If The Workers Were Able To Live On Air

"In so far as the development of productivity reduces the paid portion of the labour applied, it increases the surplus-value by lifting its rate; but in so far as it reduces the total quantity of labour applied by a given capital, it reduces the number by which the rate of surplus-value has to be multiplied in order to arrive at its mass. Two workers working for 12 hours a day could not supply the same surplus-value as 24 workers each working 2 hours, even if they were able to live on air and hence scarcely needed to work at all for themselves. In this connection, therefore, the compensation for the reduced number of workers provided by a rise in the level of exploitation of labour has certain limits that cannot be overstepped..." -- Karl Marx, Capital, Vol. 3, Part 3, Chap. 15, Sect. 2

Introduction
A maximum rate of profits arises in a model of the production of commodities by means of commodities. This maximum rate of profits is an upper limit on the rate of profits in any sublunary capitalist economy, where the workers produce commodities to consume and thereby reproduce their labor power.

This maximum rate of profits would be easily seen if the economy were a giant farm producing one commodity, corn, from inputs of labor and seed corn. The surplus would be the difference between harvested corn and the quantity of seed corn which needs to be set aside to continue production next year. The ratio of this surplus to the quantity of seed corn is the maximum rate of profits. The maximum rate of profits cannot be achieved because of the need to pay wages to the workers eats into this surplus.

Some of the simple lessons of the corn economy generalize to actual more-or-less capitalist economies, such as in the United States of America (USA). One can use the mathematics of eigenvalues and eigenvectors to set out the theory in this case.

2.0 The Standard System
Consider an economy in which each of n commodities are produced from labor and inputs of those n commodities. Let a_{0, j} be the person-years of labor used in producing one unit of the jth commodity. Let a_{i, j} be the physical units of the ith commodity used in producing one unit of the jth commodity. The direct labor coefficients are elements of the n-element row vector a₀. The remaining input-output coefficients are the entries in the nxn Leontief input-output matrix A, which is assumed to satisfy the Hawkins-Simon condition.

This data determines Sraffa's standard system, in which the gross output, the net output, and capital goods have specific properties. Let q* be an n-element column vector denoting the gross quantities output in each industry, that is to say, the gross output in the standard system. The column vector A q* represents the physical quantities of capital goods needed to produce the gross output in the standard system. Let y* be an n-element column vector denoting the net quantities output in each industry in the standard commodity. The net output is available to be divided up between wages and profits after replacing the capital goods needed to reproduce the gross output. Net output and gross output, in any proportions, are related as follows:

y* = q* - A q* = (I - A) q*

In the standard system, the ratio between gross output and the quantity of capital goods needed to produce the gross output is invariant among commodities:

q* = (1 + R) A q*

Or:

A q* = [1/(1 + R)] q*

As a matter of fact, [1/(1 + R)] is the maximum eigenvalue of A. The standard system is scaled such that the amount of labor employed in the standard system is unity:

a₀ q* = a₀ (I - A)^-1 y* = 1

y* is the standard commodity.

One chooses the maximum eigenvalue to ensure, under the Hawkins-Simon condition, the existence of a standard commodity in which all components are non-negative and at least some components are strictly positive. The commodities which enter the standard commodities are called "basic". They enter directly or indirectly into the production of all commodities. Those commodities with zero entries in the standard commodity are called "non-basic". Either non-basic commodities do not enter into the production of any other commodity. Or they enter into the production only of non-basic commodities. For each non-basic commodity, there exist some commodity such that the non-basic commodity does not enter, either directly or indirectly, into the production of that commodity.

To explicate the concept of a commodity entering indirectly into the production of another commodity, consider the output of the Motor Vehicles, Bodies And Trailers, And Parts industry, one of the 65 industries in the 2005 Use Table for the USA available from the Bureau of Economic Analysis (BEA). 0.18 units of the output of the Primary Metals industry enter (directly) into the production of each unit produced by the Motor Vehicles, etc. industry. (A quantity unit of any industry is one hundredth of the quantity output of each industry in the year 2000, where the quantity unit in each year is a chain index.) 0.15 units of the output of the Mining, Except Oil And Gas, industry is an input into each unit produced by the Primary Metals industry. Since Mining, Except Oil And Gas, enters into Primary Metals, and Primary Metals enters into Motor Vehicles, etc., then Mining, Except Oil And Gas, enters indirectly into the production of Motor Vehicles, etc. (0.040 units of Mining, Except Oil And Gas, also enter directly into each unit output of Motor Vehicles, etc..) Any number of steps can separate the indirect production of one commodity by another.

Summary of Some Empirical Results
I've implemented the above mathematics with 2005 data for the USA. Sixty two industries in the USA in 2005 are basic and enter into the standard commodity with positive components. The three non-basic industries are

• Hospitals and Nursing and Residential Care Facilities
• Federal General Government
• State and Local General Government

I think the non-basic property of the general government industries is an accounting convention. The industries Federal Government Enterprises and State and Local Government Enterprises are basic and enter into the standard commodity with positive values.

The maximum rate of profits in the USA in 2005 was approximately 106.4%.

OCC Varies Less Among Vertically Integrated Industries (Part 2)

I gave a hostage to fortune in the first part. That part notes the empirical claim that the Organic Composition of Capital (OCC) varies less among vertically integrated industries, as compared to non-vertically integrated industries. But I did not demonstrate this claim with actual data. This part retrieves this hostage by presenting empirical results.

The first part explained how to calculate the OCC for both non-vertically and vertically integrated industries, given Leontief Input Output tables. I performed these calculations with the Leontief Input Output table obtainable from the 2005 Use Table and other data available from the Bureau of Economic Analysis (BEA). Figure 1 shows these distributions of the OCC among the 65 industries aggregated by the BEA. Notice that the OCC does indeed seem to be more dispersed for non-vertically integrated industries.

Figure 1: Distribution of Ratio of OCC to Sum of Unity and Rate of Exploitation

In both cases, the distributions seem to be skewed and from a non-Gaussian distribution. Taking common logarithms yields the distributions shown in Figure 2. Table 1 presents summary statistics for these distributions. The absolute value of the coefficient of variation in the distribution of the OCC is indeed decreased by vertical integration. So these results replicate, for 2005 United States of America (USA) data, Shaikh’s and Petrovic’s earlier results for the USA in 1947 and Yugoslavia in 1976 & 1978, respectively.

Figure 2: Distribution of Common Logarithm of Ratio of OCC to Sum of Unity and Rate of Exploitation

Table 1: Logarithm of Ratio of OCC to Sum of
Unity and Rate of Exploitation

Statistic	Non-Vertically Integrated Industries	Vertically Integrated Industries
Number Industries	65	65
Mean	-0.0326576	-0.0770277
Standard Deviation	0.396980	0.225224
Coefficient of Variation (Absolute Value)	12.16	2.924

I suppose this analysis could be improved by performing formal statistical tests. In particular, one might use the Kolmogorov-Smirnov goodness of fit test to determine if the distributions of the OCC after a logarithmic transformation are Gaussian. I don’t know how to formally test for a change in the coefficient of variation. But, since the mean is so close to zero anyway, one might use an F test to contrast the variance in the distributions of the (transformed) OCC. I don’t plan on pursuing this line soon, though.

His Cousin Was A Socialist And A Great American

Francis Bellamy Family Gravesite, Rome, NY

Base of Pillar

Francis' cousin, Edward Bellamy, wrote Looking Backward: 2000-1887.

Relevance of Austrian Business Cycle Theory to USA Politics

Matthew Yglesias blogs "Live from the Paul-Dome":

"I never thought I’d hear an arena full of people cheering and clapping for 'the Austrian theory of the business cycle.'"

OCC Varies Less Among Vertically-Integrated Industries (Part 1)

1.0 Introduction
Anwar Shaikh claims that one can expect the Organic Composition of Capital (OCC) to vary less among vertically integrated industries than among non-vertically integrated industries. Shaikh shows his claim holds for the United States of America in 1947. Petrovic demonstrates the claim for Yugoslavia in 1976 and 1978.

This post lays out the theory formulating this empirical claim. Results replicating Shaikh's and Petrovic's test of the theory in new data are left for Part 2. I have yet to test the theory, and Part 2 remains unwritten for now.

