On Gale's Contribution in Revealed Preference Theory
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916840961212416 |
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| author | Hosoya, Yuhki |
| author_facet | Hosoya, Yuhki |
| contents | We investigate Gale's important paper published in 1960. This paper contains an example of a candidate of the demand function that satisfies the weak axiom of revealed preference and that is doubtful that it is a demand function of some weak order. We examine this paper and first scrutinize what Gale proved. Then we identify a gap in Gale's proof and show that he failed to show that this candidate of the demand function is not a demand function. Next, we present three complete proofs of Gale's claim. First, we construct a proof that was constructible in 1960 by a fact that Gale himself demonstrated. Second, we construct a modern and simple proof using Shephard's lemma. Third, we construct a proof that follows the direction that Gale originally conceived. Our conclusion is as follows: although, in 1960, Gale was not able to prove that the candidate of the demand function that he constructed is not a demand function, he substantially proved it, and therefore it is fair to say that the credit for finding a candidate of the demand function that satisfies the weak axiom but is not a demand function is attributed to Gale. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_07970 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Gale's Contribution in Revealed Preference Theory Hosoya, Yuhki Theoretical Economics 91B08, 91B16 We investigate Gale's important paper published in 1960. This paper contains an example of a candidate of the demand function that satisfies the weak axiom of revealed preference and that is doubtful that it is a demand function of some weak order. We examine this paper and first scrutinize what Gale proved. Then we identify a gap in Gale's proof and show that he failed to show that this candidate of the demand function is not a demand function. Next, we present three complete proofs of Gale's claim. First, we construct a proof that was constructible in 1960 by a fact that Gale himself demonstrated. Second, we construct a modern and simple proof using Shephard's lemma. Third, we construct a proof that follows the direction that Gale originally conceived. Our conclusion is as follows: although, in 1960, Gale was not able to prove that the candidate of the demand function that he constructed is not a demand function, he substantially proved it, and therefore it is fair to say that the credit for finding a candidate of the demand function that satisfies the weak axiom but is not a demand function is attributed to Gale. |
| title | On Gale's Contribution in Revealed Preference Theory |
| topic | Theoretical Economics 91B08, 91B16 |
| url | https://arxiv.org/abs/2208.07970 |