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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gorman form ： ウィキペディア英語版 Gorman polar form Gorman polar form is a functional form for indirect utility functions in economics. Imposing this form on utility allows the researcher to treat a society of utility-maximizers as if it consisted of a single 'representative' individual. Gorman showed that having the function take Gorman polar form is both necessary and sufficient for this condition to hold. == Motivation == Standard consumer theory is developed for a single consumer. The consumer has a utility function, from which his demand curves can be calculated. Then, it is possible to predict the behavior of the consumer in certain conditions, price or income changes. But in reality, there are many different consumers, each with his own utility function and demand curve. How can we use consumer theory to predict the behavior of an entire society? One option is to represent an entire society as a single "mega consumer", which has an aggregate utility function and aggregate demand curve. But in what cases is it indeed possible to represent an entire society as a single consumer? Early results by Antonelli (1886) and Nataf (1953) had shown that, assuming all individuals face the same prices in a market, their income consumption curves and their Engel curves (expenditure as a function of income) should be parallel straight lines. This means that we can calculate an income-consumption curve of an entire society just by summing the curves of the consumers. In other words, suppose the entire society is given a certain income. This income is somehow distributed between the members of society, then each member selects his consumption according to his income-consumption curve. If the curves are all parallel straight lines, the aggregate demand of society will be ''independent of the distribution of income among the agents''. Gorman's first published paper in 1953 developed these ideas in order to answer the question of representing a society by a single individual. In 1961, Gorman published a short, four-page paper in ''Metroeconomica'' which derived an explicit expression for the functional form of preferences which give rise to linear Engel curves. Suppose an individual $i$ has a utility function $u^i$. Then, his expenditure function as a function of price ($e\; ^\; i\; \backslash left\; (\; p\; \backslash right\; )$) must be an affine transformation of the utility function, with coefficients that depend on the price vector: :$e^i\; \backslash left\; (p\; \backslash right\; )\; =\; f^i(p)\; +\; u^i\; g(p)$, where both $f^i\; \backslash left\; (p\; \backslash right\; )$ and $g\; \backslash left\; (p\; \backslash right\; )$ are homogeneous of degree one in prices ($p$, a vector). This homogeneity condition ensures that $e^i\; \backslash left\; (p\backslash right\; )$ gives linear Engel curves. $f^i\; \backslash left\; (p\; \backslash right\; )$ and $g\; \backslash left\; (p\; \backslash right\; )$ have nice interpretations: $f^i\; \backslash left\; (p\; \backslash right\; )$ is the expenditure needed to reach a reference utility level of zero for each individual ($i$), while $g\; \backslash left\; (p\; \backslash right\; )$ is the price index which deflates the excess money income $e^i\; \backslash left\; (p\backslash right\; )\; -\; f^i\; (p)$ needed to attain a level of utility $\backslash bar$. It is important to note that $g\; \backslash left\; (p\; \backslash right\; )$ is the same for every individual in a society, so the Engel curves for all consumers are parallel. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gorman polar form」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.