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Walrasian 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 p a ... [...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] |
Maximum Theorem
The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The statement was first proven by Claude Berge in 1959. The theorem is primarily used in mathematical economics and optimal control. Statement of theorem Maximum Theorem. Let X and \Theta be topological spaces, f:X\times\Theta\to\mathbb be a continuous function on the product X \times \Theta, and C:\Theta\rightrightarrows X be a compact-valued correspondence such that C(\theta) \ne \emptyset for all \theta \in \Theta. Define the ''marginal function'' (or ''value function'') f^* : \Theta \to \mathbb by :f^*(\theta)=\sup\ and the ''set of maximizers'' C^* : \Theta \rightrightarrows X by : C^*(\theta)= \mathrm\max\ = \ . If C is continuous (i.e. both upper and lower hemicontinuous) at \theta, then the value function f^* is continuous, and the set of maximizers C^* is upper-hemicontinuous with nonempty and compact values. As a co ... [...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] |
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] |
Linear Utility
In economics and consumer theory, a linear utility function is a function of the form: ::u(x_1,x_2,\dots,x_m) = w_1 x_1 + w_2 x_2 + \dots w_m x_m or, in vector form: ::u(\overrightarrow) = \overrightarrow \cdot \overrightarrow where: * m is the number of different goods in the economy. * \overrightarrow is a vector of size m that represents a bundle. The element x_i represents the amount of good i in the bundle. * \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, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant Elasticity Of Substitution
Constant elasticity of substitution (CES) is a common specification of many production functions and utility function 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 economics, normative context, utility refers to a goal or ob ...s in neoclassical economics. CES holds that the ability to substitute one input factor with another (for example labour with capital) to maintain the same level of production stays constant over different production levels. For utility functions, CES means the consumer has constant preferences of how they would like to substitute different goods (for example labour with consumption) while keeping the same level of utility, for all levels of utility. What this means is that both producers and consumers have similar input structures and preferences no matter the level of output or utility. The vital economic element o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marginal Utility And Demand
Marginal may refer to: * ''Marginal'' (album), the third album of the Belgian rock band Dead Man Ray, released in 2001 * ''Marginal'' (manga) * '' El Marginal'', Argentine TV series * Marginal seat or marginal constituency or marginal, in politics See also Economics * Marginalism *Marginal analysis *Marginal concepts *Marginal cost * Marginal demand *Marginal product *Marginal product of labor *Marginal propensity to consume *Marginal rate of substitution *Marginal use *Marginal utility *Marginal rate Other * Margin (other) * Marginalization * Marginal intra-industry trade, where the change in a country's exports are essentially of the same products as its change in imports * Marginal land, land that is of little value because of its unsuitability for growing crops and other uses * Marginal model, in hierarchical linear modeling * Marginal observables, in physics; see Renormalization group * Marginal person, in sociology; see Marginalization * Marginal plant, see Bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marginal Utility
Marginal utility, in mainstream economics, describes the change in ''utility'' (pleasure or satisfaction resulting from the consumption) of one unit of a good or service. Marginal utility can be positive, negative, or zero. Negative marginal utility implies that every consumed additional unit of a commodity causes more harm than good, leading to a decrease in overall utility. In contrast, positive marginal utility indicates that every additional unit consumed increases overall utility. In the context of cardinal utility, liberal economists postulate a law of diminishing marginal utility. This law states that the first unit of consumption of a good or service yields more satisfaction or utility than the subsequent units, and there is a continuing reduction in satisfaction or utility for greater amounts. As consumption increases, the additional satisfaction or utility gained from each additional unit consumed falls, a concept known as ''diminishing marginal utility.'' This idea is us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Function
In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by the same scalar (mathematics), scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity, or simply the ''degree''. That is, if is an integer, a function of variables is homogeneous of degree if :f(sx_1,\ldots, sx_n)=s^k f(x_1,\ldots, x_n) for every x_1, \ldots, x_n, and s\ne 0. This is also referred to a ''th-degree'' or ''th-order'' homogeneous function. For example, a homogeneous polynomial of degree defines a homogeneous function of degree . The above definition extends to functions whose domain of a function, domain and codomain are vector spaces over a Field (mathematics), field : a function f : V \to W between two -vector spaces is ''homogeneous'' of degree k if for all nonzero s \in F and v \in V. This definition is often further generalized to f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upper-semicontinuous
In mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f is upper (respectively, lower) semicontinuous at a point x_0 if, roughly speaking, the function values for arguments near x_0 are not much higher (respectively, lower) than f\left(x_0\right). Briefly, a function on a domain X is lower semi-continuous if its epigraph \ is closed in X\times\R, and upper semi-continuous if -f is lower semi-continuous. A function is continuous if and only if it is both upper and lower semicontinuous. If we take a continuous function and increase its value at a certain point x_0 to f\left(x_0\right) + c for some c>0, then the result is upper semicontinuous; if we decrease its value to f\left(x_0\right) - c then the result is lower semicontinuous. The notion of upper and lower semicontinuous function was first introduced and studied by René Baire in his thesis in 1899. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Preferences
In economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, "averages are better than the extremes". This implies that the consumer prefers a variety of goods to having more of a single good. The concept roughly corresponds to the concept of marginal utility#Diminishing marginal utility, diminishing marginal utility without requiring utility functions. Notation Comparable to the greater-than-or-equal-to Order theory#Partially ordered sets, ordering relation \geq for real numbers, the notation \succeq below can be translated as: 'is at least as good as' (in Preference (economics), preference satisfaction). Similarly, \succ can be translated as 'is strictly better than' (in preference satisfaction), and Similarly, \sim can be translated as 'is equivalent to' (in preference satisfaction). Definition Use ''x'', ''y'', and ''z'' to denote three consumpti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
