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Monotone Comparative Statics
Monotone comparative statics is a sub-field of comparative statics that focuses on the conditions under which endogenous variables undergo monotone changes (that is, either increasing or decreasing) when there is a change in the exogenous parameters. Traditionally, comparative results in economics are obtained using the Implicit Function Theorem, an approach that requires the concavity and differentiability of the objective function as well as the interiority and uniqueness of the optimal solution. The methods of monotone comparative statics typically dispense with these assumptions. It focuses on the main property underpinning monotone comparative statics, which is a form of complementarity between the endogenous variable and exogenous parameter. Roughly speaking, a maximization problem displays complementarity if a higher value of the exogenous parameter increases the marginal return of the endogenous variable. This guarantees that the set of solutions to the optimization problem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Comparative Statics
In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous variable, exogenous parameter. As a type of ''static analysis'' it compares two different economic equilibrium, equilibrium states, after the process of adjustment (if any). It does not study the motion towards equilibrium, nor the process of the change itself. Comparative statics is commonly used to study changes in supply and demand when analyzing a single Market (economics), market, and to study changes in monetary policy, monetary or fiscal policy when analyzing the whole macroeconomics, economy. Comparative statics is a tool of analysis in microeconomics (including general equilibrium analysis) and macroeconomics. Comparative statics was formalized by Sir John Richard Hicks, John R. Hicks (1939) and Paul A. Samuelson (1947) (Kehoe, 1987, p. 517) but was presented graphically from at least the 1870s. For models of stable equili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Probability Distributions
In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values. Probability distributions can be defined in different ways and for discrete or for continuous variables. Distributions with special properties or for especially important applications are given specific names. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Model (economics)
An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes. Frequently, economic models posit structural parameters. A model may have various exogenous variables, and those variables may change to create various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world. Overview In general terms, economic models have two functions: first as a simplification of and abstraction from observed data, and second as a means of selection of data based on a paradigm of econometric study. ''Simplification'' is particularly important for economics given the enormous complexity of economic processes. This complexity can be attributed to the diversity of factors that determine economic activity; the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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] [Amazon] |
Comparative Statics
In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous variable, exogenous parameter. As a type of ''static analysis'' it compares two different economic equilibrium, equilibrium states, after the process of adjustment (if any). It does not study the motion towards equilibrium, nor the process of the change itself. Comparative statics is commonly used to study changes in supply and demand when analyzing a single Market (economics), market, and to study changes in monetary policy, monetary or fiscal policy when analyzing the whole macroeconomics, economy. Comparative statics is a tool of analysis in microeconomics (including general equilibrium analysis) and macroeconomics. Comparative statics was formalized by Sir John Richard Hicks, John R. Hicks (1939) and Paul A. Samuelson (1947) (Kehoe, 1987, p. 517) but was presented graphically from at least the 1870s. For models of stable equili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Risk Aversion
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome. Risk aversion explains the inclination to agree to a situation with a lower average payoff that is more predictable rather than another situation with a less predictable payoff that is higher on average. For example, a risk-averse investor might choose to put their money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value. Example A person is given the choice between two scenarios: one with a guaranteed payoff, and one with a risky payoff with same average value. In the former scenario, the person receives $50. In the uncertain scenario, a coin is flipped to decide whether the person receives $100 or nothing. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Monotone Likelihood Ratio
