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Roy's Identity
Roy's identity (named after French economist René Roy) is a major result in microeconomics having applications in consumer choice and the theory of the firm. The lemma relates the ordinary (Marshallian) demand function to the derivatives of the indirect utility function. Specifically, denoting the indirect utility function as v(p,w), the Marshallian demand function for good i can be calculated as :x_^(p,w)=-\frac where p is the price vector of goods and w is income. Derivation of Roy's identity Roy's identity reformulates Shephard's lemma in order to get a Marshallian demand function for an individual and a good (i) from some indirect utility function. The first step is to consider the trivial identity obtained by substituting the expenditure function for wealth or income w in the indirect utility function v (p, w), at a utility of u: :v ( p, e(p, u)) = u This says that the indirect utility function evaluated in such a way that minimizes the cost for achieving a certain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French People
The French people (french: Français) are an ethnic group and nation primarily located in Western Europe that share a common French culture, history, and language, identified with the country of France. The French people, especially the native speakers of langues d'oïl from northern and central France, are primarily the descendants of Gauls (including the Belgae) and Romans (or Gallo-Romans, western European Celtic and Italic peoples), as well as Germanic peoples such as the Franks, the Visigoths, the Suebi and the Burgundians who settled in Gaul from east of the Rhine after the fall of the Roman Empire, as well as various later waves of lower-level irregular migration that have continued to the present day. The Norse also settled in Normandy in the 10th century and contributed significantly to the ancestry of the Normans. Furthermore, regional ethnic minorities also exist within France that have distinct lineages, languages and cultures such as Bretons in Brittany, Occitans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shephard's Lemma
Shephard's lemma is a major result in microeconomics having applications in the theory of the firm and in consumer choice. The lemma states that if indifference curves of the expenditure or cost function are convex, then the cost minimizing point of a given good (i) with price p_i is unique. The idea is that a consumer will buy a unique ideal amount of each item to minimize the price for obtaining a certain level of utility given the price of goods in the market. The lemma is named after Ronald Shephard who gave a proof using the distance formula in his book ''Theory of Cost and Production Functions'' (Princeton University Press, 1953). The equivalent result in the context of consumer theory was first derived by Lionel W. McKenzie in 1957. It states that the partial derivatives of the expenditure function with respect to the prices of goods equal the Hicksian demand functions for the relevant goods. Similar results had already been derived by John Hicks (1939) and Paul Samuels ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Econometrica
''Econometrica'' is a peer-reviewed academic journal of economics, publishing articles in many areas of economics, especially econometrics. It is published by Wiley-Blackwell on behalf of the Econometric Society. The current editor-in-chief is Guido Imbens. History ''Econometrica'' was established in 1933. Its first editor was Ragnar Frisch, recipient of the first Nobel Memorial Prize in Economic Sciences in 1969, who served as an editor from 1933 to 1954. Although ''Econometrica'' is currently published entirely in English, the first few issues also contained scientific articles written in French. Indexing and abstracting ''Econometrica'' is abstracted and indexed in: * Scopus * EconLit * Social Science Citation Index According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 5.844, ranking it 22/557 in the category "Economics". Awards issued The Econometric Society aims to attract high-quality applied work in economics for publication in ''Eco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slutsky Equation
The Slutsky equation (or Slutsky identity) in economics, named after Eugen Slutsky, relates changes in Marshallian (uncompensated) demand to changes in Hicksian (compensated) demand, which is known as such since it compensates to maintain a fixed level of utility. There are two parts of the Slutsky equation, namely the substitution effect, and income effect. In general, the substitution effect can be negative for consumers as it can limit choices. He designed this formula to explore a consumer's response as the price changes. When the price increases, the budget set moves inward, which also causes the quantity demanded to decrease. In contrast, when the price decreases, the budget set moves outward, which leads to an increase in the quantity demanded. The substitution effect is due to the effect of the relative price change while the income effect is due to the effect of income being freed up. The equation demonstrates that the change in the demand for a good, caused by a price ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envelope Theorem
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem. As we change parameters of the objective, the envelope theorem shows that, in a certain sense, changes in the optimizer of the objective do not contribute to the change in the objective function. The envelope theorem is an important tool for comparative statics of optimization models. The term envelope derives from describing the graph of the value function as the "upper envelope" of the graphs of the parameterized family of functions \left\ _ that are optimized. Statement Let f(x,\alpha) and g_(x,\alpha), j = 1,2, \ldots, m be real-valued continuously differentiable functions on \mathbb^, where x \in \mathbb^ are choice variables and \alpha \in \mathbb^ are parameters, and consider the problem of choosing x, for a given \alpha, so as to: : \max_ f(x, \alpha) subject to g_(x,\alpha) \geq 0, j = 1,2, \ldots, m an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hicksian Demand
