Neoclassical Shenanigans: Marginal Product as Contribution

Ur David Schweickarts bok After Capitalism (2002).

                      To the question, "what is capital?" Marx offered a straightforward answer: capital is "embodied labor"--the material result of past labor. The machine the worker is using, which so greatly enhances her productivity, is the product of other people's labor. The food the worker eats, purchased with her wages, is the product of other people's labor. When you think about it, says Marx, every conceivable good we consume comes from human beings working with and on nonhuman nature. These are the only factors of production--human labor (mental as well as physical) and nonhuman nature.
                      This is a dangerous thought. If there is only labor and nature--where does "the capitalist" enter the picture? It is clear that labor should be rewarded for its contribution to production. It is equally clear that nonhuman nature need not be. (It must be replenished or conserved, but that's a separate matter.) The capitalist also demands a reward, a "fair return on his investment"--but on what basis? 
                      The standard answer, taught in every introductory economics course, is that goods are the product of three factors of production--land, labor and capital--and that the owners of these factors are rewarded on the basis of their contributions. Well, land is clear enough--that's shorthand for natural resources (i.e., nature)--and labor is labor. But what then is capital? Tools? Technology? Money? Congealed time? Embodied labor? What?
                      Marx devoted the bulk of his greatest work (called, appropriately, Capital) to pursuing the implications of his answer. His conclusions were utterly unacceptable to the capitalist class, but not so easy to refute. Marx constructed his argument using "classical" value theory, the standard theory of his day, which had developed from Adam Smith through David Ricardo--the "labor theory" of value. It became necessary to reconstruct economic theory on a new foundation to avoid the uncomfortable implications of that particular theory. A new economics, a "neoclassical" economics, thus came into being, which zeroed in on this labor theory of value, criticized it, and offered an alternative theory, a "marginalist theory" of value. This new theory quickly replaced the treasonous old theory in all respectable quarters, and has remained to this day the dominant paradigm in the economics profession.
                      We needn't pursue the value controversy here, which is normally (if wrongly) presented as a controversy as to how best to understand prices. (Is the price of a commodity determined by the amount of labor it took to produce it, or by the "marginal utility" of the commodity to the consumer, that is, the satisfaction that one more unit of that commodity would give?) This celebrated controversy is a smoke screen. The real heart of the "neoclassical revolution" is its theory of distribution.
                      The fundamental problem confronting post-Marxian economic theory is the problem of explaining (and justifying) the profits of the capitalist. If a commodity, say corn, is the product of three factors, land, labor and capital (as the neoclassical account has it), how can we determine how much of the final product should be distributed to each of the claimants, landowners, laborers and capitalists? To be sure, a free market will set a rental rate, wage rate, and interest rate, and so bring about a distribution--but what grounds do we have for saying that this is a just distribution? (Lurking in the background here is the Marxian question: If labor is the source of all value, why should the landowners or capitalists get anything?)
                      Let's forget about the capitalist for the moment and concentrate on the remaining two factors. Clearly it takes both land and labor to produce corn. How should the product be divided between landlords and laborers? The neoclassical economist answers: it should be divided according to contribution. Each factor should get what it contributes.
                      Fine. That seems fair--but how do we know how much each factor contributes? At the end of the harvest, we have Z bushels of corn. How can we say that the workers contributed X bushels and the land contributed Y bushels? You can't just say that the competitive market will take care of the distribution. Why should we think this "invisible hand" distribution has anything to do with respective contributions? Why not just say that the workers did all the work, the landowner is a parasite, and be done with it?
                      John Bates Clark, one of the pioneers of neoclassical economics, acknowledged the seriousness of this question:

