## Mathematical Investigations in the Theory of Value and Prices. Offprint from: Transactions of the Connecticut Academy of Arts and Sciences, Vol. IX, Part I, July 1892.

[New Haven, CT: Published by the Academy and printed by Tuttle, Morehouse & Taylor, 1892].

First edition, extremely rare offprint, of Fisher’s “startlingly original PhD thesis” (Blaug), which expounds his monetary theories and which established his international reputation. “As a graduate student at Yale he produced what Paul Samuelson has called ‘the greatest dissertation in economics ever written’ (quoted by Barber, in *The Works of Irving Fisher* (1997), Vol. 1, p. 4). In this work, entitled ‘Mathematical Investigations in the Theory of Value and Price’, he used algebra, geometry, calculus, vector analysis, and fluid mechanics to articulate or clarify the fundamental theorems of the marginalist revolution. Fisher’s dissertation was the first important American contribution to mathematical economics” (McGraw, p. 683). Ragnar Frisch (1947) spoke of “the crucial contribution” and “monumental importance” of Fisher’s ‘Mathematical Investigations in the Theory of Value and Price’: “I remember the intensity with which, in my younger days, I dug into Fisher’s dissertation, and the same can undoubtedly be said about many other economists of our generation … When we are speaking not about the ideas that cause the shorter swings, or even the sub-secular swings of the thinking in economics, but about those that are responsible for the really long-time trend of our science, then it will be hard to find any single work that has been more influential than Fisher’s dissertation. It will be standing there as a milestone long after our great-grandchildren are dead and forgotten.” “As William Brainard and Herbert Scarf emphasize, the Fisher machine, the ingenious hydraulic mechanism constructed by Fisher to illustrate his dissertation by solving for equilibrium prices and quantities in a model economy, is a landmark both in the history of economic modeling and the history of pre-electronic computing” (Dimand & Ben-El-Mechaiekh, p. 98). In his thesis, Fisher “was one of the first to use indifference curves in economic theory, …[and] was the first to draw the now well-known diagram where the indifference curves are combined with the budget line of the consumer, and where the optimum is located at the point of tangency between the budget line and an indifference curve. He also made a similar construction for the production side where he showed that profit maximization implied that the marginal rate of transformation between two goods – the ratio of their respective marginal costs – must be equal to the ratio of their respective prices. Thereby he had in place two central building blocks for a general equilibrium model, and he brought them together using relations that showed the flows of commodities and factors of production in the economy” (Sandmo, pp. 283-4). “Fisher must be considered one of those who laid the foundations of modern economics, particularly of econometrics. He contributed more than any other scholar to the introduction into economics of scientific methodology and mathematical thinking, and he played an essential role in the development of specific concepts and theories which lie at the base of today’s economics” (DSB). ABPC/RBH lists no copies of this offprint, and only one copy of the journal issue (Heritage, April 11, 2012, lot 36395, $4,375). Fisher’s thesis is almost always encountered in the first book edition (October 1925, reprinted May 1926).

General equilibrium theory attempts to explain the behaviour of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium.In a market system the prices and production of all goods, including the price of money and interest, are interrelated. A change in the price of one good may affect another price. Calculating the equilibrium price of just one good, in theory, thus requires an analysis that accounts for all of the millions of different goods that are available. The first attempt to model prices for a whole economy was made by Léon Walras in his *Éléments d'économie politique pure* (1874).

“As a Yale undergraduate and graduate student, Fisher (1867-1947) studied mathematics and physics with J. Willard Gibbs, but also took courses in political economy taught by a Yale celebrity, William Graham Sumner, the outspoken sociologist, free trader, anti-imperialist, and Social Darwinist who also co-supervised Thorstein Veblen’s doctoral dissertation. Fisher took courses from Gibbs on the mathematical theory of electricity, thermodynamics, and multiple algebra and vector analysis, and from Sumner on advanced political economy, finance and politics in the history of the United States, sociology, and the logic and method of the social sciences … When the time came to choose a dissertation topic, Fisher consulted Sumner on how to combine his two interests. Sumner told Fisher that, although he had not read anything about mathematical economics, he had heard of a new book on the subject by Rudolf Auspitz and Richard Lieben [*Untersuchungen über die Theorie des Preises*, 1889], two Austrian businessmen” (Dimand & Ben-El-Mechaiekh, p. 99). The only significant economic influences on Fisher’s thesis were this work of Auspitz and Lieben, and William Stanley Jevons’s *The Theory of Political Economy* (1871).