2.0 Vertical Integration

Consider an economy in which each of n commodities are produced from labor and inputs of those n commodities. Let a_{0, j} be the person-years of labor used in producing one unit of the jth commodity. Let a_{i, j} be the physical units of the ith commodity used in producing one unit of the jth commodity. The direct labor coefficients are elements of the n-element row vector a₀. The remaining input-output coefficients are the entries in the nxn Leontief input-output matrix A, which is assumed to satisfy the Hawkins-Simon condition. The challenge is to express an empirical claim about the variability of the OCC in terms of this empirically-observable data.

Let q be an n-element column vector denoting the gross quantities output in each industry. The column vector A q represents the physical quantities of capital goods needed to produce this gross output. Let y be an n-element column vector denoting the net quantities output in each industry. The net output is available to be divided up between wages and profits after replacing the capital goods needed to reproduce the gross output. Net output and gross output are related as follows:

y = q - A q = (I - A) q

Or:

q = (I - A)^-1 y

The jth column of (I - A)^-1 represents the gross output in a vertically integrated industry producing a net output of one unit of the jth commodity. This interpretation becomes apparent when one considers a net output vector consisting of one unit of the jth commodity:

y = e_j

where e_j is the jth column of the nxn identity matrix.

The above analysis of vertically integrated industries allows one to specify the amount of labor and the capital goods employed in each vertically integrated industry. Consider the n-element row vector v defined as:

v = a₀ (I - A)^-1

The jth element of v represents the labor (in person-years) employed in a vertically integrated industry producing one unit of the jth commodity net. This element is the labor directly and indirectly embodied in one unit of the jth commodity. v is the vector of labor values for this economy. The capital goods used in producing any gross output vector is found by pre-multiplying that vector by the Leontief input-output matrix A. Define the matrix H such that each column is the product of A and the gross output of a vertically integrated industry producing a net output of one unit of the corresponding commodity:

H = A (I - A)^-1

Luigi Pasinetti calls the columns of H "the vertically integrated units of productive capacities." A column "expresses in a consolidated way the series of heterogeneous physical quantities of commodities which are directly and indirectly required as stocks, in the whole economic system, in order to obtain one physical unit of [the corresponding commodity] as a final good."

3.0 The Organic Composition of Capital
According to Karl Marx, the labor value of a commodity is the sum of the labor embodied in the capital goods used in the production of that commodity, the labor value of the labor power used in the production of that commodity, and the surplus value:

v_j = c_j + w_j + s_j

where

• c_j is constant capital expended in producing one unit of the jth commodity
• w_j is variable capital (that is, the labor value of capital spent on the wages of workers) expended in producing one unit of the jth commodity
• s_j is the surplus value obtained in producing one unit of the jth commodity.

For Marx, the labor value of constant capital appears unchanged in the product. The source of profits is the appropriation by the capitalists of surplus value produced throughout a capitalist economy.

The OCC is defined to be the ratio of constant capital and variable capital, both expressed in labor values:

occ_j = c_j/w_j

where occ_j is the OCC for the jth industry. Marxist economics would be much less problematic if the OCC were invariant across industries. The rate of exploitation e is another important parameter in Marxist economics. The rate of exploitation is the ratio of surplus value to variable capital in each industry:

e = s_j/w_j

The equality of the rate of exploitation across industries follows from an assumption of competitive labor markets, inasmuch as workers are free to transition among industries in seeking work. The OCC in each industry can be expressed as a function of the rate of exploitation and the ratio of constant capital to the remaining labor value of the product:

occ_j = (e + 1) c_j/(w_j + s_j)

The rate of exploitation can be treated as a nuisance parameter in exploring the empirical question raised in this post.

Consider non-vertically integrated industries, each producing a gross output of one unit of each commodity. The jth industry in this case employs a_{0, j} person-years of labor. That is, the labor value of the product from newly applied labor is merely the corresponding direct labor coefficient:

w_j + s_j = a_{0, j}

The columns of A represent the capital goods needed in each of these industries. The labor embodied in the capital goods for the jth industry is the dot product of the row vector expressing the labor values of a unit of each commodity and the column vector denoting the quantities of these capital goods. Thus, one has:

c = v A

On the other hand, consider vertically integrated industries, each producing a net output of one unit of each commodity. The amount of labor directly employed in the jth vertically integrated industry is v_j. The labor value c^*_j embodied in the capital goods for the jth vertically integrated industry are easily found:

c^* = v H

where the elements of c^* are the desired labor values.

The above observations can be brought together to summarize the empirical claim of interest here. The OCC in each non-vertically integrated industry is proportional to the ratio of the labor value of the capital goods used in that industry and the labor directly employed in that industry:

occ_j/(e + 1) = c_j/a_{0, j}

The OCC in each vertically integrated industry is also proportional to the ratio of the labor value of the capital goods used in that industry and the labor employed in that industry:

occ^*_j/(e + 1) = c^*_j/v_j

where occ^*_j is the OCC in the jth vertically integrated industry. The proportionality constant is the same function of the rate of exploitation in the above pair of equations. The empirical claim is that the expression on the right hand side varies less among industries for vertically integrated industries than among non-vertically industries. That is, the coefficient of variation is less among vertically integrated industries. Perhaps one should take a variance-stabilizing transformation, such as natural logarithms, before calculating the coefficient of variation.

References

• Luigi L. Pasinetti (1973) "The Notion of Vertical Integration in Economic Analysis", Metroeconomica, V. 25: pp. 1-29 (Republished in Pasinetti 1980)
• Luigi L. Pasinetti (Editor) (1980) Essays on the Theory of Joint Production, Columbia University Press
• P. Petrovic (1991) "Shape of a Wage-Profit Curve, Some Methodology and Empirical Evidence", Metroeconomica, V. 42, N. 2: pp. 93-112
• Anwar Shaikh (1984) "The Transformation from Marx to Sraffa", in Ricardo, Marx, Sraffa (Ed. by E. Mandel and A. Freeman), Verso

Red-Baiting Keynesian Textbooks

What economists know now is influenced by what they could teach in the past. Perhaps where we are now has something do with interventions in the past from outside of academic economics. I think, for example, of the suppression of Lorie Tarshis' full-throated Keynesianism.

Lorie Tarshis was a Canadian who attended Cambridge while Keynes was working out the General Theory. He attended Keynes' annual lectures from 1932 to 1935. With others, he brought Keynes' economics to Cambridge, Massachusetts. Tarshis was at Tufts. He later wrote the first introductory textbook to incorporate Keynesianism. I gather this textbook, Elements of Economics (Houghton Mifflin, 1947) predates Samuelson's textbook. Let's look at a reaction to the use of this textbook in teaching the introduction to economics at Yale:

"Marx himself, in the course of his lifetime, envisaged two broad lines of action that could be adopted to destroy the bourgeoisie: one was violent revolution; the other, a slow increase of state power, through extended social services, taxation, and regulation, to a point where a smooth transition could be effected from an individualist to a collectivist society. The Communists have come to scorn the latter method, but it is nevertheless evident that the prescience of their most systematic and inspiring philosopher has not been thereby vitiated.

It is a revolution of the second type, one that advocates a slow but relentless transfer of power from the individual to the state, that has roots in the Department of Economics at Yale, and unquestionably in similar departments in many colleges throughout the country. The documentation that follows should paint a vivid picture." -- William F. Buckley, Jr. God and Man at Yale: The Superstitions of Academic Freedom, Henry Regery, 1951, p. 46-47

Buckley applies his ideologically-charged nonsense to textbooks by Tarshis, Samuelson, and a few others.

2005 USA Labor Values

Figure 1 and Table 1 list industries in order of declining labor values, as of 2005. Industries are as aggregated in the North American Industry Classification System (NAICS), and labor values are in units of person-years per $1,000 output. Table 1 also shows direct labor coefficients for each industry. Direct labor coefficients are the full time equivalent staff hired in each industry. Labor values for each industry are the sum of direct labor values and the labor embodied in the inputs purchased by that industry. For example, the labor embodied in the commodities produced by "Food Services and Drinking Places" includes the labor embodied in commodities purchased by such establishements from the Construction; Real Estate; Miscellaneous Professional, Scientific and Technical Services; and Wholesale Trade industries.

I can think of other analyses to do with this and related data, such as some measure of average wage in an appropriate numeraire. For example, one might examine the rate of exploitation, the variation in the organic composition of capital by industry, and the differences between prices and labor values.

