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In the paper “The Foundations of the Revealed Preference Theory” the author focuses on the growing tendency of greater rigor in modern economic theory. Its dedication to rigor can lead to an indiscriminate application, formalism, and a level of abstraction that makes it difficult for economists…
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Download file to see previous pages In some mathematical conditions, this differential equation can be integrated to solve it as indifference curve through x which is called the integrability problem (Newman, 1995).
6) Georgescu-Rogen proved that if we consider two goods where differential equation defining an indifferent element is always integrable, it is essential to consider that indifference is transitive relation that denotes that integral curves are indifferent curves. Georgescu proved that transitivity condition guarantees integrable differential equations in all dimensions. Therefore, integrability conditions are unnecessary. In economic terms, integral curves are meaningless unless Axiom I and II are adopted (Newman, 1995).
(8, 9) By following Sauelsons techniques, Herman Wold claimed that demand-function approach is rationally equal to the ordinal preference approach. He asserted that Houthakker's theorem is the same as his method of proof. However, an analysis of Wold's proof revealed his implicit assumption that his revealed preference is a transitive relation. Wold proved his point by using certain assumptions of perfect competition; however, it is impossible to do because Wold didn't define indifference (Newman, 1995).
(10) Wold's integrability assumptions are obsolete because the existence of a convex boundary curve comes from this implicit assumption of the transitivity of preference not from explicit assumptions of integrability.
(11) Ville deduced the existence of a utility function through excellent analytic evidence. A reasonable interpretation of his axiom can lead to a relationship that brings a complete weak ordering on the commodity space. However, his criterion for the consumer as "worse off" is insufficient (Newman, 1995).
(12) Integrability problem suddenly appears when commodity space has three goods while the transitivity problem arises when three situations are considered. Therefore, it arises even when there is a two-goods case.  ...Download file to see next pagesRead More
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