Unhappy News about Knut Wicksell

Along with Philip Wicksteed, the Swedish economist Knut Wicksell (1851-1926) constructed an elegant neoclassical model of factor-income distribution that has been remarkably enduring. I have long admired Wicksell and admit to feeling sad that the GEM Project’s generalized-exchange macro model demonstrates that his signature contribution ought to be dumped.

Wicksell was one of the best of the 19^th-century economists who pioneered marginal analysis, transforming how economics is done. He is surely the most interesting of those apparently staid theorists. His pursuits included poetry, feminism, and politics. He was a vocal critic of the institution of marriage. He once gave a public lecture satirizing the Virgin Birth, for which he was imprisoned for two months. An ardent Malthusian, he aggressively championed birth control.

Unlike most early marginalists, Wicksell understood that unemployment would not be solved by competitive markets. Such labor-market failure instead requires government intervention. He also called for greater public spending on social services, notably education which he believed would help offset some of the income inequality that results from marginal-productivity factor pricing.

Neoclassical Factor-Income Distribution

Wicksell’s model crowded out the surplus-oriented classical analysis, accepted since Ricardo, of distributive shares. As noted, his Euler-theorem treatment of factor incomes within the market-centric general-equilibrium framework is still standard fare in modern textbooks, pretty much exhausting what modern theorists have to say on the topic. Labor inputs are simultaneously paid their marginal-product and opportunity cost of time, which once added up with the marginal products of other factors equals total revenues from first-degree homogeneous production. The model is viewed by many as the apogee of general-market-equilibrium welfare analysis, providing some ethical justification for the market distribution of income.

In the long aftermath of the interrelated Walrasian and marginalist revolutions, textbook macro models have been ever more carefully constructed within the neoclassical market-centric general-equilibrium framework. In the modern consensus version cobbled together by New Classical, RBC and New Keynesian theorists, a representative household solves an intertemporal expected-utility maximization problem in the context of competitive markets, rational expectations, and the universal restriction of optimizing exchange to the marketplace. The Wicksell-Wicksteed first-degree homogeneous two-factor income-distribution equation has long played a central role in mainstream macroeconomics:

X=ƒ(H,Ҡ)=H(δX/δH)+Ҡ(δX/δҠ);

XP=HP(δX/δH)+ҠP(δX/δҠ)=W^mH+P_ҠҠ,

where P_Ҡ denotes the market price of physical capital Ҡ, X is production, H is labor hours, P and W^m stand for the market price of output and labor respectively. In the textbook model, neoclassical distribution theory powerfully links technology and optimizing marketplace exchange, deriving equality between rational payments to inputs and total revenue of the firm. I have always wondered, however, why everybody does not know that the Wicksell (and Wicksteed) model is unsuited to a building-block role in the highly-specialized production that eventually dominated world economies since the first and second industrial revolutions.

Mainstream scholars, giving in to some Ptolemaic impulse, have for a long time simply ignored obvious problems rooted in large-scale production that sharply degrade Wicksell’s capacity to describe modern economies. First, factor-market prices calibrated by labor and capital marginal productivities do not exist for large, specialized firms. Second, constant returns to scale are, in most applications, an unacceptable assumption. It is interesting that Wicksell was the first to publish that the Wicksell-Wicksteed theory requires constant returns to scale. Third, positing large-firm labor pricing equal to market opportunity cost is broadly inconsistent with the evidence. Fourth, again contrary to the evidence and deeply damaging in policy-relevant applications, Wicksell implies the non-existence of pure profit.

Only the first problem may be sufficiently misunderstood by GEM Blog readers to require attention here. Large-scale production, ubiquitous after the Second Industrial Revolution, corrupts the analytic integrity of marginal productivities for both labor hours (δX_j/δH_j) and capital stock (δX_j/δҠ_j), depriving the Wicksell model of key microfoundations. Generalized rational exchange imposes H_j=Έ_j/Ź_j on labor services, where Έ_j denotes labor input that is in 1:1 technical correspondence with production; δX_j/δΈ_j is not measurable in the marketplace. (See the website’s e-book, chapter 2.) Meanwhile, large-establishment capital stock (Ҡ_j) is both insufficiently divisible and excessively firm-specific to support Euler-theorem distribution. (Chapter 3) Given indivisibility, portions of capital cannot be withdrawn in response to relatively small reductions in output, as illustrated by the absence of small-lot capital-stock liquidations in cyclical downturns. What is instead marginally withdrawn, with a cut in output, is some utilization of capital services (Ƙ_j) that are made available by the existing capital stock. That adjustment is consistent with layoffs.

The GEM Project provides a central place for capital services, distinct from capital stock, in the large-establishment technology space. Potential production (X_j^P) is described by a capacity function (X_j^P=ƒ(Ҡ_j)), where X_j^P is increasing in physical capital Ҡ_j and provides an upper bound on output (X_j(t)≤X_j^P(t)). Capital services (Ƙ_j), the measurement of which requires no knowledge of the contemporaneous interest rate, flow from the capital stock (such that Ƙ_j^P(t)=ƒ(Ҡ_j(t), ∆Ƙ_j^P/∆Ҡ_j>0, and Ƙ_j(t)≤Ƙ_j^P(t)).

Physical-capital indivisibilities in combination with optimizing workplace exchange must be accounted for in the specification of the large establishment’s production function and consequent factor-income distribution:

X_j(t)=ƒ(Έ_j(t),Ƙ_j(t));

P_j(t)X_j(t)=Wⁿ_jH_j(t)+ř^m(t)Ҡ^r_j(t)+P_j(t),

such that Έ_j(t)=Ź_j(t)H_j(t) and Ƙ_j(t)≤Ƙ_j^P(t)=ƒ(Ҡ_j(t)), while Wⁿ denotes the efficiency wage, ř^m is the market interest rate, P is pure profit, and Ҡ^r is the capital stock net of its sunk component (Ҡ^r=Ҡ–Ҡ^S), making the term (ř^m(t)Ҡ^r(t)) the market opportunity cost of the firm’s capital stock. (Chapter 3) Generalized-exchange modeling has established that, in large-scale production, neither labor hours nor capital services can be efficiently priced in the marketplace, breaking the Wicksell’s market mechanism that eliminates pure profit. The GEM Project’s technological space also accommodates increasing returns to scale, further enriching the capacity of the residual-claim distribution model to accommodate critical determinants of economic growth. Given pure profit’s role as a residual claim by owners of sunk capital on firm revenue net of production-related outlays, P_j can be greater than, less than, or equal to zero, providing signals needed for the rational management of production capacity.

The inherent nature of large-scale production prevents, in modern applications, reliance on textbook neoclassical modeling of factor-income distribution. It is, therefore, good news is that the GEM Project microfounds distribution that features a revival of Ricardian rent along the lines pioneered by Michael Jensen (2000). Modern Ricardian rent is the subject of next week’s post.

Blog Type: Wonkish Chicago, Illinois