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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] |
Microeconomics
Microeconomics is a branch of mainstream economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics focuses on the study of individual markets, sectors, or industries as opposed to the national economy as whole, which is studied in macroeconomics. One goal of microeconomics is to analyze the market mechanisms that establish relative prices among goods and services and allocate limited resources among alternative uses. Microeconomics shows conditions under which free markets lead to desirable allocations. It also analyzes market failure, where markets fail to produce efficient results. While microeconomics focuses on firms and individuals, macroeconomics focuses on the sum total of economic activity, dealing with the issues of growth, inflation, and unemployment and with national policies relating to these issues. Microeconomics also deal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utility
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a single consumer's preference ordering over a choice set but is not comparable across consumers. This concept of utility is personal and based on choice rather than on pleasure received, and so is specified more rigorously than the original concept but makes it less useful (and controversial) for ethical decisions. Utility function Consider a set of alternatives among which a person can make a preference ordering. The utility obtained from these alternatives is an unknown function of the utilities obtained from each alternative, not the sum of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utility Function
As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophers such as Jeremy Bentham and John Stuart Mill. The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a utility function that represents a single consumer's preference ordering over a choice set but is not comparable across consumers. This concept of utility is personal and based on choice rather than on pleasure received, and so is specified more rigorously than the original concept but makes it less useful (and controversial) for ethical decisions. Utility function Consider a set of alternatives among which a person can make a preference ordering. The utility obtained from these alternatives is an unknown function of the utilities obtained from each alternative, not the sum of ... [...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] |
Indirect Utility
__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] |
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] |
Expenditure Minimization Problem
In microeconomics, the expenditure minimization problem is the dual of the utility maximization problem: "how much money do I need to reach a certain level of happiness?". This question comes in two parts. Given a consumer's utility function, prices, and a utility target, * how much money would the consumer need? This is answered by the expenditure function. * what could the consumer buy to meet this utility target while minimizing expenditure? This is answered by the Hicksian demand function. Expenditure function Formally, the expenditure function is defined as follows. Suppose the consumer has a utility function u defined on L commodities. Then the consumer's expenditure function gives the amount of money required to buy a package of commodities at given prices p that give utility of at least u^*, :e(p, u^*) = \min_ p \cdot x where :\geq = \ is the set of all packages that give utility at least as good as u^*. Hicksian demand correspondence Hicksian demand is defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hicksian Demand Function
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] |
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] |
Utility Maximization Problem
Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the goods and their preferences. Utility maximization is an important concept in consumer theory as it shows how consumers decide to allocate their income. Because consumers are rational, they seek to extract the most benefit for themselves. However, due to bounded rationality and other biases, consumers sometimes pick bundles that do not necessarily maximize their utility. The utility maximization bundle of the consumer is also not set and can change over time depending on their individual preferences of goods, price changes and increase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budget Constraint
In economics, a budget constraint represents all the combinations of goods and services that a consumer may purchase given current prices within his or her given income. Consumer theory uses the concepts of a budget constraint and a preference map as tools to examine the parameters of consumer choices . Both concepts have a ready graphical representation in the two-good case. The consumer can only purchase as much as their income will allow, hence they are constrained by their budget. The equation of a budget constraint is P_x x+P_y y=m where P_x is the price of good X, and P_y is the price of good Y, and m = income. Soft budget constraint The concept of soft budget constraints is commonly applied to economies in transition. This theory was originally proposed by János Kornai in 1979. It was used to explain the "economic behavior in socialist economies marked by shortage”. In the socialist transition economy there are soft budget constraint on firms because of subsidies, c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
