The Review of Economic Studies, Ltd.

Further CommentAuthor(s): Peter NewmanSource: The Review of Economic Studies, Vol. 28, No. 2 (Feb., 1961), p. 142Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2295713 .

Accessed: 25/06/2014 08:01

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

Oxford University Press and The Review of Economic Studies, Ltd. are collaborating with JSTOR to digitize,preserve and extend access to The Review of Economic Studies.

http://www.jstor.org

This content downloaded from 185.44.77.128 on Wed, 25 Jun 2014 08:01:29 AMAll use subject to JSTOR Terms and Conditions

Further Comment

I am grateful to Dr. Uzawa for pointing out the error in the last paragraph of the main part of my paper on this infinitely complicated subject. I had worked out what still appear to me (subject to the amendments of the " Supplementary Note" in the June 1960 issue of this journal) the simplest conditions under which the revealed preference relation may be extended to generate a complete ordering for the consumer. But I was careless in adapting Georgescu-Roegen's axiom to the revealed preference relation, in seeking con- ditions under which this derived ordering may be represented by a continuous function (paragraph 33 on pp. 74-5 of my paper).

Georgescu-Roegen (Q. J. E., 1954, p. 508) defines a " preferential set " as " a continuous sequence of alternatives arranged in their order of preference ", and his Axiom 11.7 may be paraphrased as follows: Given a particular commodity bundle x and any preferential set Y not containing x, but containing Yi and Y2 such that y1Px and xaPy2, then Y also contains a bundle y3 such that x is indifferent to y3 (by definition of the preferential set, y3 is unique). He claims that no ordinal measure of utility can be obtained without such an assumption and-by inference-that this condition allows a complete ordering to be representable by the usual continuous utility function, unique up to a monotonic or order-preserving transformation.*

My error arose from failing to observe that Georgescu-Roegen's axiom, although its wording is ambiguous on this point, must apply to every preferential set satisfying the conditions of the axiom. The Engel curves in the revealed preference problem are certainly preferential sets (in the sense of rp) that satisfy the axiom, but there may well be other preferential sets around that do not, as the reader may verify by studying Dr. Uzawa's counter-example. It is also fairly easy to see intuitively that if there are no kinks in the behaviour curves (his suggested condition), then the axiom will be satisfied for all prefer- ential sets.

Mona, Jamaica. PETER NEWMAN.

* The relations between orderings and representational functions, and the necessary proofs, have not yet been completely worked out in the literature, and will form the subject of a later paper by R. C. Read and myself. That there does exist some confusion may be seen in Maurice McManus's otherwise excellent paper in this journal (Volume 25, no. 2), where he states (p. 98, footnote 3) that " Continuity and density, however, are true properties of ordinal quantities ". Clearly any continuous representation function can be submitted to a discontinuous order-preserving transformation so that this statement is false; the only invariant property of an ordering is the order itself.

142

This content downloaded from 185.44.77.128 on Wed, 25 Jun 2014 08:01:29 AMAll use subject to JSTOR Terms and Conditions