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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 Total revenue test ： ウィキペディア英語版 Total revenue test In economics, the Total Revenue Test is a means for determining whether demand is elastic or inelastic. If an increase in price causes an increase in total revenue, then demand can be said to be inelastic, since the increase in price does not have a large impact on quantity demanded. If an increase in price causes a decrease in total revenue, then demand can be said to be elastic, since the increase in price has a large impact on quantity demanded. Different commodities may have different elasticity depending on whether people need them (necessities) or want them (accessories). Examples: 1. Product A currently sells for $10. The seller decides to increase the price to $15, but finds that he ends up making less money. This is because he is selling fewer of the product due to the increased price, and his total revenue has fallen. The demand for this product must be elastic. 2. Product A currently sells for $10. The seller decides to increase the price to $15, and finds that his revenue ends up increasing. The demand for this product must be inelastic. == Mathematical explanation == The mathematical link between them comes from the formula of the price elasticity of demand: :$E\_d\; =\; -\; \backslash left(\backslash left(Q\_2-Q\_1\backslash right)/\; \backslash left(P\_2-\; P\_1\backslash right)\backslash right)\; \backslash cdot\; \backslash left(P\_1/Q\_1\backslash right)$ where $P$ stands for Price, $Q$ for quantity demanded, $\backslash left(Q\_2-Q\_1\backslash right)$ for change in quantity demanded, and $\backslash left(P\_2-P\_1\backslash right)$ for change in price. Here the minus sign converts the result to a non-negative number, as is conventional but not universal. Using the idea of limits for infinitesimal changes in price and therefore in quantity, the formula becomes :$E\_d\; =\; -\; \backslash frac\; \backslash cdot\; \backslash frac$ Total revenue is given by $TR=P\; \backslash cdot\; Q$. Since quantity demanded Q is a function of price P, $Q\; =\; f(P),$ total revenue can be rewritten as :$TR=P\; \backslash cdot\; f(P).$ The derivative of total revenue with respect to P is thus: :$\backslash frac\; =\; 1\; \backslash cdot\; f(P)\; +\; P\; \backslash cdot\; f\text{'}(P)$ But $Q\; =\; f(P)$, so $\backslash frac\; =\; f\text{'}(P)\; \backslash cdot\; P\; +\; Q$. After both multiplying and dividing by $Q$, the equation can be rewritten as: :$\backslash frac\; =\; Q\backslash left(f\text{'}(P)\; \backslash cdot\; \backslash frac\; +\; 1\backslash right).$ The last step is to substitute the elasticity of demand for $-f\text{'}(P)\; \backslash cdot\; \backslash frac$ to obtain: :$\backslash frac\; =\; Q(-E\_d\; +\; 1)\; =\; Q(1\; -\; E\_d)$. To find the elasticity of demand using the mathematical explanation of the total revenue test, it’s necessary to use the following rule: If demand is elastic, $E\_d\; >\; 1\; \backslash !\backslash$, then : price and total revenue move in opposite directions. If demand is inelastic, , then $\backslash dfrac\; >\; 0\; \backslash !\backslash$: price and total revenue change in the same direction. If demand is unit elastic, $E\_d\; =\; 1$, then $\backslash frac\; =\; 0$: an increase in price has no influence on the total revenue. 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「Total revenue test」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.