Mathematical economics

Mathematical economics is a field that applies mathematical methods and techniques to represent economic theories, analyze economic problems, and derive economic relationships. It utilizes mathematical concepts such as calculus, linear algebra, and optimization to model economic behaviors and interactions quantitatively. The primary objectives of mathematical economics include: 1. **Modeling Economic Behavior**: Creating models that describe how individuals, firms, and markets behave under various conditions. This includes utility functions, production functions, and demand and supply models.

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.

Arrow's impossibility theorem, formulated by economist Kenneth Arrow in his 1951 work "Social Choice and Individual Values," addresses the challenges of aggregating individual preferences into a collective decision or social welfare function. The theorem states that no voting system can convert individual preferences into a collective outcome that satisfies a specific set of reasonable criteria at the same time.

Aumann's Agreement Theorem, proposed by Robert Aumann in 1976, is a result in the field of Bayesian epistemology that addresses the conditions under which two rational agents with common prior beliefs can have common knowledge of their respective beliefs and still agree to disagree about a given proposition. The theorem states that if two agents have a common prior probability distribution over a set of possible states of the world, and they are both rational (i.e.

The Bondareva–Shapley theorem is a result in cooperative game theory that provides a characterization of the core of cooperative games. This theorem effectively gives conditions under which the core of a cooperative game is non-empty. Specifically, the theorem states that a cooperative game has a non-empty core if and only if the game is balanced.

The Coase theorem, named after economist Ronald Coase, is a concept in economics that addresses the issue of externalities and property rights. It states that, under certain conditions, if property rights are well-defined and transaction costs are low or nonexistent, private parties can negotiate mutually beneficial agreements to resolve externalities on their own, regardless of the initial allocation of property rights.

Debreu's representation theorems refer to results in mathematical economics developed by Gérard Debreu, particularly concerning the representation of preferences, utility functions, and their relation to general equilibrium theory.

The Dorfman–Steiner theorem is an important result in the field of operations research and convex analysis, particularly in the study of optimal policy and control systems. It provides a way to understand the conditions under which certain policies are effective. Specifically, the theorem characterizes the optimal policies in the context of dynamic programming and resource allocation problems.

The Duggan–Schwartz theorem is a result in the field of social choice theory, specifically concerning the aggregation of preferences in social welfare functions. It addresses the impossibility of certain desirable properties in the context of collective decision-making. In its essence, the theorem states that under certain conditions, it is impossible to create a social welfare function that satisfies all of the following criteria: 1. **Unrestricted Domain:** Any individual preference order can be taken as input.

Edgeworth's limit theorem is a result in probability theory and statistics that relates to the asymptotic distribution of sample averages. Specifically, it provides insight into the behavior of the distribution of sample means as the sample size increases, particularly when the underlying distribution of the population is not normally distributed. The theorem states that under certain conditions, the distribution of the sample mean can be approximated by a normal distribution, but it goes a step further by describing the nature of the convergence.

Efficient envy-free division refers to a method of dividing a resource (which could be anything from land, goods, or any divisible items) among multiple individuals in such a way that: 1. **Envy-free**: Each participant feels they received at least as much value as anyone else. In other words, no one envies another's share; they believe their own share is at least as good as the shares of others.

The Envelope Theorem is a concept in economics, particularly in the fields of optimization and comparative statics. It describes how the value of an optimal objective function changes with respect to changes in parameters of the model. The fundamental idea is that when evaluating the impact of a change in parameters on the optimal value of the objective function, we can typically simplify the analysis by looking at the optimal solution without needing to find the explicit form of the solution again.

Factor price equalization is an economic theory that is part of the Heckscher-Ohlin model of international trade. It suggests that if countries engage in free trade, the prices of factors of production (such as labor and capital) will tend to equalize across countries, under certain conditions. This occurs as countries specialize in the production of goods that utilize their abundant factors of production more intensively.

