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Elasticity (mathematics)
In mathematics, the elasticity or point elasticity of a positive differentiable function ''f'' of a positive variable (positive input, positive output) at point ''a'' is defined as :Ef(a) = \fracf'(a) :=\lim_\frac\frac=\lim_\frac\frac=\lim_\frac\approx \frac or equivalently :Ef(x) = \frac. It is thus the ratio of the relative (percentage) change in the function's output f(x) with respect to the relative change in its input x, for infinitesimal changes from a point (a, f(a)). Equivalently, it is the ratio of the infinitesimal change of the logarithm of a function with respect to the infinitesimal change of the logarithm of the argument. Generalisations to multi-input-multi-output cases also exist in the literature. The elasticity of a function is a constant \alpha if and only if the function has the form f(x) = C x ^ \alpha for a constant C>0. The elasticity at a point is the limit of the arc elasticity between two points as the separation between those two points approaches zero. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marginal Concepts
In economics, marginal concepts are associated with a ''specific change'' in the quantity used of a good or service, as opposed to some notion of the over-all significance of that class of good or service, or of some total quantity thereof.{{citation needed, date=February 2012 Marginality Constraints are conceptualized as a ''border'' or ''margin''. Wicksteed, Philip Henry; ''The Common Sense of Political Economy'' (1910), Bk I Ch 2 and elsewhere. The location of the margin for any individual corresponds to his or her ''endowment'', broadly conceived to include opportunities. This endowment is determined by many things including physical laws (which constrain how forms of energy and matter may be transformed), accidents of nature (which determine the presence of natural resources), and the outcomes of past decisions made both by others and by the individual himself or herself. A value that holds true given particular constraints is a ''marginal'' value. A change that would b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Function
In mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, 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. For example, a homogeneous polynomial of degree defines a homogeneous function of degree . The above definition extends to functions whose domain and codomain are vector spaces over a 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 functions whose domain is not , but a cone in , that is, a subset of such that \mathbf\in C implies s\mathbf\in C for every nonzero scalar . In the case of functions of several real variables and real vecto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity (economics)
In economics, elasticity measures the percentage change of one economic variable in response to a percentage change in another. If the price elasticity of the demand of something is -2, a 10% increase in price causes the demand quantity to fall by 20%. Introduction Elasticity is an important concept in neoclassical economic theory, and enables in the understanding of various economic concepts, such as the incidence of indirect taxation, marginal concepts relating to the theory of the firm, distribution of wealth, and different types of goods relating to the theory of consumer choice. An understanding of elasticity is also important when discussing welfare distribution, in particular consumer surplus, producer surplus, or government surplus. Elasticity is present throughout many economic theories, with the concept of elasticity appearing in several main indicators. These include price elasticity of demand, price elasticity of supply, income elasticity of demand, elastici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arc Elasticity
In mathematics and economics, the arc elasticity is the elasticity of one variable with respect to another between two given points. It is the ratio of the percentage change of one of the variables between the two points to the percentage change of the other variable. It contrasts with the ''point elasticity'', which is the limit of the arc elasticity as the distance between the two points approaches zero and which hence is defined at a single point rather than for a pair of points. Like the point elasticity, the arc elasticity can vary in value depending on the starting point. For example, the arc elasticity of supply of a product with respect to the product's price could be large when the starting and ending prices are both low, but could be small when they are both high.20%/10%=2 Formula The ''y'' arc elasticity of ''x'' is defined as: :E_ = \frac where the percentage change in going from point 1 to point 2 is usually calculated relative to the midpoint: :\% \mbox x = \frac; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modified Duration
{{disambiguation ...
