We have now developed enough concepts to critically analyze both marginal productivity (MP) theory and the standard liberal "critique" of the theory. The partial derivatives of production functions (i.e., "marginal productivities") can be used in a bare-bones analytical theory of input demand in a competitive capitalist model. That piece of applied mathematics would by itself be no more controversial than the symmetrical analytical theory of input supply. But marginal productivity theory has been a center of intense ideological controversy (unlike the theory of input supply). Why? Because of the interpretation added to the bare-bones mathematics which claims to show that each factor gets what it produces in the competitive capitalist model. That is the "marginal productivity theory" analyzed here. That MP theory has two central and highly stylized tenets about the competitive capitalist (single product) firm:

Thus the competitive capitalist model operates according to what Professor Milton Friedman calls the "capitalist ethic":

One must be careful to separate the descriptive question of whether the so-called "capitalist ethic" is satisfied in the competitive capitalist model (given its assumptions) from the normative question of whether that principle ought to be satisfied. Friedman takes it as a matter of descriptive economic theory that the competitive capitalist model does satisfy the principle and hence the appellation "capitalist ethic."

But even given all the factual assumptions of the competitive capitalist model, both the above tenets are descriptively false. Both tenets are based on metaphors.

The first tenet, that each unit produces its own marginal product, is based on the animistic personalization of non-human factors of productions as "agents" using the pathetic fallacy, e.g., Friedman's reference to "what ... the instruments he owns produces." A unit of a non-human factor does not "produce" its marginal product because it does not produce at all. It is used in production by human beings carrying out the productive process.

The second tenet, that each units gets its marginal product, is based on the distributive shares metaphor. A hired factor owns no share of the product; the residual claimant appropriates the whole product. The income paid to a factor-supplier represents not a share in the product but only the satisfaction of the liability for the used-up factor, a liability which is part of the whole product appropriated by the residual claimant.

Note that this analysis and critique of MP theory has nothing to do with whether the competitive model in fact applies to reality. Both the central tenets of the theory are false (as just explained) even in the competitive model.

Friedman's "capitalist ethic" is that each factor owner should metaphorically "get" what he or his factors metaphorically "produce." By using one metaphor to justify another metaphor, the "capitalist ethic" can make a perfectly clean break with reality. The non-metaphorical facts are that labor is the de facto responsible agent of production, that labor is de facto responsible for both the positive and negative results of production (the whole product), and that one party legally appropriates the whole product.

There is a dual or inverse mythology that can be used to provide an ideological interpretation of marginal cost theory. Instead of using the active inputs view to picture the inputs as responsible agents producing the positive product (first tenet), use the active outputs view to picture them as agents using up the inputs (i.e., producing the negative product). Instead of imputing to each input "what it produces" (second tenet), impute or charge to each output "what it uses up." In value terms, each unit of the output would be charged the marginal cost and, indeed in competitive equilibrium, the price of the output is equal to marginal cost ("P = MC"). Thus one might say "each output buyer is liable for what his commodity used up."

These dual or inverse metaphors are faulty for the same reasons as the primal or original metaphors. Outputs are not responsible for using up the inputs; the people who work in the firm are the ones who perform the responsible human actions that use up the inputs in the course of producing the outputs. And the legal liabilities for the used up inputs are not assigned to the outputs or consumers. By the market mechanism of appropriation, those liabilities are laissez faire appropriated by the last owner of the used up inputs–all of which is a technical way of saying the costs lay where they fall unless a court reassigns them. The last-owner of the inputs thereby gets the legal claim on the appropriable outputs which, in turn, are sold to the consumer.

Our point in outlining these inverse metaphors is not to add to the conventional inventory of "stories" but to subtract from it. The original and inverse stories cancel out. The output-buyers do not use up the inputs anymore than the input-sellers produce the outputs. The workers both use up the inputs and produce the outputs. And the output-buyers do not appropriate distributive shares in the negative product anymore than the input-sellers appropriate shares in the positive product. Both the positive and the negative product, i.e., the whole product, is appropriated by the same legal party, the party who is thereby called the "firm."

We have throughout emphasized the algebraic symmetry (positive and negative) in property theoretic reasoning in general and in the concept of the whole product in particular. The inverse myths giving an ideological interpretation of marginal cost theory show that the same symmetry is present in price theory. That ideological interpretation is not prominent in the capitalist literature since the charge against the system is the charge of "exploiting labor" and thus the main focus is on interpreting MP theory.

