revolution and Crises of the Republic and Paul Goodman's
Growing Up Absurd.

I have been much influenced, of course, in my views on economics by Joan Robinson. I don't know if I've read these before, but I find her Tanner lectures, "The Arms Race," are available online². In fact, almost all of the Tanner lecture series can be downloaded. There's just too much to read there, but I will pick out Albert Hirschman's, since I have blogged before on his book drawing from those lectures.

Notes:

¹A crossword puzzle clue passed on by Will Shortz: "Disordered sort?" The answer is, "Anarchist."

² I was motivated to look up Robinson's Tanner lecture by listening to Geoff Harcourt's November 2009 presentation on Robinson to the Post Keynesian Study Group.

Stephen Smale Presciently On Global Financial Crisis?

I have argued before that weaknesses in mainstream economics exposed by our current macro-economic problems have been known for decades. I here note another example.

Stephen Smale is a Fields medal-winning mathematician who has advanced our understanding of chaotic dynamical systems. Smale has also contributed to mathematical economics. He wrote the following in 1976:

"A criticism commonly made of economic theory is its failure to make predictions of crises in the country or anticipate correctly unemployment or inflation. One must be cautious in the social sciences about looking towards physics for answers. However, some comparisons with the physical sciences seem profitable in connection with the above criticism. In those sciences, where theory itself is in a far more advanced state, limitations can be seen in a similar way. For example a given individual human body functions according to physical principles; however no physical scientist would predict a heart attack. The physical theory gives understanding of aspects of what goes on in the human body only under very idealized conditions. The physical theories eventually play some role in the education of medical doctors, who can then say some things, some times about a patient's susceptibility to a heart attack, preventive measures, and cures.

The economy of the world or even a nation is a very complex phenomenon, like a human body, involving a number of factors, both economic and political. It is no more reasonable to expect economic theorists to predict a nation's economic future than for a theoretical scientist to predict the future health of an individual...

...I would like to give some reasons why I feel equilibrium theory is far from satisfactory. For one thing the theory has not successfully confronted the question, 'How is equilibrium reached?' Dynamic considerations would seem necessary to resolve this problem. Another is the reliance of the theory on long range optimization.

In the main model of equilibrium theory, say as presented in Gerard Debreu's Theory of Value, economic agents make one life-long decision, optimizing some value. With future dating of commodities, time has almost an artificial role." -- Stephen Smale. "Dynamics in General Equilibrium Theory." American Economic Review V. 66, N. 2 (1976): pp. 288-294.

Celebrity Economists?

When I look at many economists who have won the "Nobel" prize, I often wonder, where is the empirical evidence for their theories? Are they making empirical claims that have passed potentially falsifying tests? It seems to me that both Solow and Lucas, for example, won prizes more on the basis that their work is frequently cited than for expanding our understanding of actually existing economies. Perhaps some, such as Leontief or Stone, won for work providing an accounting framework that is useful in organizing empirical data.

Hence, my title: a celebrity has been defined as somebody who is famous for being famous.

This is a topical post.I was inspired by this list of "top twenty" articles in the American Economic Review, selected by six senior economists.

(While I was writing this post, Merijn Knibbe posted similar thoughts.)

I append the article list for reference:

• Alchian and Demsetz (1972). "Production, Information Costs and Economic Organization".
• Arrow (1963). "Uncertainty and the Welfare Economics of Medical Care".
• Cobb and Douglas (1928). "A Theory of Production".
• Deaton and Muellbauer (1980). "An Almost Ideal Demand System".
• Diamond (1965). "National Debt in a Neoclassical Growth Model.
• Diamond and Mirrlees (1971). "Optimal Taxation and Public Production" (two parts).
• Dixit and Stiglitz (1977). "Monopolistic Competition and Optimum Product Diversity".
• Friedman (1968). "The Role of Monetary Policy".
• Grossman and Stiglitz (1980). "On the Impossibility of Informationally Efficient Markets".
• Harris and Todaro (1970). "Migration, Unemployment and Development: A Two-Sector Analysis.
• Hayek (1945). "The Use of Knowledge in Society".
• Jorgenson (1963). "Capital Theory and Investment Behaviour".
• Krueger (1974). "The Political Economy of the Rent-Seeking Society"
• Krugman (1980). "Scale Economies, Product Differentiation, and the Pattern of Trade.
• Kuznets (1955). "Economic Growth and Income Inequality".
• Lucas (1973). "Some International Evidence on Output-Inflation Tradeoffs".
• Modigliani and Miller (1958). "The Cost of Capital, Corporation Finance and the Theory of Investment".
• Mundell (1961). "A Theory of Optimum Currency Areas".
• Ross (1973). "The Economic Theory of Agency: The Principal's Problem".
• Shiller (1981). "Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends?"

