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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].

Public Goods and Technology of Consumption: A Comment

Review of Economic Studies 1977 44(1), 193
Journal Article Public Goods and Technology of Consumption: A Comment Get access A. Zabalza A. Zabalza London School of Economics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 44, Issue 1, February 1977, Pages 193–194, https://doi.org/10.2307/2296987 Published: 01 February 1977 Article history Received: 01 October 1975 Accepted: 01 May 1976 Published: 01 February 1977

A Warning Note on Empirical Research using Foreign Exchange Rates

Journal of Financial and Quantitative Analysis 1977 12(2), 315
Since we now have a data base approaching five years of more or less fluctuating exchange rates, there undoubtedly are numerous empirical studies under way comparing the movements of exchange rates with each other and with all sorts of other economic variables. A rather subtle problem with such activities is that the analysis is sensitive to which currency of an exchange rate one chooses to make the numeraire. Specifically, a time series of, say, dollars per pound sterling is not the same thing mathematically as a time series of pounds per dollar although the information content is the same. In particular it can be shown that

A Variable-Parameter Model of Exporting Behaviour

Review of Economic Studies 1977 44(1), 43
Journal Article A Variable-Parameter Model of Exporting Behaviour Get access R. A. Batchelor R. A. Batchelor National Institute of Economic and Social Research Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 44, Issue 1, February 1977, Pages 43–57, https://doi.org/10.2307/2296972 Published: 01 February 1977 Article history Received: 01 October 1975 Accepted: 01 May 1976 Published: 01 February 1977

A Note on Fisher Hypothesis and Price Level Uncertainty

Journal of Financial and Quantitative Analysis 1977 12(3), 525
The theory on the relationship between real and nominal interest rates is based on the well-known Fisher equation:where: i = nominal interest rate;r = real interest rate;λ = percentage change in price level: P /P0 - 1 where P and P0 denote end-of-period and current levels of some aggregate price index, respectively.