Liberal economists are much concerned to show how they transcend the "naive productivity ethics" embodied in some presentations of MP theory. But the standard liberal "critique" of MP theory [e.g., Thurow 1975, Appendix A] does not attack either of the basic tenets. The standard critique is based on essentially two points:

• ¥ MP theory does not account for the initial personal distribution of property or other prices that determine each person's "share of the product" and
• ¥ the perfectly competitive model is far from applicable to the real world.

Economists point out that MP theory gives no account whatever of the original personal distribution of factor ownership. Thus MP theory, coupled with a theory of input supply and product prices, can at best only give an account of the functional distribution of income, not the personal distribution of income. In the same vein, critics of conventional capital theory point out that owning capital is not a productive act so the product of capital should not be confused with the product of the capitalist.

Secondly, MP theory is almost totally non-operational. The many gaps between the idealized competitive model and the real world include:

• non-competitiveness of real markets,
• disequilibrium states,
• extreme measurement problems to determine marginal productivities,
• indivisibilities,
• informational imperfection of markets, and so forth.

The point is that this standard critique is thunderously silent about criticizing the first and second tenets of MP theory (that each unit of a factor produces its marginal product, and that each unit gets its marginal product).

Thus it is that economists can be in comfortable conformity with the core ideological content of the theory while at the same time striking an outward posture of "criticizing" marginal productivity theory. Economists who deny that the product of capital is the product of the capital owner have missed the point. The point is that capital itself does not "produce" at all; capital is used by Labor to produce the outputs. We show below how Labor produces the marginal product of capital.

Professor Friedman's capitalist ethic–"To each according to what he and the instruments he owns produces"–is clearly an attempt to generalize the Lockean principle that each person should reap the fruits of his labor. It is precisely this use of MP theory as a reinterpreted fruits-of-one's-labor (and instruments) doctrine that has made it so ideologically powerful and controversial.

The development of MP theory as a counterfeit labor theory of property can be followed in remarkable detail. For instance, in view of the equivalence between the labor theory of property and the juridical norm of imputation, the labor theory of property can be expressed in two vocabularies, that of property appropriation and that of responsibility imputation. Accordingly, MP theory imitated the labor theory by using precisely those two vocabularies. John Bates Clark [1899] was the "marginalist Locke" who developed MP theory using the vocabulary of property appropriation, and Friedrich von Wieser [1889] developed MP theory using the other vocabulary of responsibility imputation.

The basic idea is to picture each factor as "producing" its marginal product. Is that what each factor "gets"?

In competitive equilibrium, each factor price is the value of its marginal productivity. Hence, Clark concludes that each factor "gets" the share of the product it "produces" in competitive equilibrium; to labor the fruits of labor, to capital the fruits of capital, and to land the fruits of land. In this manner, Clark and later MP theorists have brilliantly attempted to co-opt the labor theory of property and to harness it in the defense of competitive capitalism.

The development of the ideological interpretation of MP theory using the vocabulary of responsibility and imputation was due to Friedrich von Wieser. Wieser's contribution is remarkable because he is one of the few conventional economists who admitted in print that of all the factors of production, only labor is de facto responsible. Thus the imputation of legal responsibility in accordance with de facto responsibility will go back through the instruments solely to the human agents.

These are astonishing remarks. Wieser at last sees the explanation of the old radical slogans "Only labor is creative" or "Only labor is productive," which even the classical laborists and Marxists could not explain clearly.

The fact that only labor could be legally or morally responsible did not, however, lead Wieser to question capitalist appropriation. Wieser's response to his insights exemplifies what passes for moral reasoning among many economists and social theorists in general. Any stable socio-economic system will provide the conditions for its own reproduction. The bulk of the people born and raised under the system will be appropriately educated so that the superiority of the system will be "intuitively obvious" to them. They will not use some purported abstract moral principle to evaluate the system; the system is "obviously" correct. Instead the moral principle itself is judged according to whether or not it supports the system. If the principle does not agree with the system, then "obviously" the principle is incorrect, irrelevant, or inapplicable.

The usual juridical principle of imputing responsibility, which recognized that only labor could be responsible, was clearly not relevant to the tasks facing capitalist economics. The usual notions would apply to merely judicial questions about the capitalist property system, whereas economists are concerned with the deeper economic questions of price theory. Capitalist apologetics would require a new notion of "economic imputation" in accordance with another new notion of "economic responsibility".

By defining "economic responsibility" in terms of the animistic version of marginal productivity, Wieser could finally draw the conclusion demanded by his calling: to show that competitive capitalism "economically" imputes the product in accordance with "economic" responsibility.