Figure 1: 2005 Embodied Labor Values

Industry	Embodied Labor Values (Person-years per Thousand $ Output)	Direct Labor Coefficient (Person-years per Thousand $ Output)
Social Assistance	0.0219	0.0185
Food Services and DrinkingPlaces	0.0200	0.0157
Forestry, Fishing, and Related Activities	0.0192	0.0103
Transit and Ground Passenger Transportation	0.0174	0.0138
Administrative and Support Services	0.0172	0.0136
Educational Services	0.0169	0.0134
Amusements, Gambling, and Recreation Industries	0.0152	0.0122
Other Services, Except Government	0.0152	0.0112
Hospitals and Nursing and Residental Care Facilities	0.0146	0.0107
Warehousing and Storage	0.0141	0.0127
Wood Products	0.0141	0.00537
Apparel and Leather and Allied Products	0.0139	0.00840
Retail Trade	0.0137	0.0106
Accomodation	0.0133	0.00986
State and Local General Government	0.0129	0.00971
Furniture and Related Products	0.0128	0.00651
Printing and Related Support Activities	0.0119	0.00719
Textile Mills and Textile Product Mills	0.0119	0.00548
Other Transportation and Support Activities	0.0111	0.00908
Construction	0.0110	0.00623
Federal Government Enterprises	0.0105	0.00803
Ambulatory Health Care Services	0.0103	0.00727
Fabricated Metal Products	0.0102	0.00555
State and Local Government Enterprises	0.00996	0.00525
Truck Transportation	0.00989	0.00539
Motor Vehicles, Bodies and Trailers, and Parts	0.00963	0.00226
Waste Management and Remediation Services	0.00923	0.00492
Plastics and Rubber Products	0.0922	0.00410
Machinery	0.00920	0.00399
Misc. Professional, Scientific and Technical Services	0.00914	0.00501
Miscellaneous Manufacturing	0.00903	0.00450
Nonmetallic Mineral Products	0.00898	0.00444
Paper Products	0.00895	0.00302
Food and Beverage and Tobacco Products	0.00890	0.00247
Computer Systems Design and Related Services	0.00888	0.00627
Computer and Electronic Products	0.00880	0.00340
Electrical Equipment, Appliances, and Components	0.00880	0.00393
Information and Data Processing Services	0.00869	0.00339
Other Transportation Equipment	0.00847	0.00349
Air Transportation	0.00841	0.00352
Performing Arts, Spectator Sports, Museums, Etc.	0.00831	0.00512
Motion Picture and Sound Recording Industries	0.00821	0.00371
Federal General Government	0.00812	0.00430
Wholesale Trade	0.00811	0.00526
Insurance Carriers and Related Activities	0.00805	0.00372
Rental and Leasing Services and Lessors of Intangible Assets	0.00784	0.00243
Water Transportation	0.00780	0.00159
Farms	0.00778	0.00264
Legal Services	0.00758	0.00512
Management of Companies and Enterprises	0.00757	0.00469
Publishing Industries (Includes Software)	0.00751	0.00317
Primary Metals	0.00736	0.00237
Rail Transportation	0.00686	0.00326
Support Activities for Mining	0.00656	0.00263
Fed. Reserve Banks, Credit Intermediation, Etc.	0.00635	0.00408
Mining, Except Oil and Gas	0.00623	0.00329
Chemical Products	0.00621	0.00160
Broadcasting and Telecommunications	0.00598	0.00188
Securities, Commodity Contracts, and Investments	0.00542	0.00246
Pipeline Transportation	0.00524	0.000922
Funds, Trusts, and Other Financial Vehicles	0.00514	0.000918
Real Estate	0.00326	0.000687
Petroleum and Coal Products	0.00325	0.000274
Utilities	0.00294	0.00133
Oil and Gas Extraction	0.00250	0.000507

Thought Control In Economics

I might as well point out this Tom Green Adbusters' article, "Thought Control in Economics". I have previously recommended works of Fred Lee.

Elsewhere

I'm continually finding articles by authors I like reading:

• Paul Davidson has written an article on oil prices for the July-August issue of Challenge
• The commentator Patch points out the Hans Böckler Summer school lectures and papers
• Last week, Talking Points Memos organized a discussion on James Galbraith's new book, The Predator State: How Conservatives Abandoned the Free Market and Why Liberals Should Too, which I have not read

As regards the second, I particularly like Marc Lavoie's first lecture, "History and Methods of Post-Keynesian Macroeconomics". It wouldn't surprise me if some of you, dear readers, find more policy-oriented lectures and papers of greater interest.

Against Propaganda Being Institutionalized In Universities

In The Chronicle of Higher Education, Marshall Sahlins criticizes the proposed establishment of the Milton Friedman Institute (MFI). (Hat tip to Brad DeLong.)

The Committee for Open Research on Economy & Society (CORES) has a web site collecting criticism of the MFI.

As indicated by my post title, I think the MFI sounds like it should shame any serious university.

Modest Barkley Rosser

Apparently, just as Barkley Rosser admires the work of János Kornai, so János Kornai admires the work of Barkley Rosser:

"Strong, wide ranging measures to harden the budget constraint came earliest in Hungary. The assessment of J. Barkley Rosser Jr. and Marina V. Rosser, in one of the best-known textbooks of comparative economics, points to the strong intellectual influence of my work on that outcome, and their assessment seems convincing. [Footnote:] 'Hungary has by far the hardest budget constraint of any of the formerly socialist economies... Arguable this reflects the immense policy influence of János Kornai in his native country' (Rosser and Rosser 2004, pp. 377-378)." -- János Kornai (2006) By Force of Thought: Irregular Memoirs of an Intellectual Journey, Massachusetts Institute of Technology

I find there is much about Kornai's views I was not aware of before reading his intellectual memoirs.

Process Recurrence

1.0 Introduction
This post presents another anomaly for neoclassical economics established in Sraffa's framework. It does not present a numeric example, but only outlines the possibility of one. Maybe Kurz and Salvadori (1995) or Woods (1990) contain specific numeric values in which a process can recur along the so-called factor price frontier without the reswitching or recurrence of techniques also arising. Han and Schefold found process recurrence empirically to be more common than reswitching. They say:

"In fact, it is often observed that returns of processes are connected with reverse capital deepening within the scope of our investigation (but it can easily be seen that either phenomenon can also occur without the other)." - Han and Schefold (2006)

2.0 The Model
Consider a simple economy in which workers produce two commodities, apples and bananas from inputs, also composed of apples and bananas. Two processes are known for producing apples, and these processes are labeled I_A and II_A. Two processes, I_B and II_B are also known for producing bananas. This a circulating capital model; all inputs are used up in each production in producing the outputs.

A technique consists of two processes, one for producing apples and one for producing bananas. The claim is that processes can be such that techniques are cost-minimizing at the rates of profits indicated in Table 1. Notice that in this table, each technique is cost-minimizing only in one interval for the rate of profits. Techniques do not reswitch or recur. Yet the first process for producing apples does recur. That process is part of the cost-minimizing technique in both the first and the last interval for the rate of profits. The reswitching of techniques is sufficient for processes to recur, but is not necessary.

Table 1: Cost-Minimizing Techniques

Rate of Profit	Technique
0 ≤ r ≤ r1	IA, IB
r1 ≤ r ≤ r2	IIA, IB
r3 ≤ r ≤ r1	IIA, IIB
r3 ≤ r ≤ rmax	IA, IIB

Rates of profit at which more than one technique is cost minimizing are called switch points. r₁, r₂, r₃, and r₄ are switch points in the example. Capital reversing is the phenomenon in which around a switch point the cost-minimizing technique at the higher rate of profit also has a higher ratio of the value of capital goods to the value of a physically-specified output. In exploded neoclassical intuition, equilibrium prices are scarcity indices. A higher price was thought to indicate that a commodity is more scarce and to lead producers to subsitute other inputs for the more scarce commodity. If the interest rate were the price of capital, a higher interest rate would lead producers to adopt less capital-intensive techniques, in some sense, from a known book of blueprints for techniques. Capital reversing is paradoxical from this perspective and shows that neoclassical heuristics are logically invalid.

Process recurrence is also paradoxical from the exploded neoclassical perspective. An ill-trained neoclassical economist might expect the principle of substitution to hold for individual industries, as well as at the level of the entire economy. In the simple sort of model from which the outlined example is drawn, a higher rate of profits is associated with a lower wage. The specification of a process includes the specification of the how many person-years of labor is needed per unit output in the given industry. Figure 1 shows this normalized direct labor input as a function of the wage. Process recurrence is incompatible with the supposed neoclassical principle of substitution.