The Fisher Separation Theorem is a fundamental principle in finance and investment theory attributed to economist Irving Fisher. It states that under certain conditions, a firm's investment decisions and its financing decisions can be separated without affecting the overall value of the firm. ### Key Points of the Fisher Separation Theorem: 1. **Investment and Consumption**: The theorem emphasizes that a firm (or investor) can choose the optimal investment project based purely on its expected return, independent of the financing method used to fund that project.

The Fundamental Theorems of Welfare Economics consist of two key results that connect the allocation of resources in a market economy with the concepts of efficiency and optimality. These theorems provide a theoretical foundation for understanding how competitive markets operate and under what conditions they lead to socially desirable outcomes.

Gibbard's theorem is a fundamental result in social choice theory that addresses the issues of strategic voting in the context of ranked voting systems. More specifically, it states that any non-dictatorial voting system that can select one winner from a set of three or more candidates is susceptible to strategic manipulation.

The Gibbard–Satterthwaite theorem is a fundamental result in social choice theory and mechanism design that addresses the limitations of voting systems. It states that any voting rule (or voting mechanism) that satisfies certain reasonable conditions is susceptible to strategic manipulation, meaning that voters can gain by misrepresenting their true preferences.

The Heckscher–Ohlin theorem is a fundamental concept in international trade theory that explains how countries engage in trade based on their factor endowments. It was developed by economists Eli Heckscher and Bertil Ohlin in the early 20th century. The theorem posits that: 1. **Factor Proportions**: Different countries have different relative supplies of factors of production, such as labor, land, and capital. These differences lead to variations in production costs and capacities.

The Henry George theorem is a concept in public finance and urban economics, named after the American economist Henry George. The theorem addresses the relationship between land values, public infrastructure investments, and the benefits received from those investments by property owners. In essence, the Henry George theorem posits that the increase in land value resulting from public investments (such as the construction of roads, parks, schools, and other public facilities) can be captured through taxation.

Holmström's theorem, named after the economist Bengt Holmström, is a result in the field of contract theory. It revolves around the design of contracts in situations where there is asymmetric information, specifically regarding effort or actions taken by agents that cannot be perfectly observed by the principal. The key insights from Holmström's theorem are: 1. **Incentive Compatibility**: The theorem underscores the importance of designing contracts that provide the right incentives for agents (e.g.

Intensity of preference refers to the strength or degree of an individual's preference for one option over another. It is a concept often used in economics, psychology, and decision-making studies to understand how much more someone prefers one choice compared to alternatives. For example, if a person prefers chocolate ice cream over vanilla ice cream, the intensity of that preference can vary.

The Lerner symmetry theorem, often associated with the economist Abba Lerner, relates to the behavior of taxes and subsidies in an economy. The theorem posits that under certain conditions, the effects of a tax and a subsidy on output can be considered symmetrical. In other words, if a good is taxed, removing the tax (or replacing it with a subsidy) leads to similar effects on the quantity produced and consumed, though the sign of the effect is reversed.

The Liberal Paradox, formulated by economist Amartya Sen, highlights a conflict between individual freedoms and collective societal welfare within the context of liberalism. It addresses the tension between two fundamental principles: 1. **Individual Liberty**: The notion that individuals should have the freedom to pursue their own interests and make choices without coercion. 2. **Pareto Efficiency**: The idea that a situation is Pareto efficient if no individual's situation can be improved without worsening someone else's situation.

The Moving Equilibrium Theorem is not a widely recognized term in standard scientific or mathematical literature. However, it might refer to concepts in dynamic systems or various fields such as economics, physics, or ecology, where equilibrium states and their dynamics are studied. In a more general sense, equilibrium refers to a state in which all forces are balanced, and there is no net change in a system. A "moving equilibrium" could involve scenarios where the system dynamically adjusts to maintain balance despite external changes.