Elsewhere

• Russell Jacoby pans Erik Olin Wright's book Envisioning Real Utopias. I don't know much about Jacoby. I find his review encourages me not to read Wright. It would help, however, if Jacoby didn't cite Wright's use of the word "interstitial" as an example of boring cant, while praising Veblen, who also used the word.
• Victoria Chick and Ann Pettifor write about the 75th anniversary, on February 3 of Keynes' General Theory.
• Eric Schliesser, a philosopher, notes Greg Mankiw's refusal to acknowledge the existence of literature on his points, a topic I've mentioned before.

Daron Acemoglu

What do you think of Daron Acemoglu?

Since he is a mainstream economist at MIT, I should be inclined to take a critical stance to be consistent with my themes. Acemoglu has written so many papers that I do not feel that I can have a comprehensive view. Maybe I should read up on the summary that must have accompanied his 2005 John Bates Clark medal.

Acemoglu writes on political economy and political science topics I think of interest - for example, power, coercion, social networks, innovation, governance, and economic development. The conclusions he and his colleagues reach are not necessarily a whitewash of capitalism. I've been trying to read, for example, Glenn Ellison and Alexander Wolitzky's paper, "A Search Cost Model of Obfuscation", in which more-or-less competitive firms deliberately put clauses hard to understand in contracts, thereby making it difficult to compare products and to obtain, for example, payouts on warranties, insurance, etc. Most of the papers I've read by Acemoglu and his colleages seem to tell just-so stories with game theory, a branch of mathematics I think can be fascinating. Empirical accounts can be used to illustrate the theories, but I wonder whether the theories are passing potentially falsifying tests. As an exemplar, I take Acemoglu, Egorov, and Sonin's accounts of incidents in the history of the Soviet Politburo in their 2008 Review of Economic Studies paper, "Coalition Formation in Non-Democracies".

Entrepreneurial Profits In A Classical Model

I came upon this passage recently:

"Thus, in the short run, the entrepreneurs introducing new techniques would reap supernormal profits. [Suppose] there is continuous technical change in the system, which Marx assumes to be in the nature of capitalist competition and a requirement for the maintenance of the 'reserve army of labour', then there arises a permanent income category that cannot be accounted for by labour-time accounting... Though Pareto does not clearly separate such entrepreneurial income from returns to capital in general, or from the notion of productivity of capital, it is plain that he foreshadows the idea that was later developed by Schumpeter...as an explanation for positive profits in a capitalist economy." -- Ajit Sinha (Theories of Value from Adam Smith to Piero Sraffa, Routledge (2010) pp. 214-215.)

This suggests to me a puzzle: can I create a model in which entrepreneurs make profits even though the workers are paid what would be the entire net output if the technology in use during the period in which they are paid were to persist unchanged? This post demonstrates that Sinha's comment is well-founded.

2.0 A Model
2.1 The Technology
Consider a simple economy in which a single commodity, corn, is produced each year. Workers produce the annual output from inputs of (seed) corn and their labor. The technology is defined by:

• a₀(t): the labor (in person-years) needed as input per bushel corn produced in the tth year.
• a₁(t): the (seed) corn needed as input per bushel corn produced in the tth year.

The coefficients of production evolve as in the following two equations:

a₀(t) = e^-λ₀t

a₁(t) = c e^-λ₁t

where the positive constants λ₀ and λ₁ are the rate of decrease in the labor and (seed) corn inputs, respectively. I impose the condition that the quantity harvested must exceed the quantity of seed corn planted in the spring:

0 < c < 1

2.2 Quantity Flows
Let Q(t) be the bushels of corn produced during the tth year and available after the harvest at the end of year. Assume:

Q(t) = e^λ₀t

The labor employed each year is a₀(t)Q(t), that is, one person-year.The seed corn, K(t), required for planting at the start of the tth year is:

K(t) = a₁(t)Q(t) = c e^{-(λ₁-λ₀)t}

The seed corn decreases each year if and only if the rate of decrease of the labor input per bushel corn produced exceeds the rate of decrease of the seed corn input per bushel corn produced:

λ₁ < λ₀

The surplus corn harvest, Y(t), over the seed corn planted at the start of the year is:

Y(t) = Q(t) - K(t) = e^λ₀t(1 - c e^-λ₁t)