Metaphors are like lies; one requires others to round out the picture. The Clark-Wieser theory uses one metaphor to justify another metaphor. Each factor's metaphorical responsibility for producing a share of the product is used to justify each factor's metaphorical property share in the product. By justifying one metaphor with another metaphor, capitalist apologetics can "slip the surly bonds" of reality and soar freely in the metaphorical void. It is the actual property relations of capitalist production, i.e., the employer's appropriation of the whole product, that need to be judged, and the notion of responsibility relevant to the structure of legal property rights is the normal non-metaphorical juridical notion of responsibility that is used every day from "the judicial point of view."

Moral philosophers understand the difference between the actions of persons and the services of things. Can they see MP theory as a bogus imitation of the labor theory of property?

Instead of differentiating MP theory from the labor theory of property, Rawls merely goes on to repeat the standard liberal critique of MP theory as not accounting for the background distribution of factors and the forces of supply and demand affecting prices.

The ideological hegemony of MP theory is evidenced by the fact that a leading moral philosopher such as John Rawls never questions the central tenet of MP theory that competitive capitalism would realize the "precept of contribution." Rawls only fusses about the background conditions which he feels limit the applicability of the precept of contribution.

The concept of marginal productivity is a very useful analytical notion that needs to be rescued from the animistic-active and engineering-passive interpretations so that it can be understood in a manner consistent with the fact that persons act and things don't. One does not have to treat persons as things or things as persons in order to trace out the logic of resource allocation (the forte of neo-classical economic theory).

Consider, for example, the "marginal product of a shovel" in a simple production process wherein three workers use two shovels and a wheelbarrow to dig out a cellar. Two of the workers use two shovels to fill the wheelbarrow which the third worker pushes a certain distance to dump the dirt. The marginal productivity of a shovel is defined as the extra product produced when an extra shovel is added and the other factors, such as labor, are held constant. The labor is the human activity of carrying out this production process. If labor was held "constant" is the sense of carrying out the same human activity, then any third shovel would just lie unused and the extra product would be identically zero.

"Holding labor constant" really means reorganizing the human activity in a more capital intensive way so that the extra shovel will be optimally utilized. For instance, all three workers could use the three shovels to fill the wheelbarrow and then they could take turns emptying the wheelbarrow. In this manner, the workers would use the extra shovel and by so doing they would produce some extra product (additional earth moved during the same time period). This extra product would be called the "marginal product of the shovel," but in fact it is produced by the workers who are also using the additional shovel. In the workers' new whole product, the positive product is expanded by the extra output and the negative product is expanded by the utilization of the services of an extra shovel.

Let the four components of the property vectors be as follows:

(Cubic Yds. per day, Shovel-days, Wheelbarrow-days, Man-days).

Before adding the third shovel, suppose the three workers use the two shovels and the wheelbarrow to move 10 cubic yards of earth in a day. The day's whole product vector produced by Labor is

(10 Cu.Yds., –2 Shovel-days, –1 Wheelbarrow-day, –3 Man-days).

By reorganizing the work process to utilize a third shovel, the three workers move 12 cubic yards a day. Hence the new whole product produced by Labor is

(12 Cu.Yds., –3 Shovel-days, –1 Wheelbarrow-day, –3 Man-days).

Labor's extra product is: (2, –1, 0, 0) = (12, –3, –1, –3) – (10, –2, –1, –3).

Labor's extra positive product is (2,0,0,0), the extra two cubic yards, and Labor's extra negative product is (0,–1,0,0), the used-up shovel-day. The ratio of Labor's extra positive product of 2 cubic yards over Labor's extra negative product of 1 shovel-day gives the "marginal product of a shovel" in physical terms, two cubic-yards per shovel-day.

It is only an animistic metaphor to picture each factor as "producing" its marginal product. Capital does not "produce" its marginal product. Capital does not "produce" at all. Capital is used by Labor to produce the output. When capital is increased, Labor produces extra output by using up the extra capital. The "marginal product of capital" is the ratio of Labor's extra positive product over its extra negative product.

The point can also be illustrated using more abstract notation with three-component vectors representing (output, capital services, labor services). Prior to adding the extra capital services D K, the workers produced the

Original Labor's product = (Q, –K, 0) = (Q, –K, –L) + (0, 0, L)

= Orig. whole product + Labor services.

New Labor's product

= New whole product + Labor services.