The Nakamura number is a concept used in mathematics, particularly in the study of large numbers and combinatorial game theory. Specifically, it refers to a sequence of extremely large numbers that arise in the context of certain games, often involving infinite moves or game positions. The Nakamura numbers are typically denoted as \(N(n)\), where \(n\) indicates the position in the sequence.

Okishio's theorem is an economic theorem proposed by the Japanese economist Yoshio Okishio in the 1960s. The theorem addresses the relationship between technological change, the rate of profit, and the value of goods in a capitalist economy. It specifically concerns the effects of technical progress on the profitability of firms.

Roy's identity is a result in the theory of statistical inference, particularly in the context of Bayesian analysis. It relates the posterior distribution of a parameter of interest given observed data to the prior distribution and the likelihood of the data observed.

The Rybczynski theorem is an important concept in international trade theory, particularly in the context of the Heckscher-Ohlin model. It addresses how changes in the endowments of factors of production (such as labor and capital) affect the output of goods in an economy.

Shephard's lemma is a concept in economic theory, particularly in the field of duality in consumer theory and production theory. It is named after David Shephard, who contributed significantly to the study of production functions and efficiency. The lemma states that the derivative of the value function of a cost minimization problem with respect to a factor price gives the corresponding input demand for that factor, assuming that the production frontier exhibits certain regularity conditions.

The Sonnenschein–Mantel–Debreu theorem is a foundational result in general equilibrium theory in economics. It addresses the relationship between individual preferences and market demand in an economy composed of many agents with potentially diverse preferences. The theorem can be summarized in the following points: 1. **Market Demand Aggregation**: The theorem shows that the aggregate demand for goods in a market can be inconsistent with the preferences of the individual consumers.

The Stolper-Samuelson theorem is a key result in international trade theory, which explains the relationship between trade, factor prices, and income distribution within a country. Named after economists Wolfgang Stolper and Paul Samuelson, who presented it in 1941, the theorem is often discussed in the context of the Heckscher-Ohlin model of international trade.

Topkis's theorem, named after Howard Topkis, is a result in the field of optimization and control theory, particularly concerning monotonic systems. The theorem provides conditions under which the optimal solutions of a dynamic programming problem are ordered in a certain way when the cost function is monotonic. Specifically, Topkis's theorem states that if the cost function is increasing in the state variable and the control variable, then the optimal value function will also be increasing.

The Utility Representation Theorem is a fundamental concept in decision theory and economics that relates to how preferences can be represented mathematically. The theorem establishes that if a decision-maker's preferences satisfy certain conditions, they can be represented using a utility function. Here are the core ideas surrounding the Utility Representation Theorem: 1. **Preferences**: The theorem begins with the notion of preferences, which are the choices individuals make among different options based on their perceived satisfaction or utility.

Uzawa's theorem, also known in the context of economics, particularly pertains to optimal growth models and is named after the economist Hirofumi Uzawa. It provides conditions under which an economy can achieve a dynamic equilibrium while maximizing utility over time, often in the context of intertemporal choice and resource allocation. In its most common formulation, Uzawa's theorem is discussed in relation to the optimal growth problem in economics, specifically the Ramsey model.

Weller's theorem, particularly in the context of number theory, is a result related to the distribution of prime numbers in certain arithmetic progressions. It essentially provides a criterion for determining when a prime number will be found in a given arithmetic sequence.

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.

Comparative statics is an analytical tool used in economics to compare the equilibrium states of a system before and after a change in an exogenous variable. It helps economists to understand how changes in external factors (such as policy changes, technological advancements, or changes in consumer preferences) impact economic agents' behaviors and outcomes in a given model. The process typically involves the following steps: 1. **Initial Equilibrium**: Establishing the initial equilibrium state of the model based on certain parameters and variables.

General equilibrium theory is a branch of economics that studies how supply and demand in multiple markets interact simultaneously and how they achieve an overall equilibrium in an economy. General equilibrium theorists analyze how changes in one part of the economy can affect the entire system, taking into account the interdependencies among different markets.