2.3 Prices, Wages, And Distribution
Assume the labor hired during a given year is paid at the end of the year out of the harvest. The Sraffian price equations for this model are:

a₁(t) + a₁(t) w(t) = 1

where w(t) is the wage per person year, and I have taken a bushel of corn as the numeraire. It is easy to solve this equation to find that the wage is the net output produced by the person-year employed:

w(t) = Y(t)

If the seed corn required for a constant labor force declines year-by-year, this model provides a source of entrepreneurial profit:

π(t) = K(t + 1) - K(t) = c e^{-(λ₁-λ₀)t}[e^{(λ₀-λ₁)} - 1]

What happens if the condition on technological progress is not met? I haven’t worked out this case, but two possibilities seem to me to arise. In the first case, workers cannot consume the entire surplus each year. Perhaps, the capitalists obtain some accounting profits on their capital and they save those profits as additions to the seed corn each year. In the second case, the number of hours worked decline.

No Crisis In Mainstream Economics...

...Instead, the situation is chronic. The long-festering situation of economics is seen in the constant literature on the "crisis" in economics, going back for maybe half a century.

The book The Crisis in Economic Theory (1981) is a timely example. It was edited by Daniel Bell and Irving Kristol, and Daniel Bell's obituary was published in the New York Times today. (See also this Crooked Timber post.) The editors wrote the introduction, and each wrote a chapter. Other contributions include Frank Hahn on general equilibrium theory, Israel Kirzner on the Austrian school, Paul Davidson on Post Keynesianism, and Edward Nell on a Sraffa-influenced interpretation of Marxist economics.

Blah, Blah, Jevon's Paradox, Blah, Blah, Backfire

Figure 1: The Carrier Dome, Named After A Manufacturer Of A/C Equipment No Longer In Syracuse, NY

The Jevon's paradox arises when increased efficiency in the use of a resource results in greater overall use of that resource. This is a severe example of "rebound", where the effects of increased efficiency are lessened by increased use. Jevon's wrote about Coal.

Some may have noticed David Owen's recent article in The New Yorker focused on air conditioning (A/C). By synchronicity, Computer, the flagship journal of the Institute of Electrical and Electronic Engineers (IEEE) Computer Society, also published an article on rebound about the same time. Tomlinson, Sliberman, and White recommend mindfulness in the pursuit of energy efficiency in Information Technology and reference a report from an organization in the United Kingdom. (I'm not as dismissive of the Jevon's paradox as my title may suggests; I just wanted a template to could apply to both articles.)

The New Yorker published three letters on their article. I select Amory Lovins' letter for not just because he is a well-known advocate of increased energy efficiency. He points out that much of the increased use of A/C that David Owens describes is due to increased wealth, not rebound. He uses the example of oil to assert that increases in efficiency could drop energy use in absolute terms, even with economic growth. Apparently, between 1977 and 1985, the United States Gross Domestic Product rose 27 percent and oil use fell 17 per cent.

For utility-sponsored research in the United States, I look to the Electric Power Research Institute (EPRI). I don't know if they have a take on the Jevon's paradox. I think Leontief Input-Output analysis and Luigi Pasinetti's structural economic dynamics provide empirical tools for investigating the question.

References

• Amory B. Lovins (2011) "Letter", The New Yorker (17 Jan.): p. 3.
• David Owen (2010). "The Efficiency Dilemma", The New Yorker (20 & 27 Dec.): pp. 78-85.
• Steve Sorrell (2007). The Rebound Effect: An Assessment of the Evidence for Economy-Wide Energy Savings From Improved Energy Efficiency, UK Energy Research Center.
• Bill Tomlinson, M. Six Sliberman, and Jim White (2011). "Can More Efficient IT Be Worse for the Environment?", Computer, V. 44, Iss. 1 (Jan.): pp. 87-89.

Krugman On The Importance Of Austrian Business Cycle Theory

Paul Krugman writes:

"Someone, I don’t know who at this point, sent me to this post by Robert Murphy, which is the best exposition I’ve seen yet of the Austrian view that’s sweeping the GOP..."

I think the Republicans are not as coherent as Krugman makes them out to be. They are even less coherent than Austrian Business Cycle Theory.

I don't know that I will pursue trying to publish my rebuttal of Austrian Business Cycle Theory. Some have previously brought up my working papers in discussions of Krugman's blog and column. So far, I have not seen my name mentioned in discussions of this Krugman blog post.

ASSA, Not AEA In Denver?

Denver In Some Other Month

The proceedings of the recent American Economic Association annual conference are online. Preliminary versions of some of the papers are available for download.