In microeconomics, a consumer's Hicksian demand function or compensated demand function for a good is his quantity demanded as part of the solution to minimizing his expenditure on all goods while delivering a fixed level of utility. Essentially, a Hicksian demand function shows how an economic agent would react to the change in the price of a good, if the agent's income was compensated to guarantee the agent the same utility previous to the change in the price of the good—the agent will remain on the same indifference curve before and after the change in the price of the good. The function is named after John Hicks. Mathematically, :h(p, \bar) = \arg \min_x \sum_i p_i x_i : \ \ u(x) \geq \bar . where ''h''(''p'',''u'') is the Hicksian demand function, or commodity bundle demanded, at price vector ''p'' and utility level \bar. Here ''p'' is a vector of prices, and ''x'' is a vector of quantities demanded, so the sum of all ''p''''i''''x''''i'' is total expenditure o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wealth
Wealth is the abundance of Value (economics), valuable financial assets or property, physical possessions which can be converted into a form that can be used for financial transaction, transactions. This includes the core meaning as held in the originating Old English word , which is from an Indo-European languages, Indo-European word stem. The modern concept of wealth is of significance in all areas of economics, and clearly so for economic growth, growth economics and development economics, yet the meaning of wealth is context-dependent. An individual possessing a substantial net worth is known as ''wealthy''. Net worth is defined as the current value of one's assets less liabilities (excluding the principal in trust accounts). At the most general level, economists may define wealth as "the total of anything of value" that captures both the subjective nature of the idea and the idea that it is not a fixed or static concept. Various definitions and concepts of wealth have been a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expenditure Function
In microeconomics, the expenditure function gives the minimum amount of money an individual needs to spend to achieve some level of utility, given a utility function and the prices of the available goods. Formally, if there is a utility function u that describes preferences over ''n '' commodities, the expenditure function :e(p, u^*) : \textbf R^n_+ \times \textbf R \rightarrow \textbf R says what amount of money is needed to achieve a utility u^* if the ''n'' prices are given by the price vector p. This function is defined by :e(p, u^*) = \min_ p \cdot x where :\geq(u^*) = \ is the set of all bundles that give utility at least as good as u^*. Expressed equivalently, the individual minimizes expenditure x_1p_1+\dots +x_n p_n subject to the minimal utility constraint that u(x_1, \dots , x_n) \ge u^*, giving optimal quantities to consume of the various goods as x_1^*, \dots x_n^* as function of u^* and the prices; then the expenditure function is :e(p_1, \dots , p_n ; u^*)=p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Income
Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms. Income is difficult to define conceptually and the definition may be different across fields. For example, a person's income in an economic sense may be different from their income as defined by law. An extremely important definition of income is Haig–Simons income, which defines income as ''Consumption + Change in net worth'' and is widely used in economics. For households and individuals in the United States, income is defined by tax law as a sum that includes any wage, salary, profit, interest payment, rent, or other form of earnings received in a calendar year.Case, K. & Fair, R. (2007). ''Principles of Economics''. Upper Saddle River, NJ: Pearson Education. p. 54. Discretionary income is often defined as gross income minus taxes and other deductions (e.g., mandatory pension contributions), and is widely used as a basis to co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economist
An economist is a professional and practitioner in the social sciences, social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. Within this field there are many sub-fields, ranging from the broad philosophy, philosophical theory, theories to the focused study of minutiae within specific Market (economics), markets, macroeconomics, macroeconomic analysis, microeconomics, microeconomic analysis or financial statement analysis, involving analytical methods and tools such as econometrics, statistics, Computational economics, economics computational models, financial economics, mathematical finance and mathematical economics. Professions Economists work in many fields including academia, government and in the private sector, where they may also "study data and statistics in order to spot trends in economic activity, economic confidence levels, and consumer attitudes. They assess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indirect Utility Function
__NOTOC__ In economics, a consumer's indirect utility function v(p, w) gives the consumer's maximal attainable utility when faced with a vector p of goods prices and an amount of income w. It reflects both the consumer's preferences and market conditions. This function is called indirect because consumers usually think about their preferences in terms of what they consume rather than prices. A consumer's indirect utility v(p, w) can be computed from his or her utility function u(x), defined over vectors x of quantities of consumable goods, by first computing the most preferred affordable bundle, represented by the vector x(p, w) by solving the utility maximization problem, and second, computing the utility u(x(p, w)) the consumer derives from that bundle. The resulting indirect utility function is :v(p,w)=u(x(p,w)). The indirect utility function is: *Continuous on R''n''+ × R+ where ''n'' is the number of goods; *Decreasing in prices; *Strictly increasing in income; *Homogenou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marshallian Demand Function
In microeconomics, a consumer's Marshallian demand function (named after Alfred Marshall) is the quantity they demand of a particular good as a function of its price, their income, and the prices of other goods, a more technical exposition of the standard demand function. It is a solution to the utility maximization problem of how the consumer can maximize their utility for given income and prices. A synonymous term is uncompensated demand function, because when the price rises the consumer is not compensated with higher nominal income for the fall in their real income, unlike in the Hicksian demand function. Thus the change in quantity demanded is a combination of a substitution effect and a wealth effect. Although Marshallian demand is in the context of partial equilibrium theory, it is sometimes called Walrasian demand as used in general equilibrium theory (named after Léon Walras). According to the utility maximization problem, there are ''L'' commodities with price vector '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
