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Economic theorems are fundamental propositions or principles in economics that are derived from a set of assumptions and are supported by logical reasoning or empirical evidence. These theorems provide insights into how economic agents behave, how markets function, and how various economic phenomena are interrelated.

General equilibrium theory is a fundamental concept in economics that seeks to explain how supply and demand in multiple markets interact simultaneously to determine prices and allocation of resources in an economy. Unlike partial equilibrium analysis, which examines a single market in isolation, general equilibrium considers the interdependencies among various markets. Key components of general equilibrium theory include: 1. **Multiple Markets**: General equilibrium takes into account various goods and services, as well as the factors of production (labor, capital, land, etc.

Mathematical economists are economists who use mathematical methods and techniques to analyze economic theories and models. Their work often involves the formulation of economic problems in mathematical terms, which allows for precise definitions, derivations, and predictions. Mathematical economists may focus on various areas of economics, including microeconomics, macroeconomics, game theory, econometrics, and optimization. Key characteristics of mathematical economists include: 1. **Mathematical Modeling**: They develop models to represent economic phenomena.

An all-pay auction is a type of auction in which all participants must pay their bids regardless of whether they win the auction or not. Unlike traditional auctions where only the highest bidder pays their bid amount, in an all-pay auction, every bidder pays what they bid, and the item is awarded to the highest bidder. This type of auction can create unique strategic considerations for bidders, as all participants have to commit their resources upfront.

The Almost Ideal Demand System (AIDS) is a model used in economics to analyze consumer demand for goods and services. It was introduced by economists Angus Deaton and John Muellbauer in 1980. The AIDS model is particularly valued for its flexibility and ability to approximate a wide range of demand systems while maintaining desirable properties such as adding up, homogeneity, and symmetry.

The Averch–Johnson effect is an economic phenomenon observed in the context of regulated utilities, particularly in industries like electricity or gas. It describes the tendency for regulated firms to over-invest in capital relative to what would be considered efficient or optimal. This effect arises when regulatory frameworks allow firms to earn a return on their invested capital.

The Brander-Spencer model is a seminal economic model that addresses issues of strategic trade theory, particularly in the context of international competition and government intervention. Developed by James Brander and Barbara Spencer in their 1983 paper, the model explores how government subsidies can affect the competitive dynamics between firms in international markets. ### Key Features of the Brander-Spencer Model: 1. **Market Structure**: The model typically examines an oligopolistic market where a small number of firms dominate.

Charles F. Roos was a prominent American mathematician known for his work in the field of statistics, particularly in the development of econometric models. He made significant contributions to the field of statistical theory and applied statistics. Roos is recognized for his research in time series analysis and regression analysis, and he played a role in advancing methods for economic data analysis. If you are looking for more specific information about Charles F. Roos or his contributions, please provide additional context or details!

The Coate-Loury model is an economic framework that explores the relationship between education, income distribution, and externalities associated with human capital accumulation. Developed by researchers Stephen Coate and David Loury in the early 1990s, the model addresses how individuals' investments in education can lead to varying income levels and thus affect overall economic inequality in a society.

Computational economics is an interdisciplinary field that utilizes computational methods and techniques to analyze economic models, conduct simulations, and solve complex economic problems. It combines elements from economics, computer science, mathematics, and statistics to better understand economic systems and behavior. Key features of computational economics include: 1. **Modeling Complexity**: Economic systems are often complex, involving multiple agents with diverse behaviors and interactions.

Contract theory is a field of study in economics and legal studies that examines how individuals and organizations formulate contracts and agreements in the presence of uncertainty and varying information. It focuses on the design, enforcement, and implications of contracts in various contexts, considering factors such as incentives, moral hazards, and the allocation of risks among contracting parties.

The elasticity of a function measures how sensitive the output of that function is to changes in its input. In economics, for instance, elasticity is commonly used to assess how quantity demanded or supplied responds to changes in price. Mathematically, the elasticity \(E\) of a function \(f(x)\) with respect to \(x\) is defined as the percentage change in the output \(f(x)\) divided by the percentage change in the input \(x\).

Ergodicity economics is an approach to understanding economic systems that emphasizes the difference between time averages and ensemble averages in the context of decision-making under uncertainty. The term "ergodicity" comes from statistical mechanics, where it refers to systems that exhibit the same statistical properties over time as they do across different states or configurations.

The Gordon–Loeb model is a theoretical framework for determining the optimal amount of investment in cyber security. It was developed by Lawrence A. Gordon and Martin P. Loeb in their paper published in 2002. The model provides a way to assess how organizations can allocate their resources to protect their information systems and data from cyber threats.

The Gravity Model of Trade is an economic theory that explains the bilateral trade flow between two countries based on their economic sizes and distance between them. The model is inspired by Isaac Newton's law of gravitation, which states that the force of attraction between two objects is proportional to their masses and inversely proportional to the square of the distance between them.

The "Iron Law of Prohibition" is a concept in drug policy and sociology proposed by the American economist and law enforcement officer Dale G. F. (Dale) H. P. (Holly) A. Keene, which posits that as the level of prohibition increases, the potency of the prohibited substances also increases. In simpler terms, when a substance is banned or heavily restricted, the illegal market responds by producing more potent forms of that substance.

An isoelastic function, often referred to in economics, is a specific type of utility function characterized by constant relative risk aversion (CRRA). It has a unique property that makes it particularly useful for modeling situations in which individuals exhibit consistent behavior toward risk across different levels of wealth or consumption.

The Karush–Kuhn–Tucker (KKT) conditions are a set of necessary conditions for a solution to be optimal for a constrained optimization problem. They are widely used in mathematical optimization, particularly in nonlinear programming. The KKT conditions generalize the method of Lagrange multipliers to handle problems with inequality constraints.

Kuhn's theorem can refer to several concepts in different fields, but one of the most prominent is related to game theory and social choice theory, specifically "Kuhn's theorem" regarding extensive form games and backward induction. In the context of game theory, Kuhn's theorem states that in certain types of complete information games represented in extensive form, rational players will make choices that can be predicted based on the backward induction method.

The Maximum Theorem is a concept in mathematical optimization and economic theory that relates to the conditions under which certain types of maximum or minimum values occur. While the term can have different meanings in different contexts, it is most commonly associated with the study of utility functions in economics and the optimization of functions under certain constraints. In the context of economics, the Maximum Theorem often refers to results concerning the maximization of utility by consumers or firms.