Figure 1: Labor Intensity Versus Wage In A Single Industry

References

• Z. Han and B. Schefold (2006) "An Empirical Investigation of Paradoxes: Reswitching and Reverse Capital Deepening in Capital Theory", Cambridge Journal of Economics, V. 30
• 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

Wicksteed Versus Marx

As far as I know, Philip Wicksteed was the first economist to oppose Marx's theory of value on the basis of the neoclassical or marginal theory. Does his essay, "The Marxian Theory of Value: Das Kapital: A Critique" even predate Böhm-Bawerk on this topic? Wicksteed's essay was published in the October 1884 issue of To-Day. Wicksteed, by the way, considered himself a socialist.

I find curious George Bernard Shaw's answer in the January issue. Shaw presented himself as calling for somebody better trained in mathematical economics to answer Wicksteed, not as answering Wicksteed himself:

"I have not the slightest intention here of defending Karl Marx against Mr. Wicksteed... I write partly to draw further attention to a controversy which seems to me of great interest because it is one on which Socialists, without at all ceasing to be Socialists, are sure to divide very soon; and partly because I wish to have a word with Mr. Wicksteed as to my own perplexities concerning 'final utility' before some more competent hand deals him the coup de grâce to which I have already alluded. Even were I economist enough to do that myself, I am not mathematician enough to confute Mr. Wicksteed by the Jevonian method. I somewhat mistrust mathematical symbols. I remember at school a plausible boy who used to prove to me by algebra that one equals two. He always began by saying, 'Let x equal a.' I saw no great harm in admitting that; and the proof followed with rigorous exactness. The effect was not to make me proceed habitually on the assumption that one equals two, but to impress upon me that there was a screw loose somewhere in the algebraic art, and a chance for me to set it right some day when I had time to look into the subject. And I feel bound to make the perhaps puerile confession that when I read Jevons's Theory of Political Economy, I no sooner glanced at the words 'let x signify the quantity of commodity,' than I thought of the plausible boy, and prepared myself for a theory of value based on algebraic proof that two and two make five." -- George Bernard Shaw

I fear many may react like this to mathematical arguments on practical matters.

(Wicksteed's critique, Shaw's response, and Wicksteed's rejoinder are all republished as an appendix to the second volume of the 1933 London School of Economics re-issue of Wicksteed's The Common Sense of Political Economy.)

Hayek and Myrdal Quotations

Hayek had a good argument about the difficulties of central planning. The planners do not have a mechanism for using tacit knowledge distributed among agents. But when it came to describing how contemporary western economies work, Hayek gave up:

"It is important to realize in any investigation of the possibilities of planning that it is a fallacy to suppose capitalism as it exists today is the alternative. We are certainly as far from capitalism in its pure form as we are from any system of central planning. The world of today is just interventionist chaos." -- F. A. Hayek (1948). "Socialist Calculation", in Individualism and Economic Order

On a different topic entirely - I am amused by this Myrdal quote:

"It has been suggested that if one tried to construct a consistent system from Marshall's footnotes and reservations, one would arrive at something very different from the Marshallian system. But it seems to me that if the job were critically, one would not arrive at any system at all." -- Gunar Myrdal, The Political Element in the Development of Economic Theory (Trans. by Paul Streeten) pp. 127-128

One such reservation is Appendix H in the eighth edition of Principles of Economics, titled "Limitations of the use of statical assumptions in regard to increasing returns".

Eatwell Exposition of a Sraffian Research Program

"The revival of the analytical principles of classical political economy that has gathered pace since the mid-1960s has been based on the firm foundation of a logically coherent theory of value and distribution. It was the failure to provide this foundation which for many years confined the classical approach to being, at best, a repository of useful ideas on growth and technological progress (Smith's discussion of the division of labour and Marx's dissection of the labour process being good examples), or, at worst, identified with simple-minded devotion of the labour theory of value as the 'qualitative' expression of capitalist exploitation - the position to which Hilferding retreated in the face of Bohm-Bawerk's critique of Marx, so depriving the surplus approach of any quantitative significance as a theory of value and distribution. The publication of Piero Sraffa's Production of Commodities by Means of Commodities changed all that. Sraffa not only generalized the mathematical solutions to the surplus approach which had been advanced by Dmitriev and Bortkeiwicz, but also presented the analytical structure of the surplus approach with stark clarity. Moreover, Sraffa produced a critique of the neo-classical theory of the rate of profit and so of the entire neo-classical explanation of value, distribution, and output - hence clearing the ground for the redevelopment of classical theory.

With the analytical core now secure, attention can be turned to the development of other facets of classical and Marxian theory and to the empirical insights which this theory provides. In stark contrast to the neo-classical approach, which reduces all economic activity to a single principle - the competitive resolution of individual attempts to maximize utility subject to the constraints of technology and endowment - classical theory is constructed from a number of analytically separable components. The core of the theory, the surplus approach to value and distribution, takes as data the size and composition of output, the technology in use (the conditions of reproduction) and the real wage (or, in some cases, the rate of profit). These data do not, however, lie outside the realm of economics (as,for example, the neo-classical economists' utility functions do). We need to provide theoretical explanations of their determination. Hence Smith, Ricardo and Marx advanced theories of the real wage and of the level of output (Say's law in the case of Ricardo), and Smith and Marx presented detailed analyses of technological change. Assembled around the core, these theories are the building-blocks of a general theory of the operations of the capitalist economy. There is in all this a clear danger of constructing a disjointed ad hoc collage of theories and empirical generalisations. This is avoided by enveloping the entire edifice in a general characterisation of the economic system, the clear specification, that is, of the capitalist mode of production. This serves both to cement the elements of the theory together and to eliminate propositions that do not fit.

Broadly, there are two jobs to be done in developing and extending the classical framework.

First, the classical theory itself must be developed and generalised. All the elements surrounding the core analysis of value and distribution - theories of output and employment, of accumulation, of technology, of the wage, of competition and so on - require restatement and 'modernisation' in the light both of Sraffa's results and of the many changing facets of the modern capitalist system. This will involve both theoretical development and empirical analysis, for one of the important characteristics of classical theorising is the manner in which theory is grounded in the socio-economic data of the system under consideration - the institutional environment is an essential part of the theory.

Second, the rejection of the now discredited neoclassical theory throws open a wide range of problems in international trade, development economics, fiscal and monetary policy and so forth, into which the classical approach can provide new insights. In part these will lead to the refreshing task of debunking the policy prescriptions of orthodox theory which revolve primarily around the fundamental theorem of welfare economics and the supposed 'efficiency' of competitive markets. But there is also a positive job to be done. The reconstruction of economic theory will inevitably precipitate a reinterpretation of economic policy and problems." -- John Eatwell (1987). "Foreword", in The Economics of François Quesnay, by Gianni Vaggi, Duke University Press

A Boy/Girl Thing

The American Mathematical Society catalogs resources for increasing diversity in mathematics. The Association for Women in Mathematics is concerned with female mathematicians. The Association for Computing Machinery (ACM) Committee on Women in Computing is for computer science. The American Statistical Society (ASA) Committee on Women in Statistics and the ASA Caucus for Women in Statistics focus on statistics.

Since this is an economics blog, I'll mention the International Association for Feminist Economics (IAFEE).

Note To Myself: Read Luigi Guiso, Ferdinando Monte, Paola Sapienza, and Luigi Zingales (2008) "Culture, Gender and Math", Science, 320, 1164 (30 May)

Two Roads Diverged In A Yellow Wood, And Sorry I Could Not Travel Both And Be One Traveler

1.0 Introduction
Brian Arthur and Paul David, two teachers at Stanford about a decade ago, have attracted a certain amount of popular attention with the concept of path dependence. Arthur, for example, has had a certain amount of influence on policy. This post is an attempt to explain the concept, primarily as it applies to stochastic processes. Path dependence is one way of formalizing the idea that history matters.

2.0 A Stochastic Process
Path dependence relates to events economists choose to model as random. This modeling choice does not imply that economists think such events are necessarily the result of the modeled agents acting capriciously, irrationally, or mistakenly. Consider such childhood games as Odds and Evens or Paper-Rock-Scissors. The optimal strategy for each player is to choose their move randomly. The winner of such games will vary randomly. Notice that apart from the players' choices, these games are deterministic. No dice are being rolled or cards shuffled.

A stochastic process is merely an indexed set of random variables:

{ X( 1 ), X( 2 ), X( 3 ), ... }

The index often represents time. The value of a given one of these random variables is frequently referred to as the state of the process at that time.

