Journal Article The Pasinetti Paradox in Neoclassical and More General Models Get access Paul A. Samuelson, Paul A. Samuelson Massachusetts Institute of Technology Search for other works by this author on: Oxford Academic Google Scholar Franco Modigliani Franco Modigliani Massachusetts Institute of Technology Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 33, Issue 4, October 1966, Pages 269–301, https://doi.org/10.2307/2974425 Published: 01 October 1966

David Levhari, Paul A. Samuelson; The Nonswitching Theorem is False, The Quarterly Journal of Economics, Volume 80, Issue 4, 1 November 1966, Pages 518–519

The fallacy that a many-period expected-utility maximizer should maximize (a) the expected logarithm of portfolio outcomes or (b) the expected average compound return of his portfolio is now understood to rest upon a fallacious use of the Law of Large Numbers. This paper exposes a more subtle fallacy based upon a fallacious use of the Central-Limit Theorem. While the properly normalized product of independent random variables does asymptotically approach a log-normal distribution under proper assumptions, it involves a fallacious manipulation of double limits to infer from this that a maximizer of expected utility after many periods will get a useful approximation to his optimal policy by calculating an efficiency frontier based upon (a) the expected log of wealth outcomes and its variance or (b) the expected average compound return and its variance. Expected utilities calculated from the surrogate log-normal function differ systematically from the correct expected utilities calculated from the true probability distribution. A new concept of ‘initial wealth equivalent’ provides a transitive ordering of portfolios that illuminates commonly held confusions. A non-fallacious application of the log-normal limit and its associated mean-variance efficiency frontier is established for a limit where any fixed horizon period is subdivided into ever more independent sub-intervals. Strong mutual-fund Separation Theorems are then shown to be asymptotically valid.

I. Introduction and review, 537. — II. Many-goods model, 539. — III. Euler necessary conditions, 541. — IV. Case of satiated production, 544. — V. Physical analogy of small vibrations, 547. — VI. Case of utility satiation, 549. — VII. Practical computation, 553. — VIII. Hamiltonian formulation, 554. — IX. Pay-off in terms of initial state, 559. — X. Conclusion, 561.