“After spending the summer of 1890 working his way through Auspitz and Lieben in the original German while tutoring the sons of railway magnate J. J. Hill in Minnesota, Fisher began writing his dissertation in September 1890, and successfully defended it in April 1891. Jevons had advocated the use of differential calculus in economics, treating marginal utility as the first derivative of a person’s utility function with respect to the quantity of a commodity consumed, but (in contrast to Walras) Jevons did not consider the problem of simultaneous determination of prices and quantities in a system of interrelated markets … The Austrian sugar magnate Rudolf Auspitz and banker Richard Lieben had more to offer Fisher, although only in a partial equilibrium framework” (*ibid*., p. 101).

“Fisher’s doctoral dissertation is a masterly exposition of Walrasian general equilibrium theory. Fisher, who was meticulous about acknowledgements throughout his career, writes in the preface that he was unaware of Walras while writing the dissertation …

“Fisher’s inventive ingenuity combined with his training under Gibbs to produce a remarkable hydraulic mechanical analogue model of a general equilibrium system, replete with cisterns, valves, levers, balances and cams. This could he display physically how a shock to demand or supply in one of ten interrelated markets altered prices and quantities in all markets and changed the incomes and consumption bundles of the various consumers. The model is described in detail in the book; unfortunately, both the original model and a second one constructed in 1925 have been lost to posterity … In his formal mathematical model building too, Fisher was greatly impressed by the analogies between the thermodynamics of his mentor Gibbs and economic systems, and he was able to apply Gibbs’s innovations in vector calculus.

“Fisher expounds thoroughly the mathematics of utility functions and their maximization, and he is careful to allow for corner solutions. He uses independent and additive utilities of commodities in his first mathematical approximation and in his physical model; later he was to show how this assumption could be exploited to measure marginal utilities empirically. But the general formulation in his dissertation makes the utility of every commodity depend on the quantities consumed of all commodities. At the same time, he states that neither interpersonally comparable utility nor cardinal utility for each individual is necessary to the determination of equilibrium. Fisher’s list of the limitations of his analysis is candid and complete. The supply side of Fisher’s model is, as he acknowledges, primitive. Each commodity is produced at increasing marginal cost, but neither factor supplies and prices nor technologies are explicitly modelled.

“Finally, Fisher shows his enthusiasm for his discovery of mathematical economics by appending to his dissertation an exhaustive survey and bibliography of applications of mathematical method to economics” (*The New Palgrave* 2, p. 371).

“Irving Fisher’s Ph.D. thesis, submitted to Yale University in 1891, is remarkable in at least two distinct ways. The thesis contains a fully articulated general equilibrium model presented with the broad scope and formal mathematical clarity that we associate with Walras and his successors. But what is even more astonishing is the presentation, in his thesis, of Fisher’s hydraulic apparatus for calculating equilibrium prices and the resulting distribution of society’s endowments among the agents in the economy …

“Even though Fisher’s construction of what we now call the Walrasian model of equilibrium was a fully original achievement, he did have contemporaries: the central ideas of equilibrium theory were independently discovered at several locations in the final decades of the [nineteenth] century. But the second theme of Fisher’s thesis was entirely novel in conception and execution. No other economist of his time suggested the possibility of exploring the implications of equilibrium analysis by constructing specific numerical models, with a moderately large number of commodities and consumers, and finding those prices that would simultaneously equate supply and demand in all markets. The profession would have to wait until rudimentary computers were available in the 1930s before Leontief turned his hand to a simplified version of this computation” (Brainard & Scarf).