I consider an example of a path-dependent stochastic process that does not exhibit certain other properties. This stochastic process can be in one of eight states, {Start, B, C, D, E, F, G, H}. It begins in the Start state. State transition probabilities are indicated by
the fractions in Figure 1. For example, consider the probability distribution for the state of the process at the second time step, X( 2 ). Figure 1 shows that if the process is in the Start state, the probability that it will transition to state B is 1/2. Likewise, given that it is in the Start state, the probability that it will transition to state C is 1/2. Hence the probability distribution of X( 2 ) is:

Pr[ X( 2 ) = B ] = 1/2

Pr[ X( 2 ) = C ] = 1/2

Notice that the probabilities leading out from each state total unity. It is left as an exercise for the reader to confirm that the proability distribution of X( 3 ) is as follows:

Pr[ X( 3 ) = Start ] = 1/3

Pr[ X( 3 ) = B ] = 1/6

Pr[ X( 3 ) = C ] = 1/6

Pr[ X( 3 ) = D ] = 1/6

Pr[ X( 3 ) = G ] = 1/6

I deliberately created this example to exhibit a certain symmetry for the transient states (defined below).

Figure 1: Markov Process State Space

This process exhibits certain properties that are particularly simple, as well as some properties that complicate analysis. Notice that the state transition properties are invariant across time. Given that the process is in the Start state, the probability that it will transition to state B is 1/2, no matter at what time the process may be in the Start state. It does not matter whether we are considering the initial time step or some later time when the process happens to have returned to the Start state.

Furthermore, the process is memoryless. State transition probabilities depend only on the current state, not the history with which the process reached the current state. This property of memorylessness is known as the Markov property. This example is a Markov process.

The Markov property and the assumption of time-inavariant state transition probabilities are simplifying assumptions. One might think relaxation of these assumptions might be one way of showing that "history matters." Since, as will be explained, this example exhibits path dependence, violations of these assumptions are clearly not necessary for path dependence. And Margolis and Liebowitz are incorrect:

"In probability theory, a stochastic process is path dependent if the probability distribution for period t+1 is conditioned on more than the value of the system in period t. ... path independence means that it doesn't matter how you get to a particular point, only that you got there." -- Stephen E. Margolis and S. J. Liebowitz (1988)

An interesting classification of sets of states is available for Markov processes, that of transient and absorbing states. Consider the states {Start, B, C}. By assumption, the process starts in a state within this set. But eventually the process will lie in a state outside this set. Once this happens, the process will never return to this set. States Start, B, and C are known as transient states. On the other hand, consider the states {D, E, F}. Once the process is in a state in this set, the process will never depart from a state in the set. Furthermore, if the process is in a state in this set, it will eventually visit all other states in the set. {D, E, F} is a set of asorbing states. This is not the unique set of absorbing states for this process. {G, H} is also a set of absorbing states.

Consider the problem of estimating the probability distribution over the states at some large number of time step, say X(10,000), after the start. The probability that the process is in a transient state is negligible. One might be tempted to estimate X(10,000) by the proportion of time steps that a single realization of the process spends in each state. A realization might be:

Start, B, D, E, F, D, E, F, E, F, D

The column for the first realization in Table 1 shows the proportion of time spent in each state in this realization as the number of time steps in the realization increases without bound. (Although transient states are observed in a realization, the proportion of time spent in transient states in such an infinite sequence is zero.)

Table 1: Limiting State Probabilities

State	From One Realization	From Another Realization	Over All Realizations
Start	0	0	0
B	0	0	0
C	0	0	0
D	1/3	0	1/6
E	1/3	0	1/6
F	1/3	0	1/6
G	0	1/2	1/4
H	0	1/2	1/4

If the process were ergodic, the limiting distribution in the first column in Table 1 would be a good estimate of the probability distribution for the state of the process at some time after transient behavior was likely to be completed. In this case, though, another realization might yield the limiting distribution shown for the second realization in Table 1. The probability distribution, in fact, at a given time, as that time increases without bound would have positive probabilities for all non-transient states. The last column in Table 1 shows this limiting probability distribution.

In general, estimates of parameters of the underlying probability distributions can be made across multiple realizations of the process or from a single realization. In a nonergodic process, such estimates will not converge as the number of realizations or the length of the single realization increases.

Another definition of ergodicity involves what states can be eventually reached from each state. In an ergodic process, each state can be eventually reached, with positive probability. In the example, all states can be reached from the transient states Start, B, and C. But states Start, B, C, G and H cannot be reached from states D, E, and F. Suppose an external occurrence changes the state transition probabilities. If the process were previously ergodic, this change could not possibly result in states arising that were previously unobserved.

To re-iterate, a nonergodic process does not have an unique limiting probability distribution. The applicable limiting distribution of any realization of the process depends on the history of that particular realization. Thus, the process exhibits path dependence.

Another branch of mathematics deals with deterministic dynamical systems. Such systems are typically defined by systems of differential or difference equations. Sometimes the solutions of such systems can be such that trajectories in phase space diverge, no matter how close they start. This is known as sensitive dependence on initial conditions, popularly known as the "butterfly effect." (The irritating mathematican character in Jurassic Park mumbles about this stuff.) Notice that path dependence is defined above without drawing on this branch of mathematics. Here, too, Margolis and Liebowitz are mistaken:

”Path dependence is an idea that spilled over to economics from intellectual movements that arose elsewhere. In physics and mathematics the related ideas come from chaos theory. One potential of the non-linear models of chaos theory is sensitive dependence on initial conditions: Determination, and perhaps lock-in, by small, insignificant events." -- Stephen E. Margolis and S. J. Liebowitz (1988)

3.0 Conclusion
Why should economists care about the mathematics of path dependence? First, models of path dependence suggest how to construct economic models that overcome frequently criticized characteristics of neoclassical economics. Neoclassical models often depict equilibria. These equilibria are end states of path independent processes. Ever since Veblen, some economists have objected to such models as being teleological and acausal. Models in which path dependence can arise are causal and show neoclassical economics to be a special case.

This claim that neoclassical economics is merely a special case, dependent on a special case assumption of ergodicity, may lead one to wonder about connections with a theory claimed to be the "General Theory." As a matter of fact, Paul Davidson claims that a consideration of nonergodicity is useful in explicating the economics of Keynes. So a second reason economists should be concerned with nonergodicity and path dependence is to further understand possible approaches to macroeconomics.

Third, some economists, e.g. Brian Arthur, have developed specific models of technological change that exhibit nonergodicity. These models, including those of a Polya urns, show how increasing returns can act as positive feedback and lead to path dependence. Inasmuch as these models cast light on economic history, path dependence can be useful for empirical work.

The theory of path dependence raises an empirical question. Are nonergodic stochastic processes useful for modeling any, or any important, economic time series? The evolution of the QWERTY keyboard seems to be an example of a path dependent process. Apparently there were several 19th century typewriter keyboard layouts. QWERTY became the dominant one, seemingly even after the jamming problem that was the rationale for its introduction had been overcome. The historical evidence suggests that with different early choices, one of the other arrangements could have become dominant. The chances that some one or other of these early arrangements can now become dominant seems quite negligible.

This discussion has been carried out without mentioning efficiency.

References

• W. Brian Arthur (1989) "Competing Technologies, Increasing Returns, and Lock-In by Historical Events", Economic Journal, V. 99: 116-131.
• W. Brian Arthur (1990) "Positive Feedbacks in the Economy", Scientific American, 262 (February): 92-99.
• W. Brian Arthur (1996) "Increasing Returns and the New World of Business", Harvard Business Review.
• Paul A. David (1985) "Clio and the Economics of QWERTY", American Economic Review 75, 2 (May)
• Paul A. David "Path Dependence, Its Critics and the Quest for 'Historical Economics'"
• Paul Davidson (1982-1983) "Rational Expectations: A Fallacious Foundation for Studying Crucial Decision-Making Processes", Journal of Post Keynesian Economics, V. 5 (Winter): 182-197.
• Stephen E. Margolis and S. J. Liebowitz (1988) "Path Dependence", The New Palgrave Dictionary of Economics and Law, MacMillan.

The Map Is Not The Territory

Suppose an orthodox economist hands you a map and says, "This is a map of New York City." You look at it and say, "It is not. It is a map of the London tube system."

Or suppose an orthodox economist hands you a map. And you look at it and say, "This cannot be right. Here are two interesecting contour lines supposedly of different elevations."

Suppose the orthodox economist responds, "Assumptions do not need to be realistic."