The term "abstract economy" is not commonly defined within economic literature, so its interpretation can vary. However, it generally refers to the theoretical or conceptual framework for understanding economic processes and relationships without being confined to specific real-world applications. 1. **Theoretical Constructs**: Abstract economy often involves the use of models, theories, and mathematical frameworks to represent and analyze economic phenomena.

Applied general equilibrium (AGE) refers to a branch of economic analysis that utilizes general equilibrium models to assess the effects of economic policies, external shocks, or changes in market conditions across multiple sectors of the economy. These models capture the interdependencies between different markets and agents, allowing for a comprehensive analysis of how various components of an economy interact with one another.

The Arrow–Debreu model is a foundational concept in modern microeconomic theory, named after economists Kenneth Arrow and Gérard Debreu, who developed it in the 1950s. The model provides a formal framework for understanding general equilibrium in a competitive market and demonstrates the conditions under which an economy can achieve Pareto efficiency.

Computable General Equilibrium (CGE) refers to a class of economic models that are used to analyze the economy as a whole and the interactions between various sectors, agents, and markets. These models are particularly useful for assessing the impacts of policy changes, economic shocks, or other external factors on an economy.

Dynamic Stochastic General Equilibrium (DSGE) is a macroeconomic modeling approach that combines elements of dynamic optimization, stochastic processes, and general equilibrium theory to analyze the behavior of an economy over time under uncertainty. DSGE models are widely used by economists for policy analysis, forecasting, and understanding the impact of economic shocks.

A Fisher market is a concept from economics, particularly in the field of market design and game theory, named after the economist, John Fisher. It typically refers to a model in which goods are allocated among several agents (consumers) based on their preferences and budget constraints. The Fisher market model provides a way to understand how prices can adjust in response to demand and supply to achieve an efficient allocation of resources.

General disequilibrium refers to a situation in an economic model where supply and demand across multiple markets are not in balance simultaneously. This is in contrast to general equilibrium, where all markets clear (i.e., supply equals demand) at the same time, leading to a stable state for the entire economy. In a state of general disequilibrium, certain markets might experience excess supply (surpluses) while others may face excess demand (shortages).

Hahn's problem is a question in mathematics, specifically in the area of number theory related to the behavior of integers along with some algebraic structures. It is closely associated with the study of *integral linear combinations* of certain sets and, more abstractly, touches on concepts from algebraic number theory and diophantine approximation. The problem is named after the mathematician Hans Hahn, who posed the original question concerning the nature of certain sequences of integers.

The IS-LM model is an economic framework that illustrates the interaction between the goods market and the money market in an economy. The model was developed by John Hicks and Alvin Hansen in the 1930s and is based on the work of John Maynard Keynes. ### Key Components of the IS-LM Model: 1. **IS Curve**: - The IS curve stands for "Investment-Savings.

The Kakutani Fixed-Point Theorem is an important result in the field of mathematical analysis and game theory, particularly in the study of convex sets and continuous functions. It generalizes the Brouwer Fixed-Point Theorem, which is applicable in Euclidean spaces, to more complex scenarios involving multi-valued functions.

Local nonsatiation is an economic concept that refers to a preference structure where, at any given consumption level, an individual can find a consumption bundle that they prefer more than their current one, no matter how much of a good they already have. This means that for any combination of goods, there exists nearby alternatives that yield higher satisfaction or utility. In simpler terms, local nonsatiation implies that consumers are never completely satisfied with what they have and can always find something better if they look closely.

Numéraire is a term used in economics, finance, and mathematics to refer to a unit of account or a standard numerical value that is used to measure the value of goods, services, or financial assets. In a broader sense, it acts as a common denominator that facilitates comparisons of value across different items. In the context of finance, numéraire can refer to a specific reference asset or currency used to express the value of other assets.