“The construction, an elaborate and ingenious hydraulic machine consisting of several interconnected water cisterns, each representing the marginal utility of an agent, won the acclaim of one well-qualified reviewer, the Italian military engineer Enrico Barone. The various shapes of the cisterns reflect the different personal preferences of the agents. Once filled, the water flows through the system to settle on an equilibrium position illustrating the equalization of marginal utilities across the agents. Barone writes: ‘The originality of this remarkable contribution to science consists essentially in the fact that for some problems of pure economics, the author has imagined – and has actually built – a device that mechanically gives the solution’” (Dimand & Ben-El-Mechaiekh, p. 105).

“Fisher’s hydraulic machine is complex and ingenious. It correctly solves for equilibrium prices in a model of exchange in which each consumer had additive, monotonic and concave utility functions, and a specified money income; the market supplies of each good are exogenously given. Both additivity and fixed money incomes make the model of exchange to which his mechanism is applied less than completely general. But we know of no argument for the existence of equilibrium prices in this restricted model that does not require the full use of Brouwer’s fixed-point theorem. Of course, fixed point theorems were not available to Fisher …

“It is hard to discover the source of Fisher’s interest in computation. He was a student of J. Willard Gibbs, and perhaps the theme of concrete models in mechanics was carried over to economics. But it is also possible that this hydraulic apparatus is simply an instance of an American passion for complex machinery that gets things done. Fisher, himself, had a passion for innovation. In the course of a long career, he invented an elaborate tent for the treatment of tuberculosis, developed a mechanical diet indicator that permitted easy calculation of the daily consumption of fats, carbohydrates and proteins, copywrited (1943) an icosahedral world glob with triangular facets, that when unfolded was allegedly an improvement on the Mercator projection, and patented w an ‘index visible filing system’ (1913) sold to Kardex Rand, later Remington Rand, in 1925 for $660,000” (Brainard & Scarf).

“Fisher’s thesis was ahead of its time. His work in mathematical economics was warmly received by Francis Y. Edgeworth, Enrico Barone, and Vilfredo Pareto, but most economists of his time and of the next two generations of economists could no more read and understand his dissertation than they could read and understand Edgeworth’s *Mathematical Psychics*. Only a handful of Yale’s mathematics students were drawn to Fisher’s course on ‘The Mathematical Theory of Prices’ … But Fisher’s thesis was not completely forgotten. The Yale University Press republished *Mathematical Investigations in the Theory of Value and Prices *in 1925, with a brief preface by Fisher and photographs of the 1893 and 1925 versions of Fisher’s hydraulic machine, and sold enough copies to warrant reprinting the book in 1937” (Dimand & Ben-El-Mechaiekh, pp. 109-110).

“Had Nobel awards in economics existed during Fisher’s lifetime (he died in 1947, and the first Nobel Prize in Economics was awarded in 1969), there is little doubt he would have been a recipient. His wide-ranging theoretical ideas have influenced modern neoclassical theory probably more than any other individual’s ideas, and many remain relevant for policy decisions today” (Formaini).

Blaug, *Great Economists before Keynes*, p. 77-81; Brainard & Scarf, ‘How to Compute Equilibrium Prices in 1891,’ *Celebrating Irving Fisher*:* The Legacy of a Great Economist* (Dimand and John Geanakoplos, ed.)*, *2005, pp. 57-92; Dimand & Ben-El-Mechaiekh, ‘General equilibrium reaches North America: The hydraulic simulation model in Irving Fishe’s Mathematical Investigations in the Theory of Value and Prices (1891),’ Journal of Economic and Social Measurement 37 (2012), pp. 97–118; Fisher, E-8; Formaini, Review of *Celebrating Irving Fisher*, *The Independent Review* 12 (2007), p. 456; Frisch, ‘Tribute to Irving Fisher,’ *Journal of the American Statistical Association* 42 (1947), pp. 2-4; McGraw, ‘Review: Lives of the Great Economists,’ *The Journal of Economic History* 55 (1995), pp. 683-693; Sandmo, *Economics Evolving*, 2011.

8vo (232 x 150 mm), pp. 124, printed ‘Compliments of the Author’ slip tipped-in before title. Original printed green wrappers (rebacked, front wrapper chipped, subsequent vertical fracture to rear wrapper close to spine repair). Housed in a drop-back cloth box.

Item #5300

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Price:
$18,500.00
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