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Originally published in Some Terms and Their Uses, pg. The Role of Historiography, pg. Greece, pg. Rome, pg. Carthage, Alexandria, Nicaea, pg. Byzantium, pg. For a given amount of land, the more labor we apply to it, the smaller the marginal and average products. This the Classicals conceived as a natural truth with regard to agriculture alone. The basic idea was that land was in fixed supply and of differing quality.
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The most fertile lands were always used first and the less fertile ones only used later. Thus, the more the scale of production increases i. Now, the Ricardians argued that at least enough output must be generated to pay for the factors of production. The wage paid to labor is w and this reflects economic earnings entirely, i.
In contrast, land, although a factor of production, does not need to paid for. One can justify this in Classical terms by saying it does not need to be maintained intact; in Neoclassical terms, this implies there are no alternative uses for land and thus no opportunity costs to be compensated.
However, and this is the gist of the Classical Ricardian story, although land makes no economic earnings, we see that because land is fixed in supply, it takes receives rental earnings. In fact, as we shall see, in Figure 3, all surplus in production resolves itself into rental payments for land. To see this, note that we can increase the scale of production, and thus take in more land and apply more labor, up until the marginal product of labor is equal to the subsistence wage.
Consequently, the surplus produced, defined as Y - wL, is the darkly shaded box in Figure 3. This is the amount of output that is produced over and above payments to factors. This remainder, the early Classicals contended, accrues to landowners , thus it is referred to as rent. The Marginalist Revolution demolished the Classical Ricardian theory of value. However, the Classical theory of distribution lingered on for a little while.
In the s, however, the Neoclassicals finally put forth their own theory -- the "Marginal Productivity" theory of distribution -- that was at the same a generalization and repudiation of the the Classical Ricardian story.
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Despite its late appearance, a general marginal productivity theory of factor price determination was already "in the air" by the s. We see hints of it in the work of J. Walker But it was not until thes that the Marginalists realized that the Ricardian "law of rent" applied to all factors and not merely land -- and that a new theory of distribution could be built on that basis. Hobson Clark and Hobson realized a very simple thing: the Classicals had claimed that the supply of labor is endogenous "men multiply like mice in a barn But, at least in theory, there is nothing "special" about the fixity of the supply of land and the variability in the supply of labor.
If we hold one factor fixed and vary the other, the rent principle should apply regardless: the quantity of the varying factor should be set where its economic earnings are equal to its marginal product. To see this, suppose that instead of varying the amount of labor applied to a fixed amount of land, why not apply varying amounts of land to a fixed amount of labor? In this case, the horizontal axis in Figure 3 would be T, the amount of land, and the curves MP and AP curves would reflect the marginal product and average product of land.
Stipulating a fixed payment per unit of land analogous to the wage , and we would reach the same conclusion: land would be employed up until its payment per unit is equal to its marginal product. Total output would still by the entire box, with the lightly-shaded box representing payments to land and the remainder the dark-shaded box representing payments to the other factors - in this case, labor. The Classicals were not unaware of this possibility. However, they contended that factor shares, computed in this way, would fail to "add up" to total output.
Now, suppose we try calculating the returns on the factor via this procedure. So far so good.
The Classical Theory of Concepts
The more enlightened Classical economists would say that, yes, perhaps such a calculation could be made, but that it revealed nothing about the theory of distribution. It is a simple accounting principle. Thus, the Classicals were willing to admit, to some extent, that there was nothing "special" about the fixity of land and the flexibility of capital-and-labor in principle , that marginal products could be calculated by fixing other things and and varying other things.
But such exercises, the Classicals contended, revealed nothing about distribution because there is no reason to presume that all three cases hold simultaneously.
In other words, it is not necessarily true that when calculating factor payments by marginal products, i. Thus, the Classicals concluded, exercises that try to calculate marginal products of other factors serve no real end as they will not "add up". But John Bates Clark , contended that this equality would hold. In other words, he asserted that when each factor is paid its marginal product, the sum of factor incomes will exhaust total output.
This proposition became known as the marginal productivity theory of distribution or the product-exhaustion theorem. Clark himself provided a rather loose verbal "proof" of this contention. Philip H. Wicksteed was the first to prove it mathematically. However, Wicksteed also revealed that there was a necessary condition for this to hold: namely, the aggregate production function must be linearly homogeneous. Wicksteed's proof, as A. Flux noted in his review, was a simple application of Euler's Theorem. Namely, by Euler's Theorem, if a function is homogeneous of degree r, then, then:.
But this is precisely the product-exhaustion result we were looking for! So, in sum, the marginal productivity theorem of distribution says that if all factors are paid their marginal products, then the sum of factor incomes will add up to total product.
The marginal productivity theory caused something of a little tornado around the turn-of-the-century, which deserve some attention as they helped clarify what the theory says and what it does not say [accounts of the debates surrounding marginal productivity abound -- those of Joan Robinson , George Stigler Ch. Also worthwhile are the accounts by Henry Schultz , Dennis H.
Robertson and Paul Douglas ]. One of the immediate debates surrounded that of priority. Who "discovered" the marginal productivity theory of distribution? The first verbal exposition of the marginal productivity hypothesis is due to John Bates Clark , which was followed up in Clark , and, independently, Hobson Largely unaware of Clark, Philip H. Wicksteed presented the same theory and proved the product-exhaustion theorem mathematically, although, as noted, it was A.
Flux who noted the equivalence between Wicksteed's mathematical statement and Euler's Theorem.
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Here a few strange footnotes begin. Enrico Barone had discovered marginal productivity theory independently, but his work was published after he had become aware of Wicksteed's achievement Barone, , , thus his claim to priority was unluckily lost. This blatantly opportunistic move outraged even Walras's supporters, and he duly withdrew the note in the fourth edition of his book. During this sorry affair, Knut Wicksell rose to defend of Wicksteed's claim as discoverer of the theory. But in a surprising twist, it turns out that Wicksell had actually discovered it himself in -- before Wicksteed -- and had just forgotten about it!
To add a bizarre finale, it turns out that a Lausanne mathematician, Hermann Amstein, had basically handed Walras the entire product-exhaustion theorem and its proof in , but Walras had not understood the mathematics and consequently ignored it cf. Despite the fight over priority, the marginal productivity theory of distribution was not immediately embraced by other economists, not even the other Neoclassicals, largely because it was not clear what the theorem said nor what its implications were.
As such, it might be useful to clarify a few points of confusion. The first and most straightforward error which is sometimes repeated today is to assume that the marginal productivity theory says that factor prices are determined by marginal products.
The tone of the exposition in John Bates Clark sometimes implies this, and many contemporaries took it at face value.
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