The Paretian Revival

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Bator's diagrammatic
demonstration of Paretian general equilibrium

The "Paretians" refers to the Neoclassical general equilibrium theorists of the period 1910-1950 who concentrated on the themes outlined by Vilfredo Pareto's Manual of Political Economy (1906): namely, the analysis of individual optimization, market efficiency and social optima via classical programming techniques (differentiable calculus, Lagrangian multipliers, etc.). Naturally, Pareto is himself a member of the "Lausanne School", and thus much of his own work draws upon that of Leon Walras and others. However, unlike Walras, Pareto enjoyed something of a faithful following, at least in Italian-speaking circles. Walras's own concerns - e.g. existence and stability of equilibrium - took a very different route. It was largely ignored during this time period and only really took off in the 1950s, during what we refer to as the "Neo-Walrasian" phase of general equilibrium theory. In contrast, Pareto's research program, channeled primarily by Enrico Barone (1908, 1912), was taken up in the first half of the century, particularly in the Giornale degli economisti.

The Paretian Revival reached its height of activity in the 1930s and 1940s, through John Hicks, Paul Samuelson, Abba Lerner, Oskar Lange, Maurice Allais, Harold Hotelling and others. The 1930s thus represent the "resurrection" (or "consolidation") of the Marginalist Revolution, which had begun to run out of steam in the 1890s and was in a moribund state by the 1920s. It also represents the first time that the work of the "Lausanne School" began breaking the English-language barrier.

During the 1930s and 1940s, there were at least four discernable locations that could be deemed to be the home of "Paretian" economics during this time period: the L.S.E., Chicago, Harvard, and the French planning school. Much of the Paretian research program is captured in the grand treatises of the 1930s and 1940s: John Hicks's Value and Capital (1939), Maurice Allais's A la recherche d'une discipline economique (1943), Paul Samuelson's Foundations of Economic Analysis (1947) and Abba Lerner's Economics of Control (1944). The Journal of Political Economy was, early on, its main home, but it was given a very big boost by the founding of two new journals, Econometrica and the Review of Economic Studies.

The first task of the day was the rigorous derivation of demand curves from individual utility-maximization subject to a budget constraint. This was a minor concern for Walras, but a central one for Pareto and Barone. This was pursued by W.E. Johnson (1913) and Eugene Slutsky (1915) and resurrected by John Hicks and R.G.D. Allen (1934). Grounding these results in preference theory was pursued by Ragnar Frisch (1926), Nicholas Georgescu-Roegen (1936) and Herman Wold (1943). Production theory was also recast in the Paretian mould and derived formally from profit-maximization production decisions by Harold Hotelling (1932, 1935), R.G.D. Allen (1938), John Hicks (1932, 1939), Paul Samuelson (1947) and Ragnar Frisch (1965).

The use of the calculus and Lagrangian multipliers in Paretian consumption and production theory permitted these components to slip easily into place into a single, all-encompassing "Paretian" theory of general equilibrium by the grand Paretians (Hicks, Lange, Allais, Samuelson, etc.). International trade theory, which often employed two-sector model reasoning, was a particularly fertile ground for this approach -- as we see in the work of Abba Lerner (1932, 1934, 1936), Theodore Yntema (1932), Jacob Mosak (1944), Paul Samuelson (1938, 1948) and others.

Yet the most distinctive aspect of the Paretian system was the "New Welfare Economics" of the late 1930s, which sought to connect criteria for "efficiency" to competitive equilibria. The first step towards this was the famous "marginal cost pricing" principle introduced by Abba Lerner (1934) and Harold Hotelling (1932, 1938), and taken up with fervor by the French engineer-economists. The greatest result of this research avenue were the two Fundamental Welfare Theorems, originally suggested by Pareto and Barone: namely, that every competitive equilibrium is Pareto-optimal (First Welfare Theorem) and that any Pareto-optimal allocation can be obtained as a competitive equilibrium given an appropriate transfer of initial endowments (Second Welfare Theorem). The Fundamental Welfare Theorems were demonstrated graphically by Abba Lerner (1934) and then proved mathematically by Oskar Lange (1942) and Maurice Allais (1943). Abba Lerner (1936) and Oskar Lange (1938) went on to use the results on Paretian efficiency to pursue the case for economic planning and market socialism in the Socialist Calculation debate with the Austrian School.

Correlated with this debate was the definition of the social optimum, i.e. which Pareto-optimal allocation is "the best". This was the heart of the "New Welfare Economics", to which the London School of Economics (L.S.E.) provided its great contingent of scholars, despite the opposition of Lionel Robbins (1934) to such an exercise. Nicholas Kaldor (1938) and John Hicks (1939) proposed a new set of compensation criteria by which one could judge allocations that are not comparable by the Pareto criteria. Criticisms and suggestions for improvements of the Kaldor-Hicks criteria were pursued by Tibor Scitovsky (1941), Paul Samuelson (1950), Ian M.D. Little (1950) and William M. Gorman (1955). A different approach to the social optimum was followed by the Harvard contingent, via the "social welfare function" introduced by Abram Bergson (1938) and expanded upon by Paul Samuelson (1938, 1947, 1950), Gerhard Tintner (1946) and Jan de Van Graaff (1957). Other notable contributions to welfare theory in this time period included Hicks's "rehabilitation" of the Marshallian consumer's surplus via compensating and equivalent variations ( Hicks, 1940, 1956), the "theory of second best" (Boiteux, 1956; Lancaster and Lipsey, 1956) and the theory of public goods (Samuelson, 1954).

The Paretian school received what was effectively a broad-side challenge by the "Neo-Walrasian" system of Koopmans, Arrow and Debreu, along two fronts. Firstly, by dispensing with differentiability and placing convex analysis at the center of their system, the Neo-Walrasians abandoned many of the old Paretian concerns which required them, e.g. public goods, marginal cost pricing, increasing returns, etc. Secondly, Arrow's Impossibility Theorem on social choice orderings seemed to dishearten much of the social optimum literature which had sprung around the New Welfare Economics. This was not a permanent exclusion: the field of social choice spawned its own literature and items like public goods, marginal cost pricing, increasing returns, etc. eventually re-emerged in the Neo-Walrasian framework, although in a somewhat different dress.

Early Lausanne School Paretians

The Grand Paretians

The London School of Economics Contingent

The Harvard Contingent

The French Contingent

The Chicago Contingent

Later Paretians and their Critics

Resources on the Paretian School

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