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Overtaking Criterion
In economics, the overtaking criterion is used to compare infinite streams of outcomes. Mathematically, it is used to properly define a notion of optimality for a problem of optimal control on an unbounded time interval. Often, the decisions of a policy-maker may have influences that extend to the far future. Economic decisions made today may influence the economic growth of a nation for an unknown number of years into the future. In such cases, it is often convenient to model the future outcomes as an infinite stream. Then, it may be required to compare two infinite streams and decide which one of them is better (for example, in order to decide on a policy). The overtaking criterion is one option to do this comparison. Notation X is the set of possible outcomes. E.g., it may be the set of positive real numbers, representing the possible annual gross domestic product. It is normalized X^\infty is the set of infinite sequences of possible outcomes. Each element in X^\infty is of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyzes the economy as a system where production, consumption, saving, and investment interact, and factors affecting it: employment of the resources of labour, capital, and land, currency inflation, economic growth, and public policies that have impact on glossary of economics, these elements. Other broad distinctions within economics include those between positive economics, desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimality
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Optimality may refer to: * Mathematical optimization * Optimality Theory in linguistics * optimality model, approach in biology See also * * Optimism (other) * Optimist (other) * Optimistic (other) * Optimization (other) * Optimum (other) The optimum is the best or most favorable condition, or the greatest amount or degree possible under specific sets of comparable circumstances. Optimum may also refer to: * Optimum (cable brand), a digital cable service * Optimum Releasing, a fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Control
Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory. Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Growth
Economic growth can be defined as the increase or improvement in the inflation-adjusted market value of the goods and services produced by an economy in a financial year. Statisticians conventionally measure such growth as the percent rate of increase in the real gross domestic product, or real GDP. Growth is usually calculated in real terms – i.e., inflation-adjusted terms – to eliminate the distorting effect of inflation on the prices of goods produced. Measurement of economic growth uses national income accounting. Since economic growth is measured as the annual percent change of gross domestic product (GDP), it has all the advantages and drawbacks of that measure. The economic growth-rates of countries are commonly compared using the ratio of the GDP to population (per-capita income). The "rate of economic growth" refers to the geometric annual rate of growth in GDP between the first and the last year over a period of time. This growth rate represents the trend in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gross Domestic Product
Gross domestic product (GDP) is a money, monetary Measurement in economics, measure of the market value of all the final goods and services produced and sold (not resold) in a specific time period by countries. Due to its complex and subjective nature this measure is often revised before being considered a reliable indicator. List of countries by GDP (nominal) per capita, GDP (nominal) per capita does not, however, reflect differences in the cost of living and the inflation, inflation rates of the countries; therefore, using a basis of List of countries by GDP (PPP) per capita, GDP per capita at purchasing power parity (PPP) may be more useful when comparing standard of living, living standards between nations, while nominal GDP is more useful comparing national economies on the international market. Total GDP can also be broken down into the contribution of each industry or sector of the economy. The ratio of GDP to the total population of the region is the GDP per capita, p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Order
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The relation itself is called a "partial order." The word ''partial'' in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable. Informal definition A partial order defines a notion of comparison. Two elements ''x'' and ''y'' may stand in any of four mutually exclusive relationships to each other: either ''x'' ''y'', or ''x'' and ''y'' are ''incompar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinal Utility
In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations. Two utility indices are related by an affine transformation if for the value u(x_i) of one index ''u'', occurring at any quantity x_i of the goods bundle being evaluated, the corresponding value v(x_i) of the other index ''v'' satisfies a relationship of the form :v(x_i) = au(x_i) + b\!, for fixed constants ''a'' and ''b''. Thus the utility functions themselves are related by :v(x) = au(x) + b. The two indices differ only with respect to scale and origin. Thus if one is concave, so is the other, in which case there is often said to be diminishing marginal utility. Thus the use of cardinal utility imposes the assumption that levels of absolute satisfaction exist, so that the magnitudes of increments to satisfaction can be compared across different situations. In consumer choice theory, ordinal utility with its weaker assumption ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Countable Set
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements. In more technical terms, assuming the axiom of countable choice, a set is ''countable'' if its cardinality (its number of elements) is not greater than that of the natural numbers. A countable set that is not finite is said countably infinite. The concept is attributed to Georg Cantor, who proved the existence of uncountable sets, that is, sets that are not countable; for example the set of the real numbers. A note on terminology Although the terms "countable" and "countably infinite" as defined here are quite co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Order
In mathematics, a total or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation \leq on some set X, which satisfies the following for all a, b and c in X: # a \leq a ( reflexive). # If a \leq b and b \leq c then a \leq c ( transitive). # If a \leq b and b \leq a then a = b ( antisymmetric). # a \leq b or b \leq a ( strongly connected, formerly called total). Total orders are sometimes also called simple, connex, or full orders. A set equipped with a total order is a totally ordered set; the terms simply ordered set, linearly ordered set, and loset are also used. The term ''chain'' is sometimes defined as a synonym of ''totally ordered set'', but refers generally to some sort of totally ordered subsets of a given partially ordered set. An extension of a given partial order to a total order is called a linear extension of that partial order. Strict and non-strict total orders A on a set X is a strict partial o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Relation
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as '' discontinuities''. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is . Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity. Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debreu Theorems
In economics, the Debreu theorems are several statements about the representation of a preference ordering by a real-valued function. The theorems were proved by Gerard Debreu during the 1950s. Background Suppose a person is asked questions of the form "Do you prefer A or B?" (when A and B can be options, actions to take, states of the world, consumption bundles, etc.). All the responses are recorded. Then, preferences of that person are represented by a numeric ''utility function'', such that the utility of option A is larger than option B if and only if the agent prefers A to B. The Debreu theorems come to answer the following basic question: what conditions on the preference relation of the agent guarantee that such representative utility function can be found? Existence of ordinal utility function The 1954 Theorems say, roughly, that every preference relation which is complete, transitive and continuous, can be represented by a continuous ordinal utility function. St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repeated Games
In game theory, a repeated game is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of his or her current action on the future actions of other players; this impact is sometimes called his or her reputation. ''Single stage game'' or ''single shot game'' are names for non-repeated games. For the real-life example of a repeated game, consider two gas stations that are adjacent to one another. They compete by publicly posting pricing and have the same and constant marginal cost c (the wholesale price of gasoline). Assume that when they both charge p = 10, their joint profit is maximized, resulting in a high profit for everyone. Despite the fact that this is the best outcome for them, they are motivated to deviate. By modestly lowering the price, anyone can steal all of their c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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