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Expenditure Function
In microeconomics, the expenditure function represents the minimum amount of expenditure needed to achieve a given level of utility, given a utility function and the prices of goods. Formally, if there is a utility function u that describes preferences over ''n ''goods, the expenditure function e(p, u^*) is defined as: :e(p, u^*) = \min_ p \cdot x where p is the price vector u^* is the desired utility level, \geq(u^*) = \ is the set of providing at least utility 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_1 x_1^*+\dots + p_n x_n^*. Properties Suppose u is a continuous utility function representing a locally non-satiated preference relation on \textbf R^n_+. Then e(p, u^*) is # Homo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microeconomics
Microeconomics is a branch of economics that studies the behavior of individuals and Theory of the firm, firms in making decisions regarding the allocation of scarcity, 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 economy as a 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 Economic efficiency, efficient results. While microeconomics focuses on firms and individuals, macroeconomics focuses on the total of economic activity, dealing with the issues of Economic growth, growth, inflation, and unemployment—and with national policies relati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consumption Set
The theory of consumer choice is the branch of microeconomics that relates preferences to consumption expenditures and to consumer demand curves. It analyzes how consumers maximize the desirability of their consumption (as measured by their preferences subject to limitations on their expenditures), by maximizing utility subject to a consumer budget constraint. Factors influencing consumers' evaluation of the utility of goods include: income level, cultural factors, product information and physio-psychological factors. Consumption is separated from production, logically, because two different economic agents are involved. In the first case, consumption is determined by the individual. Their specific tastes or preferences determine the amount of utility they derive from goods and services they consume. In the second case, a producer has different motives to the consumer in that they are focussed on the profit they make. This is explained further by producer theory. The models tha ... [...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 their 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 , and P_y is the price of good , and is income. Soft budget constraint The concept of soft budget constraint is commonly applied to centrally planned economies, later 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 o ... [...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, optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a Natural borrowing limit, constraint on total spending (income), the prices of the goods and their Preference (economics), preferences. Utility maximization is an important concept in consumer theory as it shows how consumers decide to allocate their income. Because consumers are modelled as being Rational choice theory, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slutsky Equation
In microeconomics, the Slutsky equation (or Slutsky identity), 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 is negative. Slutsky derived this formula to explore a consumer's response as the price of a commodity changes. When the price increases, the budget set moves inward, which also causes the quantity demanded to decrease. In contrast, if 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 change is the resul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hicksian Demand Function
In microeconomics, a consumer's Hicksian demand function (or compensated demand function) represents the quantity of a good demanded when the consumer minimizes expenditure while maintaining a fixed level of utility. The Hicksian demand function illustrates how a consumer would adjust their demand for a good in response to a price change, assuming their income is adjusted (or compensated) to keep them on the same indifference curve—ensuring their utility remains unchanged. 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_ix_i is the total expenditure on all goods. The Hicksian demand function isolates the effect of relative prices on demand, assuming utility remains constant. It contrasts with the Marshallian demand function, which acco ... [...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 define ... [...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 their 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; * Homogenous wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utility
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. * In a normative context, utility refers to a goal or objective that we wish to maximize, i.e., an objective function. This kind of utility bears a closer resemblance to the original utilitarian concept, developed by moral philosophers such as Jeremy Bentham and John Stuart Mill. * In a descriptive context, the term refers to an ''apparent'' objective function; such a function is revealed by a person's behavior, and specifically by their preferences over lotteries, which can be any quantified choice. The relationship between these two kinds of utility functions has been a source of controversy among both economists and ethicists, with most maintaining that the two are distinct but generally related. Utility function Consider a set of alternatives among which a person has a preference ordering. A utility fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shephard's Lemma
Shephard's lemma is a 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 proved it using the distance formula in his book ''Theory of Cost and Production Functions'' in 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 Samuelson (1947). Definition In consumer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