Partial equilibrium is an economic analysis tool used to examine the equilibrium conditions in a specific market in isolation from other markets. It focuses on the supply and demand dynamics within that particular market, assuming that other markets remain constant or unaffected by changes in this market. In a partial equilibrium framework, key elements include: 1. **Supply and Demand Curves**: The model uses supply and demand curves to determine the equilibrium price and quantity for a good or service.

Perfect competition is a theoretical market structure characterized by a set of specific conditions that foster an idealized form of competition among firms. In a perfectly competitive market, the following key assumptions typically hold true: 1. **Many Buyers and Sellers**: There are a large number of buyers and sellers in the market, none of whom has significant market power to influence prices. Each firm is a price taker.

Quantity adjustment refers to the process of modifying the quantity of goods or services to align with demand, inventory levels, production capabilities, pricing strategies, or contractual obligations. This adjustment can be applied in various contexts, including: 1. **Inventory Management**: Businesses may adjust the quantity of stock on hand to meet changing customer demands, avoid overstock situations, and minimize holding costs.

Radner equilibrium is a concept in economic theory that extends the idea of general equilibrium in markets to an environment where agents have incomplete information and trading occurs over time. It is particularly relevant in the context of dynamic models of asset pricing and markets where agents face uncertainty regarding the state of the world. The concept is named after economist Roy Radner, who developed the framework in the 1970s.

The term "regular economy" is not commonly used in economic literature, and its meaning can vary based on context. However, it may refer to a stable and conventional form of economic activity characterized by consistent patterns of production, distribution, and consumption of goods and services.

The Temporary Equilibrium Method is a concept used primarily in economics to analyze situations where an economy or market does not reach a long-term equilibrium. Instead, it examines the equilibrium conditions in a short-term frame, where certain factors are held constant or assumed to be fixed in the analysis. ### Key Features of the Temporary Equilibrium Method: 1. **Short-term Focus**: The method looks at the market dynamics over a brief period, rather than a long-term perspective.

Walras's law is an economic theory that states that in a general equilibrium model, the sum of the values of excess demands across all markets must equal zero. In simpler terms, it asserts that if there is excess supply in one market, there must be excess demand in another market, such that the overall market isn't deficient.

A Walrasian auction is a theoretical concept in economics that stems from the work of Léon Walras, a French economist known for his contributions to general equilibrium theory. The Walrasian auction is not an auction in the traditional sense but rather a method used to achieve market equilibrium where supply equals demand. In a Walrasian auction, a hypothetical auctioneer plays a crucial role in the market. The auctioneer announces prices for goods and allows buyers and sellers to respond to these prices.

The Wicksellian differential refers to the difference between the natural rate of interest and the actual market interest rate. It is named after the Swedish economist Knut Wicksell, who discussed the concept in the context of his monetary theory in the early 20th century. According to Wicksell, the natural rate of interest is the rate that would equilibrate savings and investment in an economy, without causing inflation or deflation.

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.

Computational economists are researchers who use computational methods and tools to analyze economic problems and simulate economic models. This interdisciplinary approach combines economics with computer science, mathematics, and statistics to tackle complex issues that may be difficult to solve using traditional analytical methods. Key aspects of computational economics include: 1. **Modeling Economic Systems**: Computational economists develop and analyze models that simulate the behavior of economic agents (such as consumers, firms, and governments) and how these agents interact within economic systems.

The Fellows of the Econometric Society is an honorary group within the Econometric Society, an international organization founded in 1930 to promote the advancement of economic theory in its relation to statistics and mathematics. The Society recognizes distinguished contributions to the field of econometrics and economic theory by electing a select group of scholars as Fellows. Being named a Fellow is a mark of distinction that acknowledges individuals who have made significant contributions to the understanding of economic phenomena through mathematical and statistical methods.