I have encountered several economists who distract from those pointing out the logical inconsistencies and factual errors in their theories. They make dismissive non sequiturs about methodology, as illustrated in the parables above.

Davidson And Eatwell On Current Events

This post points out some recent interventions by two leading economists in schools of thought in which I am interested.

Paul Davidson is the leader of American Post Keynesians and the editor of the Journal of Post Keynesian Economics. He argues that Sraffa's economics is not compatible with Keynes insofar as it is not set in historical time. And he advocates for the economics of Keynes over Sraffa.

His recent article "Crude Oil Prices: 'Market Fundamentals' or Speculation?" is available in the Heterodox Economics Newsletter (Issue 63, 12 June 2008). Davidson argues that "the absence of any excess supply adjustment is not ... evidence of the lack of a speculative force" driving current high oil prices.

John Eatwell, or Lord Eatwell, has contributed to attempting to synthesize the ideas of Keynes and Sraffa. I am thinking the 1983 book, Keynes's Economics and the Theory of Value and Distribution, which Eatwell co-edited with Murray Milgate. He also wrote, with Carlo Panico, the New Palgrave entry on Sraffa and has influenced my understanding on how Sraffa's standard commodity can be used to understand Marx.

In a 3 July letter in the Financial Times, Eatwell argues that regulators of financial institutions should monitor the details of the systematic risks which firms are taking on. In a 17 July comment, also in the Financial Times, Eatwell and Avinash Persaud comment on Fannie Mae and Freddie Mac and argue that markets with diverse players are thicker and more liquid.

"On Labour Demand and Equilibria of the Firm"

The above is from my 2005 Manchester School article. H/T to Crooked Timber.

In Economics Departments, Marx's Days Are Like Grass, Like A Flower Of The Field He Bloomed

Russell Jacoby asks, in the 25 July 2008 issues of The Chronicle of Higher Education, "How is it that Freud is not taught in psychology departments, Marx is not taught in economics, and Hegel is hardly taught in philosophy?"

I occasionally point out treatments of Marx using the techniques of modern mathematical economics. Lots of work has been done in this vein. I might as well mention analytical Marxism, as developed by, for example, John Roemer; Morishima's 1970s work drawing on Johnny Von Neumann; and, of course, Sraffians, such as John Eatwell or Ian Steedman. In regard to the latter, some economists have disputed Steedman's interpretation of Marx's work. I here have in mind Dumenil, Lipietz, and Foley's "New interpretation" and the Temporal Single System approach associated with such economists as Alan Freeman and Andrew Kliman. Perhaps Jacoby is aware that if economists chose to teach Marx, they have much work to draw on. After all, Jacoby notes that Wassily Leontief taught a 1936 seminar on Marx at Harvard. Duncan Foley's testimony (I believe in Colander, Holt and Rosser (204)) is just one demonstration that the ignorance of Marx among orthodox economists cannot be justified on normal scholarly or scientific norms.

I don't expect vulgar political economic monopolists to even acknowledge the existence of their suppressed competition. Orthodox economists just refuse to reference lots of literature, for example, in heterodox journals.

Reminder to myself: Read Andras Bródy's Proportions, Prices, and Planning: A Mathematical Restatement of the Labor Theory of Value (Akadémiai Kiadó, 1970) for an early analytical examination of Marx. Read Victor S. Venida's "Marxian Categories Empirically Estimated: The Philippines, 1961-1994" (Review of Radical Political Economics, V. 39, N. 1 (2007): 58-579) for recent econometric work.

Those Who Believed Shared All Things In Common

Greg Mankiw Still A Fool

Greg Mankiw presents a non-argument from authority to the readers of The New York Times.

Is what a majority of members of the American Association of Economists believe of any interest? How abut a majority of the Association For Evolutionary Economics (AFEE), the International Association For Feminist Economics (IAFFE), or the Union for Radical Political Economics (URPE)?

I care about the beliefs of the majority of AEA members as data for the sociology of economics. (I deliberately don't write here of the sociology of knowledge.) As guidance for deciding on public policy - not so much.

Insofar as Mankiw claims to believe in the distinction between positive and normative economics, he should even agree.

Better public intellectuals, please.

Ricardo And The Iron Law Of Wages

1.0 Introduction
The interpretation of classical economists by historians of economic thought is an area of intense debate that Sraffians have contributed to. Sraffians claim that Classical economics has a distinct and coherent approach to economics. And that the theory of value and distribution within this theory has a different structure and role than within so-called neoclassical theory. I want to focus here particularly on the interaction of the Classical theory of wages and the theory of value. I think Ricardo's treatment of wages is a particularly controversial topic in this interpretation. This post notes a couple of difficulties for understanding Ricardo on wages. I developed it in response to an essay on the iron law of wages that the author e-mailed me.

2.0 Contending Interpretations of Classical Political Economy
As usual, I deny much, if any, originality. But I am going to be vague on references. As I understand it, Sraffa and Dobb's introduction in Sraffa (1951) was not initially perceived as offering a novel interpretation of Ricardo. Bharadway (1989) and Garegnani (1984) offer other statements of the Sraffian interpretation. Stirati (1994) focuses specifically on the theory of wages.

Samuel Hollander, I think, has the highest stature of those today arguing, pace Sraffa, for the continuous evolution of Classical economics into Neoclassical economics. I take Hollander to be continuing the line of argument to be found in Appendix I of Alfred Marshall's Principles of Economics. Despite my respect for Hollander, I have yet to thoroughly read any of his massive tomes of scholarship (e.g., Hollander 1979). My acquaintance with Hollander's primary work is mainly in the journal literature, such as his tournament with Giancarlo de Vivo in the mid 1980s and later Cambridge Journal of Economics over de Vivo's discovery in Robert Torrens of something much like Sraffa's standard commodity.

Others have entered into this controversy, while taking positions that I think differ from both Sraffian positions and Hollander's. I mention Carvale and Tosato (1980), which, as I recall, contains dynamic models which formalize an interpretation of Ricardo's views on wages. I also like Peach (1993), which surveys other interpretations and offers Peach's own reading of Ricardo.

2.0 Sraffian Interpretation
The givens in Ricardo's theory of value include, the level of effective demand for the output of each industry and the technique in use. From these givens, the capital equipment that must be advanced in each industry is also known. The level of wages is also among the givens of the theory of value. The rate of profit then is roughly the ratio of the surplus to the advances, including wages.

A problem arises here. The surplus output of the economy, the commodities on which wages are spent, and the capital equipment are each heterogeneous collections. How can these quantities be treated as commensurate? Ricardo's corn-ratio model, the labor theory of value, and Sraffa's standard commodity are all approaches to address this issue.

So the Sraffians claim that the Classical theory of value makes sense, at least formally if the natural rate of wages is exogenous to the theory of value, albeit still to be explained within Political Economy. This is not a novel position:

"Therefore the foundation of modern political economy, whose business is the analysis of capitalist production, is the conception of the value of labour-power as something fixed, as a given magnitude-as indeed it is practice in each particular case. The minimum of wages therefore correctly forms the pivotal point of Physiocratic theory. They were able to establish this although they had not yet recognised the nature of value itself, because this value of labour-power is manifested in the price of the necessary means of subsistence, hence in a sum of definite use-values. Consequently, without being in any way clear as to the nature of value, they could conceive the value of labour-power, so far as it was necessary to their inquiry, as a definite magnitude. If moreover they made the mistake of conceiving this minimum as an unchangeable magnitude-which in their view is determined entirely by nature, and not by the stage of historical development, which is itself a magnitude subject to fluctuations-this in no way affects the abstract correctness of their conclusions, since the difference between the value of labour-power and the value it creates does not at all depend on whether the value is assumed to be great or small." -- Karl Marx (1963) p. 45

4.0 The Natural Wage Outside The Stationary State
I have pointed to a theory of the natural level of prices above, where the natural level of prices is to be contrasted with market prices. Adam Smith uses the metaphor of centers of gravitation for the natural levels. They attract market prices. Ricardo focuses his analysis on natural levels. One might think the given wage in Ricardo's theory of value and distribution must be the natural rate of wages.