I have trouble getting a sense of what mainstream economists are about from such a massive list. Doubtless I would find some of these papers of interest, despite the forbidding technical titles. I regret that downloads are not available for panel discussions (for example, "What's Wrong (and Right) with Economics? Implications of the Financial Crisis", "Lessons for Economics from the Great Recession", "Grand Challenges for Social Science...", "History, Crisis, Institutions and Economic Analysis", and "The Ethics of Professional Economic Practice"). (Actually, doing a search on the word "Panel" does cut down the list of titles to a manageable size that may give a feel to the direction of the profession.)

I also look in this list for economists of schools of thought and fields in which I'm interested. The Union of Radical Political Economics has only one session co-sponsored with the AEA. Steve Keen provides videos and download links. The History of Economics Society also has one co-sponsored session. As far as I can see, the Association for Evolutionary Economics (AFEE) and the International Association for Feminist Economics have no sessions. Brad DeLong's presentation is the only one with the word "Keynes" or "Keynesian" in the title. This sample should not lead one to conclude that heterodox economists were not represented in Denver, for they appear in the program of the Allied Social Science Associations. Explicitly identified heterodox economists just seem to be banished from the AEA, to the AEA's shame.

And The Life Of Man, Solitary, Poore, Nasty, Brutish, And Short

I am hostile to the notion of logically deriving an ideal society from first principles. Ideal norms can only be understood by us humans in a context that will evolve over time, not from some timeless, interest-free view from nowhere. Humans, in arguing about society, invariably base themselves on some partial perspective or faction. And to understand how to apply some principle articulated from some interest, one will have to draw on empirical results. (Is this an institutionalist, pragmatic view?)

Perhaps, nevertheless, some (not necessarily inconsistent) norms can be stated in keeping with these ideas. I suggest the following:

• Human society should be able to reproduce itself (Karl Marx).
• Unnecessary suffering should be alleviated (Karl Popper).
• Everybody should have the freedom to develop their capabilities to the best of their abilities (Aristotle, Marx).

Other norms don't seem to be compatible with my views on how to think about political philosophy. "People should be able to keep what they make" is a meaningless norm, maybe common among current intellectually and ethically impoverished mainstream economists.

Robert Nozick, as I understand him, begs a definition of natural rights. And then he argues for the following principles on that basis:

• A person who acquires a holding in accordance with the principle of justice in acquisition is entitled to that holding.
• A person who acquires a holding in accordance with the principle of justice in transfer, from someone else entitled to the holding, is entitled to the holding.
• Unjust acquisitions or transfer should be rectified

He ends up arguing for a more-or-less night-watchman state.

Perhaps these sorry days are ripe for an immanent critique of the idea of equality of opportunity.

I did not manage to mention above the Austrian-school economist Israel Kirzner's defense of returns to entrepeneurship with what he calls a "finders keepers" ethic. I have not read John Rawls.

Both Sides Now

Eric Schoenberg, of Columbia Business School, has a very confused response to the usual idiocy from Greg Mankiw. Schoenberg quotes Mankiw as saying

"under a standard set of assumptions... the factors of production [i.e., workers] are paid the value of their marginal product... One might easily conclude that, under these idealized conditions, each person receives his just deserts."

Schoenberg thinks the above is coherent. He merely questions whether the standard assumptions apply in our economy.

But marginal productivity is not a theory of the distribution of income, as I have demonstrated. It is a theory of the choice of technique. Income distribution can be anywhere on the factor price frontier and all agents will be receiving the value of the marginal product of the factors of production that they own. (I don't know if anybody in the comments at the Huffington Post points out that Mankiw does not know what he is talking about, even given all of his assumptions.)

By the way, Bill Mitchell has a recent post that wanders into my theme.

Canonical Statements Of Current Mainstream Price Theory?

I find puzzling where contemporary mainstream economists would point for good statements of a theory to explain prices in, say, the United States economy. I can think of a couple of possibilities.

The first would be General Equilibrium models in which a complete set of spot and future markets exist and in which goods are distinguished by location, date of delivery, and contingent events. Canonical statements of such a theory include:

• Gerard Debreu (1959). Theory of Value: An Axiomatic Analysis of Economic Equilbrium, Cowles Foundation Monograph.
• Kenneth J. Arrow and Frank Hahn (1971). General Competitive Analysis, Holden-Day.