The increment to Labor's product is:

In the shovel example, the workers additionally produced the "marginal product of the shovel" by using up the services of one more shovel. The factual non-metaphorical description of the "marginal product of the shovel" has exactly the same implications for MP theory in its role as a non-ideological theory of input demand. If the value of their extra positive product exceeded the value of their extra negative product, then it would be profitable (other things being equal) to use the extra shovel.

If a shovel could be rented for $1 a day and the removal of a cubic yard of earth was worth $.75, then the value of Labor's extra positive product (2 x .75 = $1.50) exceeds the cost of Labor's extra negative product ($1) so it would be worthwhile to rent the shovel.

In this manner, the concept of marginal productivity can be understood in an analytically useful fashion while recognizing a basic fact of the social sciences that people act and things don't.

The debate surrounding "the labor theory" in economics provides a fascinating illustration of the role of ideology in the social sciences. Orthodox economists earnestly try to understand the labor theory (or, at least, portray themselves that way). Why should so many people adopt the labor theory which singles out just one input, labor, as the only productive or creative input? What is so special about labor? Economists have a terrible time answering that question–not because the answer isn't obvious–but because the obvious answer is not ideologically acceptable.

The answer–that only human actions (a.k.a., labor services) can be responsible–is quite easy to understand. It is not an obscure esoteric fact that only humans can be responsible, and that tools, no matter what their causal efficacy, cannot be responsible for anything. When explained, students have no trouble understanding it–even children can grasp the point. College students can even understand that burglary tools are not responsible for a share of the burglary even though they have positive marginal productivity.

But economists seem to have a "professional blindspot." Look at the explanation given for the "labor theory of value" in the economics texts of our day. This author has not been able to find a single economics textbook which makes the point about the unique responsibility of human actions in contrast to the causal efficacy of the services of things. Not one.

For instance, William Baumol is a neo-classical economist who, over the years, has made a serious attempt to sympatheticly understand and interpret Marx's labor theory of value and exploitation. Yet when it comes to the point most fundamental in a "labor theory" to specify what is relevantly unique about labor, Baumol can only say that labor is the only "human" or "social" input.

One might readily agree that in some sense labor is the only human or social input, but Baumol gives no shred of explanation how that would make labor into the only "creative" or "productive" factor or into the sole source of the value of the product. The point is not to find some unique attribute of labor, e.g., labor services are the only services performed by featherless bipeds. The point is to determine if labor has some unique attribute relevant to the analysis and/or critique of capitalist production.

Economists are puzzled at how anyone could think that labor was the only "productive" agent overlooking capital, land, and time. Even if capital can be dissolved into past labor, there is still land including all natural resources and time. Proponents of the labor theory of value "seemed to deny that scarce land and time-intensive processes can also contribute to competitive costs and to true social costs..." [Samuelson 1976, 545]. What could those proponents possibly have meant? Fortunately, the advance of modern economic science allows contemporary economists to discover the existence of land and time as scarce and efficacious factors and thus to advance beyond those early economists who thought that labor was the only "productive" factor.

Contemporary texts have a studied ignorance of the fact that labor is the only responsible agent of production. They ignore the possibility that the early radical proponents of the "labor theory of value" (e.g., the so-called Ricardian socialists) may well have meant "productive agent" in that sense of "responsible agent."

"Responsibility" is the "R-word" that cannot be used in contemporary economics. The unique responsibility of labor is unmentioned in contemporary texts. The reason cannot be the "subtley" of the notion since the non-responsibility of burglary tools in spite of their causal effectiveness is understandable by any intelligent person. The reason cannot be simple ignorance since, as the previous quotation from Wieser shows, the unique responsibility of labor has been explicitly pointed out in the capitalist literature (a century ago). Economists should also be aware of it from their general background knowledge.

Perhaps orthodox economists recognize the unique responsibility of labor but consider it an irrelevant characteristic–like workers being featherless bipeds. That position is difficult to sustain since neo-classical economists themselves formulate the basic problem of distribution as a problem of imputation–the problem of ascribing or attributing the product to the various factors. In fact, it was Wieser who introduced the word "imputation" (Zurechnung) and who considered it the problem of determining "economic responsibility." All this is viewed through the distorting lens of the distributive shares metaphor (seeing the product as being divided) and the pathetic fallacy (seeing causal efficacy as responsibility). But when economists formulate the question of distribution using metaphors of "imputation," "attribution," "ascription," and "economic responsibility," then it is difficult for them to plausibly assert the irrelevance of the non-metaphorical notion of responsibility used every day in the legal system.

The simple truth is that orthodox economics ignores the unique de facto responsibility of labor because it is an ideologically unacceptable fact.