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Noise and Signal in Debates among Classical Economists: A Reply

Journal of Economic Literature 1980
It is high praise when so expert a * scholar as Samuel Hollander (1980) hails my canonical classical model (1978) as likely to become locus classicus for the next generation of textbook writers. Like Fletcher I care not who makes a nation's laws if I can shape its textbook writers' songs. But with power comes responsibility. I must weigh and respond to the doubts Dr. Hollander raises about some positions I took in the three-seventeenths of my positivistic text that digresses to interpret particular historical controversies. I shall be brief and deal only with most essential points.

St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described

Journal of Economic Literature 1977
THE St. Petersburg paradox constitutes a fascinating chapter in the history of ideas. What other subject can link together Edward Gibbon and the father-inlaw of Thomas Mann? Or can, in the conceit of Maynard Keynes, link together the Bernoullis and Darwin?' Substantively, the Petersburg paradox served as a dramatic paradigm, alerting people to the fact that their utility of gain exceeded their utility of equivalent money lost. As a byproduct, the discussion generated an interest of its own: the idiocies it evoked from various writers are scarcely less fascinating than the lasting insights. Yet when I came recently to review the matter, I found to my surprise that no one seems to have provided anything like a complete survey of the subject. The standard sources provide us with tantalizing glimpses: the useful 1954 English translation of the classic Latin work of Daniel Bernoulli [4, 1738]; the references and discussion in histories of probability, such as those of Isaac Todhunter [39, 1865] and Leonid Maistrov [17, 1966]; the selective but perspicacious accounts in the work of Keynes [15, 1921] and George Stigler [37, 1950]; the new lease on life given to the subject by Karl Menger [19, 1934] with the discussion there of SuperPetersburg paradoxes creatable when the utility function is unbounded; the recent observation by Kenneth Arrow [2, 1971] that not all stochastic processes can be ordered by the expected value of their utility outcomes when such Mengerian super-paradoxes are allowed to exist. The number of post-Mengerian writers is large, including L. S. Shapley [36, 1972], D. L. Brito [6, 1975], Samuelson [28, 1960], Robert J. Aumann [3, 1975], and many others. Given my own limited linguistic abilities and leisure time, I have not been able to provide anything like a definitive survey, one that checks back on and quotes copiously from the original sources. After all, the list of writers connected with the St. Petersburg paradox reads like a veritable who's who in probability and the social sciences. Here is but a sample: Nicholas Bernoulli (1687-1759), Montmort (1678-1719), Gabriel Cramer (1704IThe continuity and oneness of modern European thought may be illustrated, if such things amuse the reader, by the reflection that Condorcet derived from Bernoulli, that Godwin was inspired by Condorcet, that Malthus was stimulated by Godwin's folly into stating his famous doctrine, and that from the reading of Malthus on Population Darwin received his earliest impulse [15, Keynes, 1921, p. 83, n. 1].

Complementarity-An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory

Journal of Economic Literature 1974
THE TIME is ripe for a fresh, modern look at the concept of complementarity. Whatever the intrinsic merits of the concept, forty years ago it helped motivate Hicks and Allen to perform their classical reconsideration of ordinal demand theory. And, as I hope to show, the last word has not yet been said on this ancient preoccupation of literary and mathematical economists. The simplest things are often the most complicated to understand fully. For this reason, I have redrafted the present paper along the following lines: The main discussion is primarily literary. Then comes a mathematical section. Finally, I give a brief survey of the history of the subject.