But is this the current theory? Even though more textbooks have been written, the references would seem old to most young economists. The Sonnenschein-Mantel-Debreu results show that dynamic equilibrium paths are not limited by the theory. The theory does not allow for the existence of money to have any effect. Since the quantities of initial endowments are givens of the theory and any groping out of equilibrium, particularly with production going on, would change the data defining the equilibria, any time to reach equilibrium is too long. I think many mainstream economists would tell me General Equilibrium theory was abandoned in the 1980s.

Another possibility is models of temporary equilibrium. I look at the following as canonical statements of this theory

• J. R. Hicks (1946). Value and Capital: An Inquiry into Some Fundamental Principles of Economic Theory, 2nd edition, Oxford University Press.
• J. M. Grandmont (1977). "Temporary General Equilibrium Theory", Econometrica, V. 45, N. 3 (Apr.): pp. 535-572.

In this theory, only spot markets and maybe future markets for the numeraire commodity clear in equilibrium. The plans of different agents for future activities are not brought into agreement in equilibrium. Maybe this approach is related to Samuelson's model of overlapping generations. In addition to all the problems of General Equilibrium Theory, this approach has the difficulty of modeling how expectations alter, something that hardly seems observable or easy to model in a mechanical fashion.

Maybe game theory is the foundation of contemporary mainstream price theory. But cannot a game be found to rationalize almost any observed behavior? Is it not more a bag of tricks than a theory? Nevertheless, I have heard mainstream economists say good things about the following text:

• David M. Kreps (1990). A Course in Microeconomic Theory, Princeton University Press.

As I understand it, the dominant introductory graduate textbooks in mainstream microeconomics remain:

• Andreu Mas Colell, Michael D. Whinston, and Jerry R. Green (1995). Microeconomic Theory, Oxford University Press.
• Hal R. Varian (1992). Microeconomic Analysis, 3rd edition, W. W. Norton.

When I have perused these, I have found them to be more a collection of mathematics than a clear presentation of price theories. And I have found them very unclear on why the student should accept anything in them as applicable to actually existing capitalism.

Increase In The Feasibility Of Economic Planning

Mathematical programming is a key technique for economic planning. And we can solve linear programs much better now:

"Even more remarkable - and even less widely understood - is that in many areas, performance gains due to improvements in algorithms have vastly exceeded even the dramatic performance gains due to increased processor speed.

The algorithms that we use today for speech recognition, for natural language translation, for chess playing, for logistics planning, have evolved remarkably in the past decade. It's difficult to quantify the improvement, though, because it is as much in the realm of quality as of execution time.

In the field of numerical algorithms, however, the improvement can be quantified. Here is just one example, provided by Professor Martin Gröschel of Konrad-Zuse-Zentrum für Informationstechnik Berlin. Grötschel, an expert in optimization, observes that a benchmark production planning model solved using linear programming would have taken 82 years to solve in 1988, using the computers and the linear programming algorithms of the day. Fifteen years later - in 2003 - this same model could be solved in roughly 1 minute, an improvement by a factor of roughly 43 million. Of this, a factor of roughly 1,000 was due to increased processor speed, whereas a factor of roughly 43,000 was due to improvements in algorithms! Grötschel also cites an algorithmic improvement of roughly 30,000 for mixed integer programming between 1991 and 2008.

The design and analysis of algorithms, and the study of the inherent computational complexity of problems, are fundamental subfields of computer science." -- Report to the President and Congress - Designing a Digital Future: Federally Funded Research and Development in Networking and Information Technology, Executive Office of the President, President's Council of Advisors on Science and Technology (December 2010)

I don't know how such speedup was accomplished. I assume it cannot be merely a tradeoff between Dantzig's simplex algorithm and interior point methods (such as Karmarkar's algorithm). The simplex algorithm, for example, has never struck me, from what I recall, as naturally parallelizable. But parts of it can be done in parallel, I think. I think of choosing a pivot element, multiplying a vector by a scalar, and taking the inner product of two vectors as parallelizable operations. I think these improvements must have been accomplished by customizing an implementation with a well defined Application Programming Interface for a specific architecture.

(H/T: Noam Nisan)

Update: I've been reading Robert E. Bixby's "Solving Real-World Linear Programs: A Decade and More of Progress" (Journal of Operations Research, V. 50, Issue 1 (2002)). Apparently speedups were accomplished by algorithm improvements such as matrix operations that exploit the sparcity of the matrices, removing redundant constraints, aggregating decision variables under specified conditions, and many improvements I do not understand. The simplex algorithm, the dual simplex algorithm, and interior point methods all remain competitive on different problems. Bixby considers example problems with millions of decision variables and constraints. I think a couple of more orders of magnitude of improvements can be achieved with parallelization. Maybe somebody has tried that since Bixby's publication.