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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 Linear utility ： ウィキペディア英語版 Linear utility In economics and consumer theory, a linear utility function is a function of the form: ::$u(x\_1,x\_2,\backslash dots,x\_m)\; =\; w\_1\; x\_1\; +\; w\_2\; x\_2\; +\; \backslash dots\; w\_m\; x\_m$ or, in vector form: ::$u(\backslash overrightarrow)\; =\; \backslash overrightarrow\; \backslash cdot\; \backslash overrightarrow$ where: * $m$ is the number of different goods in the economy. * $\backslash overrightarrow$ is a vector of size $m$ that represents a bundle. The element $x\_i$ represents the amount of good $i$ in the bundle. * $\backslash overrightarrow$ is a vector of size $m$ that represents the subjective preferences of the consumer. The element $w\_i$ represents the relative value that the consumer assigns to good $i$. If $w\_i=0$, this means that the consumer thinks that product $i$ is totally worthless. The higher $w\_i$ is, the more valuable a unit of this product is for the consumer. A consumer with a linear utility function has the following properties: * The preferences are strictly monotone: having a larger quantity of even a single good strictly increases the utility. * The preferences are weakly convex, but not strictly convex: a mix of two equivalent bundles is equivalent to the original bundles, but not better than it. * The marginal rate of substitution of all goods is constant. For every two goods $i,j$: ::$MRS\_\; =\; w\_i/w\_j$. * The indifference curves are straight lines (when there are two goods) or hyperplanes (when there are more goods). * Each demand curve (demand as a function of price) is a step function: the consumer wants to buy zero units of a good whose utility/price ratio is below the maximum, and wants to buy as many units as possible of a good whose utility/price ratio is maximum. * The consumer regards the goods as perfect substitute goods. == Economy with linear utilities == Define a ''linear economy'' as an exchange economy in which all agents have linear utility functions. A linear economy has several properties. Assume that each agent $A$ has an initial endowment $\backslash overrightarrow$. This is a vector of size $m$ in which the element $e\_$ represents the amount of good $i$ that is initially owned by agent $A$. Then, the initial utility of this agent is $\backslash overrightarrow\backslash cdot\; \backslash overrightarrow$. Suppose that the market prices are represented by a vector $\backslash overrightarrow$ - a vector of size $m$ in which the element$p\_i$ is the price of good $i$. Then, the ''budget'' of agent $A$ is $\backslash overrightarrow\backslash cdot\; \backslash overrightarrow$. While this price vector is in effect, the agent can afford all and only the bundles $\backslash overrightarrow$ that satisfy the budget constraint: $\backslash overrightarrow\backslash cdot\; \backslash overrightarrow\; \backslash leq\; \backslash overrightarrow\backslash cdot\; \backslash overrightarrow$. 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「Linear utility」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.