A Further Note on Revealed Preference
Bibliographic Data
| ID | 9722296 |
|---|---|
| Authors | Peter Newman (0000-0002-0272-0250) |
| Year | 1959 |
| Volume | 26 |
| Issue | 102 |
| Pages | 158 |
| Publication date | 1959-05-01 |
| Open Access | No |
| Type | ARTICLE |
| Venue | Economica (JOURNAL) |
| Journal identifiers | ISSN: 0013-0427 • E-ISSN: 1468-0335 |
| Publisher | JSTOR (PUBLISHER) |
| DOI | 10.2307/2550396 |
| OpenAlex | W2315812546 |
| Language | EN |
| Citations received | 1 |
1. Dr. Green's recent paper' carried forward the application of relational algebra to the theory of revealed preference in a very stimulating way. His main conclusion was the dethronement of the Strong (p. 323) and its replacement by an alternative gearing axiom which seems to have a better claim than [the Strong Axiom] to be regarded as the central proposition of the theory of consumer's behaviour (p. 321). I shall argue here that this conclusion is false; there is no need for-nor likelihood of-a usurpation of the Strong Axiom's sovereignty.2 2. The difficulties in Dr. Green's paper occur essentially in his statement that certain postulates (in particular Green's P8 and P9) are implicit in Houthakker's demonstration.3 This is not true; Houthakker proves these postulates, which together assert that for any given batch x0, and for any Engel curve, say ln, on which xo does not lie, there exists a unique batch xn such that xo is not indirectly revealed preferred to x8, nor xn indirectly revealed preferred to x?. Further, this batch is a boundary between points better (in the rp sense) than xo, and points worse than x0. In order to prove this result it is necessary to assume the Strong Axiom. Houthakker is misleading in implying that the Strong Axiom is needed only to prove that the equivalence relation E of revealed preference is transitive. It is needed logically long before that, in order to show that the limit curve is a true boundary curve and that its points x are such that x?Ex. Hence if Dr. Green assumes P8 and P9 he implicitly assumes the Strong Axiom. Once it is shown that batches connected by E actually exist, it is easy to show that E is transitive, without using the Strong Axiom directly at all
Axiom · Boundary (topology) · Combinatorics · Economics · Epistemology · Equivalence (formal languages) · Geometry · Mathematical analysis · Mathematical economics · Order (exchange) · Preference · Proposition · Pure mathematics · Statement (logic) · Statistics · Transitive relation · Advanced Algebra and Logic · Business Strategy and Innovation · Decision-Making and Behavioral Economics · Mathematics · Philosophy
| Citations per year | 0.14 |
|---|---|
| Citation span | 2019 - 2019 (1) |
| Highly cited | No |