Abraham Wald was a Hungarian-born statistician, widely recognized for his contributions to statistical decision theory and mathematical statistics, particularly during World War II. He was born on October 31, 1902, and went on to pursue a distinguished academic career. One of Wald's most notable contributions is the concept of "survivorship bias," which he illustrated through his work with the U.S. military. During the war, he was tasked with analyzing the effectiveness of aircraft armor.

As of my last knowledge update in October 2023, there isn't a widely recognized figure named Alain A. Lewis in popular culture, politics, academia, or other notable fields. It's possible that he could be a private individual, a professional in a specific niche, or a figure who has gained prominence after my last update. If you have more context or specifics about Alain A.

Alexander Rinnooy Kan is a Dutch academic, politician, and business leader, known for his work in economics and public administration. He was born on March 6, 1949, in Amsterdam, the Netherlands. Rinnooy Kan has held various prominent roles throughout his career, including serving as a professor of economics at the University of Amsterdam and as a member of the Dutch Senate.

Allan Gibbard is an American philosopher known for his work in ethics, political philosophy, and the philosophy of language. He is particularly noted for his contributions to the field of normative ethics, especially regarding the concept of meta-ethical expressivism, which asserts that ethical statements express emotional attitudes rather than factual claims. Gibbard is also recognized for his exploration of issues related to moral disagreement, moral reasoning, and the nature of normativity.

"Alpha Chiang" typically refers to a well-known textbook in the field of economics titled "Fundamentals of Economics" by Alpha C. Chiang and Kevin Wainwright. The book is often used in introductory economics courses and covers key concepts in microeconomics and macroeconomics, focusing on both theoretical and practical aspects. Alpha Chiang is recognized for his contributions to economic theory, particularly in the areas of mathematical economics and optimization.

Andranik Tangian is a well-known figure in the field of mathematics, particularly recognized for his contributions to mathematical logic, set theory, and related areas. He may have several academic publications and works that detail his research findings.

Andreu Mas-Colell is a prominent Spanish economist known for his contributions to economic theory, particularly in the fields of microeconomics, game theory, and auction theory. He has published extensively and is recognized for his work on the foundations of economic mechanisms and the mathematical underpinnings of economic models. In addition to his research contributions, Mas-Colell has held significant academic and administrative positions.

Antoine Augustin Cournot (1801–1877) was a French mathematician and economist best known for his foundational contributions to the field of economics, particularly in the areas of monopolistic competition and the theory of demand. He is often recognized as one of the first economists to apply mathematical techniques to economic theories.

Charalambos D. Aliprantis is a notable mathematician primarily recognized for his contributions to functional analysis and economics. He has published extensively in various mathematical fields, and his work often intersects with applications in economic theory. Aliprantis is also known for co-authoring the widely-used textbook "Finite Dimensional Analysis in Econometrics," which is a key resource in both mathematics and economics education. His research touches on topics such as real analysis, optimization, and theory in applied mathematics.

David Easley is a prominent figure in the field of economics and is known for his work in game theory, market dynamics, and network theory. He is a professor at Cornell University, where he has contributed to the academic community through teaching, research, and publications. His research often intersects with various aspects of economics, including the behavior of markets and the strategic interactions of agents within those markets.

David M. Kreps is an American economist, renowned for his contributions to the fields of microeconomics, game theory, and economic dynamics. He is a professor at Stanford University's Graduate School of Business and has made significant contributions to understanding strategic behavior in economics, particularly in relation to incomplete information and sequential games. Kreps is known for his work on the theory of firm behavior, economic decision-making, and the role of information in markets.

It seems there may be some confusion, as "Donald John Roberts" does not refer to a widely recognized public figure or concept as of my last knowledge update in October 2021. It is possible you meant to refer to "Donald John Trump," the 45th President of the United States, or "John Roberts," the Chief Justice of the United States Supreme Court.

Elyès Jouini is a notable figure in the fields of economics and finance, particularly recognized for his contributions to research and academia. His work often focuses on topics related to financial markets, decision-making, and economic theory. Jouini has been involved in various academic institutions and has published numerous scholarly articles and papers.

