Knowledge that Transforms

Much attention in the theory of revealed preference has been devoted to the problem of demand functions generated from continuous utility functions. First Samuelson (1938), the originator of the theory of revealed preference, presented assumptions for P2+. Later Houthakker (1950) developed this model of consumer's behaviour for the n-dimensional case. A gap in Houthakker's proof has been recently closed by B. Stigum (1973). Uzawa (1960) presented a different version of Houthakker's theorem. His conditions AI-AIV and the Strong Axiom of Revealed Preference establish the existence of an upper semicontinuous utility function generating the given demand function. Uzawa's query whether these conditions guarantee the existence of a continuous utility function was answered in the negative by a counterexample of Hurwicz and Richter (1971). At approximately the same time E. Gordon (1971) published an article in the Review of Economic Studies where he tried to demonstrate that the axioms AI-AIV and the Strong Axiom do imply the existence of a continuous utility function. Unfortunately the proof of his Proposition 3 (p. 327) contains an error which led to this wrong conclusion. The purpose of this paper is to correct Gordon's theorem by adding conditions which are essentially due to Stigum. We will see that supporting hyperplanes play an important part in the method of the proof. The correction of Gordon's proof, based on results of Uzawa, turns out to be another method to prove Houthakker's theorem.

Akio Kagawa, Kiyoshi Kuga; Notes and Comments: On Professor Hahn's Tâtonnement Stability Theorem: Comment and Example, The Review of Economic Studies, Volu

Journal Article Target Controllability Get access Alfred L. Norman, Alfred L. Norman Board of Governors of the Federal Reserve System, Washington, and University of Texas at Austin Search for other works by this author on: Oxford Academic Google Scholar Woo S. Jung Woo S. Jung Vanderbilt University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 2, January 1980, Pages 451–457, https://doi.org/10.2307/2297004 Published: 01 January 1980 Article history Received: 01 January 1977 Accepted: 01 November 1978 Published: 01 January 1980

Journal Article Employment and Dividend Policy of the Firm under Risk Get access Pierre Dehez Pierre Dehez Centre for Operations Research and Econometrics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 3, April 1980, Pages 503–511, https://doi.org/10.2307/2297301 Published: 01 April 1980 Article history Received: 01 November 1978 Accepted: 01 August 1979 Published: 01 April 1980

John A. Ferejohn, David M. Grether, Steven A. Matthews, Edward W. Packel; Continuous-Valued Binary Decision Procedures, The Review of Economic Studies, Vol

In most of the developed countries provision is now made, by either the state or a private institution, for individuals to provide for themselves a retirement income which is a return on the accumulated value of regular payments made during the working life. Given that for many individuals the discounted present value of expected pension rights is one of the most important components of personal wealth it would seem desirable to include an estimate of the former in any measure of the latter. This will require the discounting of anticipated future payments and receipts at an appropriate rate. In the absence of uncertainty and with perfect capital markets anticipated future payments and receipts would be discounted at the prevailing rate of interest on financial assets. Where the individual's lifetime is of uncertain length but there exist perfect insurance markets of the type considered by Yaari (1965) the appropriate rate of discount would be the actuarially fair rate of interest prevailing on insurance notes. Now whilst the individual is uncertain as to how long he will live it is not the case that individuals are observed trading in actuarially fair insurance notes as suggested by the Yaari model. The aim of this paper is to try and obtain some insight into the appropriate rate of discount to be used in the valuation of pension wealth when insurance markets are less perfect than those described by Yaari.

Journal Article Efficient Programmes for Polyhedral Technologies are Competitive Get access Ahmet U. Alkan Ahmet U. Alkan Middle East Technical University, Ankara, Turkey Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 2, January 1980, Pages 465–471, https://doi.org/10.2307/2297006 Published: 01 January 1980 Article history Received: 01 January 1977 Accepted: 01 February 1979 Published: 01 January 1980

Journal Article The Existence of Optimal Invariant Stocks in a Multi-Sector Economy Get access James Flynn James Flynn Cleveland State University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 4, July 1980, Pages 809–811, https://doi.org/10.2307/2296946 Published: 01 July 1980 Article history Received: 01 August 1978 Accepted: 01 September 1979 Published: 01 July 1980

Journal Article Economics of Depletable Resources and Price Ceiling Induced Bias Get access Dwight R. Lee Dwight R. Lee Virginia Polytechnic Institute and State University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 5, October 1980, Pages 999–1002, https://doi.org/10.2307/2296929 Published: 01 October 1980 Article history Received: 01 May 1979 Accepted: 01 April 1980 Published: 01 October 1980