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Leontief Utilities
In economics, especially in consumer theory, a Leontief utility function is a function of the form: u(x_1,\ldots,x_m)=\min\left\ . where: * m is the number of different goods in the economy. * x_i (for i\in 1,\dots,m) is the amount of good i in the bundle. * w_i (for i\in 1,\dots,m) is the weight of good i for the consumer. This form of utility function was first conceptualized by Wassily Leontief. Examples Leontief utility functions represent complementary goods. For example: * Suppose x_1 is the number of left shoes and x_2 the number of right shoes. A consumer can only use pairs of shoes. Hence, his utility is \min(x_1,x_2). * In a cloud computing environment, there is a large server that runs many different tasks. Suppose a certain type of a task requires 2 CPUs, 3 gigabytes of memory and 4 gigabytes of disk-space to complete. The utility of the user is equal to the number of completed tasks. Hence, it can be represented by: \min(, , ). Properties A consumer with a Leonti ... [...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] |
Indifference Curve
In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is ''indifferent''. That is, any combinations of two products indicated by the curve will provide the consumer with equal levels of utility, and the consumer has no preference for one combination or bundle of goods over a different combination on the same curve. One can also refer to each point on the indifference curve as rendering the same level of utility (satisfaction) for the consumer. In other words, an indifference curve is the locus of various points showing different combinations of two goods providing equal utility to the consumer. Utility is then a device to represent preferences rather than something from which preferences come. The main use of indifference curves is in the representation of potentially observable demand patterns for individual consumers over commodity bundles. There are infinitely many indifference curves: one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bimatrix Game
In game theory, a bimatrix game is a simultaneous game for two players in which each player has a finite number of possible actions. The name comes from the fact that the normal form of such a game can be described by two matrices - matrix A describing the payoffs of player 1 and matrix B describing the payoffs of player 2. Player 1 is often called the "row player" and player 2 the "column player". If player 1 has m possible actions and player 2 has n possible actions, then each of the two matrices has m rows by n columns. When the row player selects the i-th action and the column player selects the j-th action, the payoff to the row player is A ,j/math> and the payoff to the column player is B ,j/math>. The players can also play mixed strategies. A mixed strategy for the row player is a non-negative vector x of length m such that: \sum_^m x_i = 1. Similarly, a mixed strategy for the column player is a non-negative vector y of length n such that: \sum_^n y_j = 1. When the players ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs. If each player has chosen a strategy an action plan based on what has happened so far in the game and no one can increase one's own expected payoff by changing one's strategy while the other players keep their's unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduction (complexity)
In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently efficient reduction from one problem to another may be used to show that the second problem is at least as difficult as the first. Intuitively, problem ''A'' is reducible to problem ''B'', if an algorithm for solving problem ''B'' efficiently (if it existed) could also be used as a subroutine to solve problem ''A'' efficiently. When this is true, solving ''A'' cannot be harder than solving ''B''. "Harder" means having a higher estimate of the required computational resources in a given context (e.g., higher time complexity, greater memory requirement, expensive need for extra hardware processor cores for a parallel solution compared to a single-threaded solution, etc.). The existence of a reduction from ''A'' to ''B'', can be written in the shorthand notation ''A'' ≤m ''B'', usually with a subscript on the ≤ to indicate the t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Competitive Equilibrium
Competitive equilibrium (also called: Walrasian equilibrium) is a concept of economic equilibrium introduced by Kenneth Arrow and Gérard Debreu in 1951 appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices. Competitive markets are an ideal standard by which other market structures are evaluated. Definitions A competitive equilibrium (CE) consists of two elements: * A price function P. It takes as argument a vector representing a bundle of commodities, and returns a positive real number that represents its price. Usually the price function is linear - it is represented as a vector of prices, a price for each commodity type. * An allocation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrow–Debreu Model
In mathematical economics, the Arrow–Debreu model suggests that under certain economic assumptions (convex preferences, perfect competition, and demand independence) there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy. The model is central to the theory of general (economic) equilibrium and it is often used as a general reference for other microeconomic models. It is named after Kenneth Arrow, Gérard Debreu, and sometimes also Lionel W. McKenzie for his independent proof of equilibrium existence in 1954 as well as his later improvements in 1959. The A-D model is one of the most general models of competitive economy and is a crucial part of general equilibrium theory, as it can be used to prove the existence of general equilibrium (or Walrasian equilibrium) of an economy. In general, there may be many equilibria; however, with extra assumptions on consumer preferences, namely that their utility function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Good
In economics, a normal good is a type of a Good (economics), good which experiences an increase in demand due to an increase in income, unlike inferior goods, for which the opposite is observed. When there is an increase in a person's income, for example due to a wage rise, a good for which the demand rises due to the wage increase, is referred as a normal good. Conversely, the demand for normal goods declines when the income decreases, for example due to a wage decrease or layoffs. Analysis There is a positive correlation between the income and demand for normal goods, that is, the changes income and demand for normal goods moves in the same direction. That is to say, that normal goods have an elastic relationship for the demand of a good with the income of the person consuming the good. In economics, the concept of elasticity, and specifically income elasticity of demand is key to explain the concept of normal goods. Income elasticity of demand measures the magnitude of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marshallian Demand
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 ... [...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". The concept roughly corresponds to the concept of diminishing marginal utility without requiring utility functions. Notation Comparable to the greater-than-or-equal-to ordering relation \geq for real numbers, the notation \succeq below can be translated as: 'is at least as good as' (in 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 consumption bundles (combinations of various quantities of various goods). Formally, a preference relation \succeq on the consumption set ''X'' is called convex if whenever :x, y, z \in X where y \succeq x a ... [...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] |
Monotone Preferences
In economics, an agent's preferences are said to be weakly monotonic if, given a consumption bundle x, the agent prefers all consumption bundles y that have more of all goods. That is, y \gg x implies y\succ x. An agent's preferences are said to be strongly monotonic if, given a consumption bundle x, the agent prefers all consumption bundles y that have more of at least one good, and not less in any other good. That is, y\geq x and y\neq x imply y\succ x. This definition defines monotonic increasing preferences. Monotonic decreasing preferences can often be defined to be compatible with this definition. For instance, an agent's preferences for pollution may be monotonic decreasing (less pollution is better). In this case, the agent's preferences for lack of pollution are monotonic increasing. Much of consumer theory relies on a weaker assumption, local nonsatiation. An example of preferences which are weakly monotonic but not strongly monotonic are those represented by a Leontief ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
