Theorems - Theorem, Liouville's Theorem, Corollary, List of Theorems, Okishio's Theorem, List of Published Incomplete Proofs (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 30. Chapters: Theorem, Liouville's theorem, Corollary, List of theorems, Okishio's theorem, List of published incomplete proofs, Von Neumann-Morgenstern utility theorem, List of misnamed theorems, Disquotational principle, Ugly duckling theorem, Universal approximation theorem, Norm residue isomorphism theorem, Gabbay's separation theorem. Excerpt: This is a list of theorems, by Wikipedia page. See also Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied fields. Okishio's theorem is a mathematical theorem formulated by Japanese economist Nobuo Okishio. It has had a major impact on debates about Marx's theory of value. Intuitively, it can be understood as saying that if one capitalist raises his profits by introducing a new technique that cuts his costs, the collective or general rate of profit in society - for all capitalists - goes up. Okishio establishes this theorem under the assumption that the real wage - the price of the commodity basket which workers consume - remains constant. Thus, the theorem isolates the effect of 'pure' innovation from any consequent changes in the wage. For this reason the theorem, first proposed in 1961, excited great interest and controversy because, according to Okishio, it contradicts Marx's law of the tendency of the rate of profit to fall. Marx had claimed that the new general rate of profit, after a new technique has spread throughout the branch where it has been introduced, would be lower than before. In modern words, the capitalists would be caught in a rationality trap or prisoner's dilemma: that which is rational from the point of view of a single capitalist, turns out to be irrational for the system as a whole, for the collective of all capitalists. This result was widely understood, including by Marx himself, as e...