This quote seems to say that the natural rate of wages is defined to be the wage that prevails in the stationary state:

"Notwithstanding the tendency of wages to conform to their natural rate, their market rate may, in an improving society, for an indefinite period, be constantly above it; for no sooner may the impulse, which an increased capital gives to a new demand for labour be obeyed, than another increase of capital may produce the same effect; and thus, if the increase of capital be gradual and constant, the demand for labour may give a continued stimulus to an increase of people." -- David Ricardo (p. 94-95 in Sraffa 1951)

And Ricardo says that the stationary state is far distant:

"But if our progress should become more slow; if we should attain the stationary state, from which I which I trust we are far distant, then will the pernicious nature of these [Poor] laws become more manifest and alarming; and then, too, will their removal be obstructed by many additional difficulties." -- David Ricardo (p. 109 in Sraffa 1951)

So Ricardo seems to be inconsistent. He thinks that the system of natural prices and wages is explanatory for empirical tendencies at any moment, that the stationary state is far distant, and the natural rate of wages is defined only for the stationary state. Maybe he has different theories for the long run and the intermediate run, so to speak.

5.0 The Iron Law of Wages and Ricardo
As I understand it, the iron law of wages is that wages tend towards the natural rate of wages, defined as physiological subsistence. Outdated teaching in the history of economic thought is that Ricardo held to this iron law.

Ricardo clearly states that natural rate of wages is not defined solely by physiological requirements. It includes habits and social norms:

"It is not to be understood that the natural price of labour, estimated even in food and necessaries, is absolutely fixed and constant. It varies at different times in the same country, and very materially differs in different countries. It essentially depends on the habits and customs of the people. An English labourer would consider his wages under their natural rate, and too scanty to support a family, if they enabled him to purchase no other food than potatoes, and to live in no better habitation than a mud cabin; yet these moderate demands of nature are often deemed sufficient in countries where 'man's life is cheap', and his wants are easily satisfied. Many of the conveniences now enjoyed in an English cottage, would have been thought luxuries in an earlier period of our history." -- David Ricardo (p. 96-67 in Sraffa 1951)

Hystersis arises in this approach. If the market rate is above the natural wage for a long time, the norms and habits embodied in workers' consumption can change. In a sense, the natural level of wages moves towards the market wage, as well as vice-versa. Ricardo draws on this idea for some policy ideas:

"The friends of humanity cannot but wish that in all countries the labouring classes should have a taste for comforts and enjoyments, and that they should be stimulated by all legal means in their exertions to procure them. There cannot be a better security against a superabundant population. In those countries, where the labouring classes have the fewest wants, and are contented with the cheapest food, the people are exposed to the greatest vicissutudes and miseries. They have no place of refuge from calamity; they cannot seek safety in a lower station; they are already so low, that they can fall no lower..." -- David Ricardo (p. 100-101 in Sraffa 1951)

You can see the same idea later in John Stuart Mill:

"It would, however, be of little avail that either or both these measures of relief [emigration for colonization and something like homesteading] should be adopted, unless on such a scale as would enable the whole body of hired labourers remaining on the soil to obtain not merely employment, but a large addition to the present wages - such an addition as would enable them to live and bring up their children in a degree of comfort and independence to which they have hitherto been strangers. When the object is to raise the permanent condition of a people, small means do not merely produce small effects, they produce no effect at all. Unless comfort can be made as habitual to a whole generation as indigence is now, nothing is accomplished..." J. S. Mill (1848, Book II, Chapter XIII)

How can Ricardo's words be reconciled with the claim that Ricardo held the iron law? My preferred approach is to reject the claim. Ricardo did not endorse the iron law of wages.

This raises the question of who came up with the iron law of wages, if it was not Ricardo. Apparently the "Iron Law" was named by Ferdinand Lassalle. Stirati (1994) reads Marx as here saying that Malthus was the law's creator:

"It is well known that nothing of the 'iron law of wages' is Lassalle's except the word 'iron' borrowed from Goethe's 'great, eternal iron laws'. The word 'iron' is a label by which the true believers recognize one another. But if I take the law with Lassalle's stamp on it, and consequently in his sense, then I must also take it with his substantiation for it. And what is that? As Lange already showed, shortly after Lassalle's death, it is the Malthusian theory of population (preached by Lange himself). But if this theory is correct, then again I cannot abolish the law even if I abolish wage labor a hundred times over, because the law then governs not only the system of wage labor but every social system. Basing themselves directly on this, the economists have been proving for 50 years and more that socialism cannot abolish poverty, which has its basis in nature, but can only make it general, distribute it simultaneously over the whole surface of society!" - Karl Marx (1875)

As I understand it, the formal mathematics of the theory of value merely requires the wage to be given. But, as my email correspondent points out, if the wage is above subsistence, workers can save and class structure of capitalism will not be reproduced.

As I understand it, in the formal mathematics of the theory of value, the wage, for example, is taken as given. The formalism does not require the wage to be any particular value between zero and some maximum. But, as my email correspondent points out, if the wage is appreciably is above subsistence, workers can accumulate capital before retirement age and the class structure of capitalism will not be reproduced.

Updated 19 July 2008

References

• Krishna Bharadwaj (1989) Themes in Value and Distribution: Classical Theory Reappraised, Unwin Hyman
• Giovanni A. Caravale and Domenico A. Tosato (1980) Ricardo and the Theory of Value, Distribution and Growth, Routledge & Kegan Paul
• P. Garegnani (1984) "Value and Distribution in the Classical Economists and Marx", Oxford Economic Papers, V. LXXIII: 291-325
• Samuel Hollander (1979) The Economics of David Ricardo, Toronto: University Press
• Karl Marx (1875) Critique of the Gotha Program
• Karl Marx (1963) Theories of Surplus Value, Part I (Trans. by E. Burns), Progress Publishers
• John Stuart Mill (1848) Principles of Political Economy
• Terry Peach (1993) Interpreting Ricardo, Cambridge University Press
• Piero Sraffa (editor) (1951) The Works and Correspondence of David Ricardo: Volume I: On the Principles of Political Economy and Taxation, Cambridge University Press
• Antonella Stirati (1994). The Theory of Wages in Classical Economics: A Study of Adam Smith, David Ricardo and Their Contemporaries (trans. by Joan Hall), Edward Elgar

A Different World

Suppose that all equipment used in production were privately owned by individuals. Being fairly well-off, I might have a house with some sort of blast furnace in the back yard. Production in this imaginary world would be performed entirely by self-employed artisans.

One can allow some people in this world to perform no work. Some of these artisans would be lending or borrowing specific equipment from others. So any specific piece of capital equipment would have a rental price. If I happened to own equipment that could command high enough rents, I would be able to lend all my equipment out and live off these rents.

It seems to me that inasmuch as a neoclassical theory of value exists that is logically consistent in its assumptions, it is a map of the above sort of society. It is not even an attempt to describe a society in which one can loan out money at interest or buy and sell shares in firms that themselves own capital equipment. Given the lack of a stock market in this imaginary world, I do not see the point of introducing wage labor into the model either. One would still not end up with a model of a capitalist economy.

References

• Joan Robinson (1962) Essays in the Theory of Economic Growth, Macmillan
• Joan Robinson (1973) Economic Heresies: Some Old-Fashioned Questions in Economic Theory, Basic Books

What Has Been, That Will Be; What Has Been Done, That Will Be Done

Stiglitz has an editorial in "Egypt's only independent newspaper in English:

"Neo-liberal market fundamentalism was always a political doctrine serving certain interests. It was never supported by economic theory. Nor, it should now be clear, is it supported by historical experience. Learning this lesson may be the silver lining in the cloud now hanging over the global economy." -- Joseph E. Stigliz, , 7 July 2008

And some bloggers are flabbergasted. Interestingly enough, Stiglitz said the same thing last October. Maybe if enough economists say the same thing over and over and over, other economists should examine their rationale. Clearly, Stiglitz is not just saying whatever momentarily passes through his mind.

Some History of the Label 'Neoclassical"

I suppose if I want to note the origin of the term "neoclassical" in relation to economics, I should quote Aspromourgos. But I happen to have a Colander essay nearer at hand. The term grew to have a extremely general connotation:

"The term, neoClassical, was initially coined by Thorstein Veblen (1900) in his 'Preconceptions of Economic Science.'...

Hicks (1932, 1934) and Stigler (1941) extended the meaning of neoClassical to encompass all marginalist writers, including Menger, Jevons, and J.B. Clark. Most writers after Hicks and Stigler used the term inclusively. Thus it lost most of its initial meaning. Instead of describing Marshallian economics, it became associated with the use of calculus, the use of marginal productivity theory, and a focus on relative prices. As has been noted by a number of authors, while the neoClassical terminology makes some sense for Marshall, who emphasized the connection of his approach with the Classical approach, it makes far less sense for the others, such as Jevons, who emphasized the difference between his views and those of the Classicals. Some have suggested that anti-Classical would have been preferable.

