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Corner Solution
A corner solution is a special solution to an agent's maximization problem in which the quantity of one of the arguments in the maximized function is zero. In non-technical terms, a corner solution is when the chooser is either unwilling or unable to make a trade-off between goods. In economics In the context of economics the corner solution is best characterised by when the highest indifference curve attainable is not tangential to the budget line, in this scenario the consumer puts their entire budget into purchasing as much of one of the goods as possible and none of any other. When the slope of the indifference curve is greater than the slope of the budget line, the consumer is willing to give up more of good 1 for a unit of good 2 than is required by the market. Thus, it follows that if the slope of the indifference curve is strictly greater than the slope of the budget line: \text > \text; \ \forall \text Then the result will be a corner solution intersecting the x-axis. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Corner Solution
A corner solution is a special solution to an agent's maximization problem in which the quantity of one of the arguments in the maximized function is zero. In non-technical terms, a corner solution is when the chooser is either unwilling or unable to make a trade-off between goods. In economics In the context of economics the corner solution is best characterised by when the highest indifference curve attainable is not tangential to the budget line, in this scenario the consumer puts their entire budget into purchasing as much of one of the goods as possible and none of any other. When the slope of the indifference curve is greater than the slope of the budget line, the consumer is willing to give up more of good 1 for a unit of good 2 than is required by the market. Thus, it follows that if the slope of the indifference curve is strictly greater than the slope of the budget line: \text > \text; \ \forall \text Then the result will be a corner solution intersecting the x-axis. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consumer Theory
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: 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 by the primary individual, individual tastes or preferences determine the amount of pleasure people derive from the goods and services they consume.; in the second case, a producer might make something that he would not consume himself. Therefore, different motivations and abilities are involved. The models that make up consumer theory ar ... [...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] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interior Solution (optimization)
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assumptions Section
Assumption, in Christianity, refers to the Assumption of Mary, a belief in the taking up of the Virgin Mary into heaven. Assumption may also refer to: Places * Assumption, Alberta, Canada * Assumption, Illinois, United States ** Assumption Township, Christian County, Illinois * Assumption Island, Seychelles ** Assumption Island Airport * Assumption, Minnesota, United States * Assumption, Nebraska, United States * Assumption, Ohio, United States * Assumption Parish, Louisiana, United States Arts, entertainment, and media * "Assumption" (short story), a 1929 story by Samuel Beckett * Assumption of Moses, a Jewish apocryphal pseudepigraphical work of uncertain date and authorship Churches * Assumption Chapel, Minnesota, United States * Assumption of the Blessed Virgin Mary Church, Michigan, United States * Assumption – St. Paul, New York, United States * Cathedral of the Assumption (other) * Church of the Assumption (other) Logic * Closed-world assumpti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian
Lagrangian may refer to: Mathematics * Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier ** Lagrangian relaxation, the method of approximating a difficult constrained problem with an easier problem having an enlarged feasible set ** Lagrangian dual problem, the problem of maximizing the value of the Lagrangian function, in terms of the Lagrange-multiplier variable; See Dual problem * Lagrangian, a functional whose extrema are to be determined in the calculus of variations * Lagrangian submanifold, a class of submanifolds in symplectic geometry * Lagrangian system, a pair consisting of a smooth fiber bundle and a Lagrangian density Physics * Lagrangian mechanics, a reformulation of classical mechanics * Lagrangian (field theory), a formalism in classical field theory * Lagrangian point, a position in an orbital configuration of two large bodies * Lagrangian coordinates, a way of describing the motions of particles ... [...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] |
Objective Function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economics, for example, this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Agent (economics)
In economics, an agent is an actor (more specifically, a decision maker) in a model of some aspect of the economy. Typically, every agent makes decisions by solving a well- or ill-defined optimization or choice problem. For example, ''buyers'' (consumers) and ''sellers'' ( producers) are two common types of agents in partial equilibrium models of a single market. Macroeconomic models, especially dynamic stochastic general equilibrium models that are explicitly based on microfoundations, often distinguish households, firms, and governments or central banks as the main types of agents in the economy. Each of these agents may play multiple roles in the economy; households, for example, might act as consumers, as workers, and as voters in the model. Some macroeconomic models distinguish even more types of agents, such as workers and shoppers or commercial banks. The term ''agent'' is also used in relation to principal–agent models; in this case, it refers specifically to someone de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Extrema
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function at a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Elegance
Mathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful or describe mathematics as an art form, e.g., a position taken by G. H. Hardy) or, at a minimum, as a creative activity. Comparisons are made with music and poetry. In method Mathematicians describe an especially pleasing method of proof as ''elegant''. Depending on context, this may mean: * A proof that uses a minimum of additional assumptions or previous results. * A proof that is unusually succinct. * A proof that derives a result in a surprising way (e.g., from an apparently unrelated theorem or a collection of theorems). * A proof that is based on new and original insights. * A method of proof that can be easily generalized to solve a family of similar problems. In the search for an elegant proof, mathematicians oft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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