Modified may refer to: * ''Modified'' (album), the second full-length album by Save Ferris *Modified racing, or "Modifieds", an American automobile racing genre See also * Modification (other) * Modifier (other) Modifier may refer to: * Grammatical modifier, a word that modifies the meaning of another word or limits its meaning ** Compound modifier, two or more words that modify a noun ** Dangling modifier, a word or phrase that modifies a clause in an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supply Function
In economics, supply is the amount of a resource that firms, producers, labourers, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or to an individual. Supply can be in produced goods, labour time, raw materials, or any other scarce or valuable object. Supply is often plotted graphically as a supply curve, with the price per unit on the vertical axis and quantity supplied as a function of price on the horizontal axis. This reversal of the usual position of the dependent variable and the independent variable is an unfortunate but standard convention. The supply curve can be either for an individual seller or for the market as a whole, adding up the quantity supplied by all sellers. The quantity supplied is for a particular time period (e.g., the tons of steel a firm would supply in a year), but the units and time are often omitted in theoretical presentations. In the goods market, supply is the amount of a product per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ray (geometry)
In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word ''line'' may also refer to a line segment in everyday life, which has two points to denote its ends. Lines can be referred by two points that lay on it (e.g., \overleftrightarrow) or by a single letter (e.g., \ell). Euclid described a line as "breadthless length" which "lies evenly with respect to the points on itself"; he introduced several postulates as basic unprovable properties from which he constructed all of geometry, which is now called Euclidean geometry to avoid confusion with other geometries which have been introduced since the end of the 19th century (such as non-Euclidean, projective and affine geometry). In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Demand Function
In economics, a demand curve is a graph depicting the relationship between the price of a certain commodity (the ''y''-axis) and the quantity of that commodity that is demanded at that price (the ''x''-axis). Demand curves can be used either for the price-quantity relationship for an individual consumer (an individual demand curve), or for all consumers in a particular market (a market demand curve). It is generally assumed that demand curves slope down, as shown in the adjacent image. This is because of the law of demand: for most goods, the quantity demanded falls if the price rises. Certain unusual situations do not follow this law. These include Veblen goods, Giffen goods, and speculative bubbles where buyers are attracted to a commodity if its price rises. Demand curves are used to estimate behaviour in competitive markets and are often combined with supply curves to find the equilibrium price (the price at which sellers together are willing to sell the same amount as buy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differentiable Function
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp. If is an interior point in the domain of a function , then is said to be ''differentiable at'' if the derivative f'(x_0) exists. In other words, the graph of has a non-vertical tangent line at the point . is said to be differentiable on if it is differentiable at every point of . is said to be ''continuously differentiable'' if its derivative is also a continuous function over the domain of the function f. Generally speaking, is said to be of class if its first k derivatives f^(x), f^(x), \ldots, f^(x) exist and are continuous over the domain of the func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity Of Demand
A good's price elasticity of demand (E_d, PED) is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others. The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant. If the elasticity is −2, that means a one percent price rise leads to a two percent decline in quantity demanded. Other elasticities measure how the quantity demanded changes with other variables (e.g. the income elasticity of demand for consumer income changes). Price elasticities are negative except in special cases. If a good is said to have an elasticity of 2, it almost always means that the good has an elasticity of −2 according to the formal definition. The phrase "more elastic" means that a good's elasticity has greater magnitude, ignoring the sign. Veblen and Giffen goods are two classes of good ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity Coefficient
The rate of a chemical reaction is influenced by many different factors, such as temperature, pH, reactant, and product concentrations and other effectors. The degree to which these factors change the reaction rate is described by the elasticity coefficient. This coefficient is defined as follows: : \varepsilon_^v=\left(\frac \frac\right)_=\frac \approx \frac where v denotes the reaction rate and s denotes the substrate concentration. Be aware that the notation will use lowercase roman letters, such as s, to indicate concentrations. The partial derivative in the definition indicates that the elasticity is measured with respect to changes in a factor S while keeping all other factors constant. The most common factors include substrates, products, and effectors. The scaling of the coefficient ensures that it is dimensionless and independent of the units used to measure the reaction rate and magnitude of the factor. The elasticity coefficient is an integral part of metabolic con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