...In the third edition of his principles textbook Samuelson (1955) built on Keynes' classification and turned it around on Keynes by developing the neoClassical synthesis. In the neoClassical synthesis, Keynes' dispute with Classical economists was resolved. This use of the term 'neoClassical' as an alternative to Keynesian models provides another confusion because it adds another reference point that brings to mind different elements of thought than would other comparisons." -- David Colander

By the way, shortly before World War II, Austrian economists did not see themselves as lying outside neoclassical economics or putting forth a separate doctrine:

"Referring to the usual separation of economic theorists into three schools of thought, 'the Austrian and the Anglo-American schools and the School of Lausanne', Mises (citing Morgernstern) emphasizes that these groups 'differ only in their mode of expressing the same fundamental idea and that they are divided more by their terminology and by peculiarities of presentation than by substance of their teachings' (Mises 1960 [1933])." - Israel Kirzner

For completeness, I expand the references in the above quotations.

References

• Tony Aspromourgos, "On the Origins of the Term 'Neoclassical'", Cambridge Journal of Economics, V. 10, N. 3: 265-270
• David Colander, "The Death of Neoclassical Economics"
• J. R. Hicks (1932) "Marginal Productivity and the Principle of Variation", Economica (February)
• J. R. Hicks (1934) "Leon Walras", Econometrica (October)
• Israel Kirzner (1987) "The Austrian School of Economics", The New Palgrave Dictionary of Economics
• L. von Mises (1960) Epistemological Problems of Economics, Van Nostrand (translation of Grundprobleme der Nationalökonomie, 1933)
• G. J. Sigler (1941) Production and Distribution Theories, Macmillan

Marx Was Skint - But He Had Sense / Engels Lent Him The Necessary Pence

Marx may or may not be correct in these passages. But these, and expansions of these passages, certainly contain claims worth thinking about:

"Let us take England. Its political economy belongs to the period in which the class-struggle was as yet undeveloped. Its last great representative, Ricardo, in the end, consciously makes the antagonism of class-interests, of wages and profits, of profits and rent, the starting point for his investigations, naively taking this antagonism for a social law of nature. But by this start the science of bourgeois economy had reached the limits beyond which it could not pass. Already in the lifetime of Ricardo, and in opposition to him, it was met by the criticism, in the person of Sismondi.

The succeeding period, from 1820 to 1830, was notable in England for scientific activity in the domain of Political Economy. It was the time as well of the vulgarizing and extending of Ricardo's theory, as of the contest of that theory with the old school. Splendid tournaments were held... The literature of Political Economy in England at this time calls to mind the stormy forward movement in France after Dr. Quesnay's death, but only as a Saint Martin's summer reminds us of spring. With the year 1830 came the decisive crisis.

In France and in England the bourgeoise had conquered political power. Thenceforth, the class-struggle, practically as well as theoretically, took on more and more outspoken and threatening forms. It sounded the death knell of scientific bourgeois economy. It was no longer a question, whether this theorem or that was true, but whether it was useful to capital or harmful, expedient or inexpedient, politically dangerous or not. In place of disinterested enquirers, there were hired prize-fighters; in place of genuine scientific research, the bad consequence and the evil intent of apologetic..." -- K. Marx, Capital, Volume 1, Author's Preface to the Second Edition

"A commodity is therefore a mysterious thing, simply because in it the social character of men's labour appears to them as an objective character stamped upon the product of that labour; because the relation of the producers to the sum total of their own labour is presented to them as a social relation, existing not between themselves, but between the products of their labour. This is the reason why the products of labour become commodities, social things whose qualities are at the same time perceptible and imperceptible by the senses... With commodities... the existence of the things qua commodities, and the value relation between products of labour which stamps them as commodities, have absolutely no connection with their physical properties and with the material relations arising therefrom. There it is a definite social relation between men, that assumes, in their eyes, the fantastic form of a relation between things. In order, therefore, to find an analogy, we must have recourse to the mist-enveloped regions of the religious world. In that world the productions of the human brain appear as independent beings endowed with life, and entering into relation both with one another and the human race. So it is in the world of commodities with products of men's hands. This I call the Fetishism which attaches itself to the products of labour, so soon as they are produced as commodities, and which is therefore inseperable from the production of commodities." -- K. Marx, Capital, Volume 1, Chapter 1, Section 4: The Fetishism of Commodities and the Secret Thereof

"Capital - profit (profit of enterprise plus interest), land - ground-rent, labour - wages, this is the trinity formula which comprises all the secrets of the social production process.

Furthermore, since as previously demonstrated interest appears as the specific characteristic product of capital and profit of enterprise on the contrary appears as wages independent of capital, the above trinity formula reduces itself more specifically to the following: Capital - interest, land - ground-rent, labour - wages, where profit, the specific characteristic form of surplus-value belonging to the capitalist mode of production, is fortunately eliminated.

On closer examination of this economic trinity, we find the following: First, the alleged sources of the annually available wealth belong to widely dissimilar spheres and are not at all analogous with one another. They have about the same relation to each other as lawyer's fees, red beets and music.

Capital, land, labour! However, capital is not a thing, but rather a definite social production relation, belonging to a definite historical formation of society, which is manifested in a thing and lends this thing a specific social character. Capital is not the sum of the material and produced means of production. Capital is rather the means of production transformed into capital, which in themselves are no more capital than gold or silver in itself is money. It is the means of production monopolised by a certain section of society, confronting living labour-power as products and working conditions rendered independent of this very labour-power, which are personified through this antithesis in capital. It is not merely the products of labourers turned into independent powers, products as rulers and buyers of their producers, but rather also the social forces and the future [? illegible] [A later collation with the manuscript showed that the text reads as follows: "die Gesellschaftlichen Kräfte und Zusammenhängende Form dieser Arbeit" (the social forces of their labour and socialised form of this labour). - Ed.] form of this labour, which confront the labourers as properties of their products. Here, then, we have a definite and, at first glance, very mystical, social form, of one of the factors in a historically produced social production process.

And now alongside of this we have the land, inorganic nature as such, rudis indigestaque moles, [Ovid, Metamorphoses, Book I, 7. - Ed] in all its primeval wildness. Value is labour. Therefore surplus-value cannot be earth. Absolute fertility of the soil effects nothing more than the following: a certain quantity of labour produces a certain product - in accordance with the natural fertility of the soil. The difference in soil fertility causes the same quantities of labour and capital, hence the same value, to be manifested in different quantities of agricultural products; that is, causes these products to have different individual values. The equalisation of these individual values into market-values is responsible for the fact that the 'advantages of fertile over inferior soil ... are transferred from the cultivator or consumer to the landlord'. (Ricardo, Principles, London, 1821, p.62.)

And finally, as third party in this union, a mere ghost - 'the' Labour, which is no more than an abstraction and taken by itself does not exist at all, or, if we take... [illegible], the productive activity of human beings in general, by which they promote the interchange with Nature, divested not only of every social form and well-defined character, but even in its bare natural existence, independent of society, removed from all societies, and as an expression and confirmation of life which the still non-social man in general has in common with the one who is in any way social." -- K. Marx, Capital, Volume 3, Part Seven, "Revenue and Theirs Sources", Chapter 48: The Trinity Formula

"The form of revenue and the sources of revenue are the most fetishistic expression of the relations of capitalist production. It is their form of existence as it appears on the surface, divorced from the hidden connections and the intermediate connecting links. Thus the land becomes the source of rent, capital is the source of profit, and labour the source of wages. The distorted form in which the real inversion is expressed is naturally reproduced in the views of the agents of this mode of production. It is a kind of fiction without fantasy, a religion of the vulgar. In fact, the vulgar economists - by no means to be confused with the economic investigators we have been criticizing - translate the concepts, motives, etc., of the representatives of the capitalist mode of production who are held in thrall to this mode of production and in whose consciousness only its superficial appearance is reflected. They translate them into a doctrinaire language, but they do so from the standpoint of the ruling section, i.e., the capitalists, and their treatment is therefore not naive and objective, but apologetic. The narrow and pedantic expression of vulgar conceptions which are bound to arise among those who are the representatives of this mode of production is very different from the urge of political economists like the Physiocrats, Adam Smith and Ricardo to grasp the inner connection of the phenomena." -- K. Marx, Theories of Surplus Value, Part III, Addenda, "Revenue and Its Sources. Vulgar Political Economy", 1.