Frank Hahn was a prominent British economist known for his significant contributions to economic theory, particularly in the areas of monetary economics, mathematical economics, and the theory of general equilibrium. He was born in 1925 and passed away in 2018. Hahn's work often focused on fundamental concepts such as the role of equilibrium in economic systems and the implications of economic policies.

Frederik Zeuthen may refer to a notable figure or concept related to economics, mathematics, or another field, but without more context, it is difficult to pinpoint precisely who or what you are referring to.

George Dantzig was an American mathematician and statistician, best known for his contributions to operations research and linear programming. He was born on November 8, 1914, and passed away on May 13, 2005. Dantzig developed the simplex algorithm, a method for solving linear programming problems, which has had a profound impact on various fields, including economics, engineering, and military logistics.

As of my last knowledge update in October 2023, there isn't widely known information about an individual named Gerald L. Thompson that would be relevant across general topics. It's possible that he may be a private individual, a professional in a specific field, or perhaps a lesser-known public figure.

Graciela Chichilnisky is an Argentine-American economist and mathematician known for her contributions to various fields, including economic theory, climate change economics, and the development of markets for environmental assets. She has played a significant role in the establishment of carbon trading systems and is one of the architects of the concept of "carbon credits". Chichilnisky has also been involved in international policy discussions regarding climate change and sustainable development.

Gérard Debreu (1921–2014) was a French economist and mathematician known for his significant contributions to the field of economic theory. He is best known for his work on general equilibrium theory, which analyzes how supply and demand in multiple markets interact and achieve balance through price mechanisms. Debreu's most notable achievement is his development of the mathematical framework for general equilibrium, which earned him the Nobel Prize in Economic Sciences in 1983.

Harold Hotelling (1895–1973) was an American mathematician and statistician known for his work in various fields, including economics, statistics, and operations research. He is particularly well-known for several contributions: 1. **Hotelling's T-squared Distribution**: This is a multivariate statistical test that generalizes the Student's t-test to higher dimensions. It is used in hypothesis testing for comparing the means of multivariate data.

Ismat Beg is not widely recognized as a specific term or entity in the broader cultural, historical, or literary contexts available up to October 2021. It could potentially be a personal name or a reference to a less commonly known subject, such as a person, place, or brand.

Ivar Ekeland is a prominent Norwegian mathematician known for his work in mathematical analysis, optimization, and the philosophy of mathematics. He has made significant contributions to various fields, including variational analysis and nonlinear analysis. Ekeland is perhaps best known for Ekeland's Variational Principle, a fundamental result in optimization theory that provides conditions under which a minimizer exists for certain types of optimization problems.

John G. Kemeny (1926-1992) was an American mathematician and computer scientist, best known for his contributions to the development of computer programming and for co-designing the BASIC programming language. He served as the president of Dartmouth College from 1970 to 1981, during which he advocated for the integration of computers into education.

Kenneth Arrow (1921–2017) was an influential American economist and a key figure in modern economic theory. He is best known for his work on general equilibrium theory and for the Arrow's Impossibility Theorem, which demonstrates that no voting system can convert individual preferences into a collective decision while meeting a specified set of fair criteria. This theorem has profound implications for social choice theory and the fields of economics and political science.

Laura Gardini is an Italian mathematician known for her contributions to the fields of analysis and applied mathematics. Her work often involves the study of dynamical systems, mathematical models, and their applications in various scientific domains.

Lawrence E. Blume is an American economist known for his work in various areas of economic theory, including game theory, experimental economics, and social choice theory. He has contributed to understanding how economic agents interact and how such interactions affect economic outcomes. Blume is also recognized for his role in academia, having held positions at several prestigious institutions. He has published numerous papers and articles in prominent economic journals, contributing to the advancement of economic thought.