The welfare of the laboring class depends on whether they get much or little; but their attitude toward other classes--and therefore the stability of society--depends chiefly on the question of whether the amount they get, be it large or small, is what they produce.  If they create a small amount of wealth and get the whole of it, they may not seek to revolutionize society; but if it were to appear that they produce an ample amount and get only a part of it, many of them would become revolutionists and all would have the right to do so.[i]
                      Surprisingly enough, Clark and his neoclassical colleagues were able to answer the question in a non-circular manner. This is no mean feat. Here we have sacks of corn, the result of the harvest. Without making any question-begging references to competitive markets, you cannot say, can you, how much of that corn is due to labor and how much due to land? The neoclassical economist smiles and replies, "But I can. Not only that, I can prove to you that in a competitive capitalist economy, the market will set the wage rate at exactly the contribution of the laborer and the rent at exactly the contribution of the land. I can also show that if we allow monopoly--either of laborers or landowners--the market will not distribute in accordance with contribution but will return to the monopolists more than they contribute."
                      The argument is technical, but worth understanding, for it has had enormous ideological impact, and has done much to give neoclassical economics an aura of scientific respectability. Let me explain it by way of an example. Suppose we have five acres of land and ten workers. We will assume that the land is of uniform quality and that the workers are equally skilled. At the end of harvest, we have one hundred bushels of corn. How many were contributed by the land, and how many by labor?  (The restless reader will want to say, "This is silly. Obviously each and every bushel required both land and labor." But wait . . .)
                      Let us calculate the "marginal product" of labor. Suppose one worker were to work the five acres and suppose the yield is twelve bushels. Now let two workers work the land. Because there is plenty of land, and because they can cooperate and take advantage of economies of scale, they will likely produce more than twenty-four bushels.  Let us suppose they produce twenty-six. In this case we will say that the "marginal product" of the second worker is fourteen--the gain in total production brought about by adding that second worker to the workforce. (In reality no one is going to conduct this experiment. The point is simply that these marginal products have scientific validity because they could, in principle, be calculated experimentally.)
                      Now use three workers. If there are still economies of scale to be had, his marginal product might be even higher, perhaps fifteen bushels. Sooner or later, however, economies of scale give way to "diminishing returns," that basic, beloved law of neoclassical economics. After a while, the laborers begin to crowd one another. Adding a new laborer will increase production, since the land can be cultivated more intensively, but the extra output you get by adding another laborer, his marginal product, is less than what you got from the last one. If we graph the marginal product of each laborer, we have a step curve that rises for a while, but then steadily declines (figure 2.1).
                      Suppose we define the "contribution" of each worker to the total output of ten workers working five acres (in our example, one hundred bushels) to be the marginal product of the last laborer. Suppose this is six bushels. In that case the total contribution of labor is sixty bushels, ten times the marginal product of that last laborer. Graphically, this is the shaded portion of the area under the step curve in the top graph.