A monotonic likelihood ratio in distributions \ f(x)\ and \ g(x)\ The ratio of the probability density function, density functions above is monotone in the parameter \ x\ , so \ \frac\ satisfies the monotone likelihood ratio property. In statistics, the monotone likelihood ratio property is a property of the ratio of two probability density functions (PDFs). Formally, distributions \ f(x)\ and \ g(x)\ bear the property if : \ \textx_2 > x_1, \quad \frac \geq \frac\ that is, if the ratio is nondecreasing in the argument x. If the functions are first-differentiable, the property may sometimes be stated :\frac \left( \frac \right) \geq 0\ For two distributions that satisfy the definition with respect to some argument \ x\ , we say they "have the MLRP in \ x ~." For a family of distributions that all satisfy the definition with respect to some statistic \ T(X)\ , we say they "have the MLR in \ T(X) ~." Intuition The MLRP is used to represent a data-generating process tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Budget Set
In economics, a budget set, or the opportunity set facing a consumer, is the set of all possible consumption bundles that the consumer can afford taking as given the prices of commodities available to the consumer and the consumer's income. Let the number of commodities available to the consumer in an economy be finite and equal to k. Thus, for commodity amounts \mathbf = \left x_, x_, \ldots, x_ \right/math>, also known as consumption plans which should not exceed the income, with associated prices \mathbf = \left p_, p_, \ldots, p_ \right/math> and consumer income m, the budget set is defined as :B_ = \left\, where the consumption set is taken to be X = \mathbb^_. It is typically assumed that \mathbf \gg 0 and m \in \mathbb_, in which case B is also known as the Walrasian, or competitive, budget set. The budget set is bounded above by a k-dimensional budget hyperplane characterized by the equation \mathbf \mathbf = m, which in the two-good case corresponds to the budget line. Gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Supermodular Function
In mathematics, a supermodular function is a function on a lattice that, informally, has the property of being characterized by "increasing differences." Seen from the point of set functions, this can also be viewed as a relationship of "increasing returns", where adding more elements to a subset increases its valuation. In economics, supermodular functions are often used as a formal expression of complementarity in preferences among goods. Supermodular functions are studied and have applications in game theory, economics, lattice theory, combinatorial optimization, and machine learning. Definition Let (X, \preceq) be a lattice. A real-valued function f: X \rightarrow \mathbb is called supermodular if f(x \vee y) + f(x \wedge y) \geq f(x) + f(y) for all x, y \in X. If the inequality is strict, then f is strictly supermodular on X. If -f is (strictly) supermodular then ''f'' is called (strictly) submodular. A function that is both submodular and supermodular is called modula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Stochastic Dominance
Stochastic dominance is a Partially ordered set, partial order between random variables. It is a form of stochastic ordering. The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble for a broad class of decision-makers. It is based on shared preference (economics), preferences regarding sets of possible outcomes and their associated probabilities. Only limited knowledge of preferences is required for determining dominance. Risk aversion is a factor only in second order stochastic dominance. Stochastic dominance does not give a total order, but rather only a partial order: for some pairs of gambles, neither one stochastically dominates the other, since different members of the broad class of decision-makers will differ regarding which gamble is preferable without them generally being considered to be equally attractive. Through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hyperrectangle
In geometry, a hyperrectangle (also called a box, hyperbox, k-cell or orthotopeCoxeter, 1973), is the generalization of a rectangle (a plane figure) and the rectangular cuboid (a solid figure) to higher dimensions. A necessary and sufficient condition is that it is Congruence (geometry), congruent to the Cartesian product of finite interval (mathematics), intervals. This means that a k-dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every k-cell is compact (mathematics), compact. If all of the edges are equal length, it is a ''hypercube''. A hyperrectangle is a special case of a parallelohedron#Related shapes, parallelotope. Formal definition For every integer i from 1 to k, let a_i and b_i be real numbers such that a_i < b_i. The set of all points in whose coordinates satisfy the inequalities is a -cell. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Implicit Function Theorem
In multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does so by representing the relation as the graph of a function. There may not be a single function whose graph can represent the entire relation, but there may be such a function on a restriction of the domain of the relation. The implicit function theorem gives a sufficient condition to ensure that there is such a function. More precisely, given a system of equations (often abbreviated into ), the theorem states that, under a mild condition on the partial derivatives (with respect to each ) at a point, the variables are differentiable functions of the in some neighborhood of the point. As these functions generally cannot be expressed in closed form, they are ''implicitly'' defined by the equations, and this motivated the name of the theorem. In other words, under a mild condition on the partial derivatives, the set of zero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