Leonid Kantorovich (1912-1986) was a prominent Soviet mathematician and economist, best known for his contributions to the fields of operational research and linear programming. He was awarded the Nobel Prize in Economic Sciences in 1975, sharing the honor with Tjalling C. Koopmans, for their groundbreaking work in the theory of optimal resource allocation. Kantorovich developed a mathematical approach to optimize resource allocation in economics, effectively laying the groundwork for linear programming methods.

Lloyd Shapley was an influential American mathematician and economist, renowned for his work in game theory, particularly in the areas of cooperative games and the Shapley value, which assigns a value to each player based on their contribution to the overall payoff. His contributions have had a significant impact on economics, political science, and evolutionary biology. Shapley was awarded the Nobel Memorial Prize in Economic Sciences in 2012, jointly with Alvin E.

Olga Bondareva could refer to various individuals, as it is a relatively common name. However, without additional context, it's difficult to pinpoint a specific person or subject associated with that name.

Paul Milgrom is an American economist known for his significant contributions to auction theory, game theory, and contract theory. Born on April 20, 1948, he has served as a professor at Stanford University, where he has been a key figure in advancing the understanding of how auctions operate and how they can be designed effectively.

Pierre-André Chiappori is a prominent French economist known for his contributions to economic theory, particularly in the areas of labor economics, contract theory, and the economics of information. He is a professor at Columbia University and has a significant body of work that addresses issues in theoretical and applied economics. Chiappori is perhaps best known for his work on the theory of individual and collective choice, which explores how individuals make decisions in various contexts, including the family and marriage markets.

Robert B. Wilson is an American economist known for his significant contributions to the field of economic theory and auction design. He is particularly recognized for his work on auction design, market mechanisms, and game theory. In 2020, he was awarded the Nobel Prize in Economic Sciences, along with Paul R. Milgrom, for their advancements in auction theory and the practical implementation of innovative auction formats.

Robert Remak was a mathematician known for his contributions to various areas of mathematics, particularly in the fields of number theory and algebra. He is perhaps best known for his work on the Remak decomposition, which is related to the structure theory of finite groups. This decomposition is akin to the Jordan-Hölder theorem, which deals with the composition series of groups.

Roger Guesnerie is a prominent French economist known for his contributions to economic theory, particularly in the areas of public economics, social choice theory, and the roles of information and uncertainty in economic systems. He has a distinguished academic career, having held positions at various institutions, including the École des hautes études en sciences sociales (EHESS) and the Collège de France.

"Ross Starr" could refer to different entities or topics depending on the context, but there isn't a well-known figure or concept widely recognized by that exact name. If you're referring to a particular person, company, or cultural reference, additional information would help clarify your query.

Roy Radner is an American economist known for his contributions to the field of economic theory, particularly in the areas of game theory, decision theory, and organizational economics. He has made significant contributions to understanding how individuals and organizations make decisions under uncertainty and interaction with others. Radner is also recognized for his work on the theory of firms and the design of organizational structures that facilitate efficient decision-making. Over his career, he has published numerous papers and has been involved in various academic and professional organizations.

Samuel Karlin (1924–2007) was an influential American mathematician known for his significant contributions to various fields, including probability theory, statistics, and operations research. He was particularly recognized for his work in areas such as stochastic processes, queuing theory, and the mathematical theory of natural selection. In addition to his research, Karlin authored several important texts and research papers that have had a lasting impact on mathematics and related disciplines.

Semën Samsonovich Kutateladze is a notable figure in the fields of science and technology, particularly associated with aeronautics and machine learning. He is recognized for his contributions and research in these areas.

Serge-Christophe Kolm is a French economist and academic known for his work in various areas of economics including welfare economics, social choice theory, and economic philosophy. He has contributed to the understanding of how social welfare can be evaluated and how economic policies can address issues of equity and efficiency. Kolm is associated with the concept of measuring inequality and has developed frameworks for considering fairness in economic systems.