Figure 2.1  Marginalist Calculation of the Contributions of Labor and Land
                      This might seem to be a wholly arbitrary definition. Why should the contribution of each worker be defined as the marginal contribution of the last worker? To be sure, we have assumed them all to be equally skilled, and it is true that if we pulled any one of them from production, the total product would decline by exactly the marginal product of the last worker, but so what?  If we removed two workers, the total product would decline by more than their combined "contribution." If we removed them all, there would be no product at all. What is so special about the marginal of the last worker?
                      Well, consider the following. Suppose we reverse our procedure and calculate the marginal product of the land. Suppose we hold our labor force constant, and have them work first one acre, then two acres, then three, four and five, each time calculating the marginal product of the land. We'd likely see similar phenomenon to what we observed with labor. At first there would be increasing returns to scale, so the marginal product of land would go up, but then, after a while, diminishing returns would set in. Adding an additional acre would always increase total production, but adding that fifth acre wouldn't increase the output by as much as adding the fourth because the workers would have to spread themselves ever more thinly. Suppose we define the "contribution" of each acre of land to be the marginal product of the last acre--just as we defined the contribution of each worker to be the marginal product of the last worker. Thus, the total contribution of the land is the shaded area of the lower graph.
                      Notice, we have derived both the contribution of labor and the contribution of land from purely technical considerations. We have made no assumptions about ownership, competition, or any other social or political relationship. No covert assumptions about capitalism have been smuggled into the analysis. Notice too, we have a technical problem on our hands. We have determined, by means of a rather esoteric definition, both the contribution of labor and the contribution of land--but what makes us think these contributions are going to add up to the total product? What grounds do we have for thinking that the shaded area of the top graph will equal the white area of the bottom graph and vice versa? If they don't, then we cannot claim to have separated our hundred bushels of corn into the respective contributions of labor and land.
                      But they do add up. That's the mathematical result that gave neoclassical economics its intellectual respectability. In fact, the portions don't always add up. In an example such as I've given, they probably wouldn't. But if the numbers are large--of workers and acres--and if you make enough assumptions about homogeneous fertility and skills, substitutability of land and labor, and diminishing returns, then Euler's Theorem can be invoked--a purely mathematical result having nothing to do with economics per se (first proven by the great eighteenth century mathematician Leonard Euler)--to demonstrate that the total product will in fact be equal to the contribution of labor (defined as the marginal product of the last laborer multiplied by the number of laborers) plus the contribution of land (defined as the marginal product of the last acre multiplied by the number of acres.)
                      A remarkable result, which, moreover, can be extended to include capital. If we allow capital into our story, say, money to purchase seed and tools, it can be shown that our corn harvest subdivides neatly into the contribution of land, labor and capital. Moreover--as mentioned above--it can be further demonstrated (again with appropriate simplifying assumptions) that a free competitive market will set the land rent at the marginal product of land, the wage rate at the marginal product of labor, and the interest rate at the marginal product of capital. (Actually, the argument concerning capital is a whole lot murkier and more controversial than the argument for land and labor, but we needn't go into that.)
                      A remarkable technical accomplishment, separating out quantities associated with each separate factor in such a way that they all add up to the total output--but utterly bogus as an ethical argument. Our original objection was correct: there is something arbitrary in defining the "contribution" of each laborer to be the marginal product of the last laborer. Actually, not "arbitrary." "Deceptive" is a better word. To call the marginal product of the last laborer the "contribution" of each laborer is to invoke an ethical category suggesting entitlement. Since each worker "contributed" that amount, each is entitled to that amount, right? And lo and behold, that's exactly what the free market gives the worker. In a competitive free market economy, wages are what they should be, rent is what it should be, interest is what it should be. Monopolies generate injustice, but pure competitive capitalism is fair capitalism. Workers get precisely what they contribute--and hence have no right to "become revolutionists."
                      But this conclusion, so much more comforting to landlords and capitalists than Marx's conclusion, in no way follows from the technical premises of the argument. Suppose our ten workers had cultivated the five acres as a worker collective. In this case they would receive the entire product, all one hundred bushels, instead of sixty. Is this unfair? To whom should the other forty bushels go? To the land, for its "contribution"? Should the collective perhaps burn forty bushels as an offering to the Land-God? (Is the Land-Lord the representative on earth of this Land-God?)
                      We can see that a moral sleight-of-hand has been performed.  A technical demonstration has passed itself off as a moral argument by its choice of terminology, namely, by calling a marginal product a “contribution.” The "contribution = ethical entitlement" of the landowner has been identified with the "contribution = marginal product" of the land. Had we not called that marginal product "contribution," it would have been impossible to conclude that our original question had been answered. We wanted to know why we should think that what the market gives the landlord has anything to do with his actual contribution. To say that the market gives him sacks of corn equal to the marginal product of his last acre multiplied by the number of acres he owns in no way answers the question. Why should that amount count as his contribution?
                      At issue here is something more than just a quantitative problem, our inability to specify the magnitude of the landowner's contribution. We have a quantitative problem because we have a qualitative problem. What is the exact nature of the landowner's "contribution" here? We can say that the landlord contributed the land to the workers, but notice the qualitative difference between his "contribution" and the contribution of his workforce. He "contributes" his land--but the land remains intact and remains his at the end of the harvest, whereas the labor contributed by each laborer is gone. If the laborers do not expend more labor during the next harvest, they will get nothing more, whereas the landowner can continue to "contribute" year after year (lifting not a finger), and be rewarded year after year for doing so. Labor and land (and capital) are not so symmetrical as the neoclassical tale makes them appear to be. Our "factors of production" do not meet as equals on a level playing field. The owners of one of the factors must expend their physical and mental energy year after year to continue their "contribution," whereas the owners of the other two factors need do nothing at all.
                      I am not saying that in actuality landlords and capitalists do nothing. Often they too expend physical and mental energy during the process of production (although often they do not). What is interesting, indeed paradoxical, about the neoclassical argument is that in making enough simplifying assumptions to be able to so elegantly invoke a mathematical theorem, it assumes away everything the landlord or capitalist might actually be doing to justify his reward. In the neoclassical story landlords and capitalists are wholly passive. They don't supervise workers; they don't invent anything; they don't make any decisions as to what to produce or what technologies to employ. They are wholly absent from the production process, merely
granting permission  for their land and capital to be used--in exchange for a healthy cut of the proceeds. But since "granting permission" is not a productive activity, Marx's question retains its bite. To produce material goods, we need human labor and we need nonhuman raw materials--but why do we need landlords or capitalists?

[i]. John Bates Clark, The Distribution of Wealth (New York: Kelley and Millman, 1956), 4. [Originally published in 1899] 

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