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.

Journal Article Social Choice Theory: The Single-profile and Multi-profile Approaches Get access Kevin W. S. Roberts Kevin W. S. Roberts MIT and St Catherine's College, Oxford Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 2, January 1980, Pages 441–450, https://doi.org/10.2307/2297003 Published: 01 January 1980 Article history Received: 01 November 1976 Accepted: 01 March 1979 Published: 01 January 1980

Linda Cohen, Steven Matthews; Constrained Plott Equilibria, Directional Equilibria and Global Cycling Sets, The Review of Economic Studies, Volume 47, Issu

Journal Article Possibility Theorems with Interpersonally Comparable Welfare Levels Get access Kevin W. S. Roberts Kevin W. S. Roberts Massachusetts Institute of Technology and St. Catherine's College, Oxford Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 2, January 1980, Pages 409–420, https://doi.org/10.2307/2297001 Published: 01 January 1980 Article history Received: 01 April 1976 Accepted: 01 January 1978 Published: 01 January 1980

Journal Article Interpersonal Comparability and Social Choice Theory Get access Kevin W. S. Roberts Kevin W. S. Roberts MIT and St Catherine's College, Oxford Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 2, January 1980, Pages 421–439, https://doi.org/10.2307/2297002 Published: 01 January 1980 Article history Received: 01 July 1976 Accepted: 01 March 1979 Published: 01 January 1980

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

T. S. Breusch, A. R. Pagan; The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics, The Review of Economic Studies, Volume 47,

Journal Article Disaggregated Demand Analysis: The Estimation of a Class of Non-linear Demand Systems Get access S. E. Pudney S. E. Pudney London School of Economics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 5, October 1980, Pages 875–892, https://doi.org/10.2307/2296919 Published: 01 October 1980 Article history Received: 01 September 1978 Accepted: 01 March 1980 Published: 01 October 1980