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| euler equation in economics: Advanced Macroeconomics David Romer, 2001 This text helps lay the groundwork for students to begin doing research in macroeconomics and monetary economics. A series of formal models are used to present and analyse important macroeconomic theories. The theories are supplemented by examples of relevant empirical work, which illustrate the ways that theories can be applied and tested. |
| euler equation in economics: Euler's Pioneering Equation Robin Wilson, 2018-02-22 In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics. Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'. While there were many worthy competitors, the winner was 'Euler's equation'. In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations. The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence. What is it that makes Euler's identity, eiπ + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; π an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers. Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula. |
| euler equation in economics: Handbook of Macroeconomics Michael Woodford, 1999 |
| euler equation in economics: Analytical Methods in Economics Akira Takayama, 1993 An accessible introduction to the analytical foundation of economics |
| euler equation in economics: Dynamic Economics Jerome Adda, Russell W. Cooper, 2023-05-09 An integrated approach to the empirical application of dynamic optimization programming models, for students and researchers. This book is an effective, concise text for students and researchers that combines the tools of dynamic programming with numerical techniques and simulation-based econometric methods. Doing so, it bridges the traditional gap between theoretical and empirical research and offers an integrated framework for studying applied problems in macroeconomics and microeconomics. In part I the authors first review the formal theory of dynamic optimization; they then present the numerical tools and econometric techniques necessary to evaluate the theoretical models. In language accessible to a reader with a limited background in econometrics, they explain most of the methods used in applied dynamic research today, from the estimation of probability in a coin flip to a complicated nonlinear stochastic structural model. These econometric techniques provide the final link between the dynamic programming problem and data. Part II is devoted to the application of dynamic programming to specific areas of applied economics, including the study of business cycles, consumption, and investment behavior. In each instance the authors present the specific optimization problem as a dynamic programming problem, characterize the optimal policy functions, estimate the parameters, and use models for policy evaluation. The original contribution of Dynamic Economics: Quantitative Methods and Applications lies in the integrated approach to the empirical application of dynamic optimization programming models. This integration shows that empirical applications actually complement the underlying theory of optimization, while dynamic programming problems provide needed structure for estimation and policy evaluation. |
| euler equation in economics: A Most Elegant Equation David Stipp, 2017-11-07 An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers Bertrand Russell wrote that mathematics can exalt as surely as poetry. This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. More than two centuries after Euler's death, it is still regarded as a conceptual diamond of unsurpassed beauty. Called Euler's identity or God's equation, it includes just five numbers but represents an astonishing revelation of hidden connections. It ties together everything from basic arithmetic to compound interest, the circumference of a circle, trigonometry, calculus, and even infinity. In David Stipp's hands, Euler's identity formula becomes a contemplative stroll through the glories of mathematics. The result is an ode to this magical field. |
| euler equation in economics: Recursive Methods in Economic Dynamics Nancy L. Stokey, 1989-10-10 This rigorous but brilliantly lucid book presents a self-contained treatment of modern economic dynamics. Stokey, Lucas, and Prescott develop the basic methods of recursive analysis and illustrate the many areas where they can usefully be applied. |
| euler equation in economics: Dynamic Optimization, Second Edition Morton I. Kamien, Nancy L. Schwartz, 2013-04-17 Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition. |
| euler equation in economics: Computational Techniques for Econometrics and Economic Analysis D.A. Belsley, 1994 It is unlikely that any frontier of economics/econometrics is being pushed faster, further than that of computational techniques. The computer has become a tool for performing as well as an environment in which to perform economics and econometrics, taking over where theory bogs down, allowing at least approximate answers to questions that defy closed mathematical or analytical solutions. Tasks may now be attempted that were hitherto beyond human potential, and all the forces available can now be marshalled efficiently, leading to the achievement of desired goals. Computational Techniques for Econometrics and Economic Analysis is a collection of recent studies which exemplify all these elements, demonstrating the power that the computer brings to the economic analysts. The book is divided into four parts: 1 -- the computer and econometric methods; 2 -- the computer and economic analysis; 3 -- computational techniques for econometrics; and 4 -- the computer and econometric studies. |
| euler equation in economics: Representation and Structure in Economics Hsiang-Ke Chao, 2020-04-08 This book provides a methodological perspective on understanding the essential roles of econometric models in the theory and practice. Offering a comprehensive and comparative exposition of the accounts of models in both econometrics and philosophy of science, this work shows how econometrics and philosophy of science are interconnected while exploring the methodological insight of econometric modelling that can be added to modern philosophical thought. The notion of structure is thoroughly discussed throughout the book. The studies of the consumption function of Trygve Haavelmo, Richard Stone, Milton Friedman, David Hendry and Robert Lucas are taken as the case studies to investigate their methodological implications of model and structure. In addition to the semantic view of the scientific theories, various philosophical accounts concerning scientific models are used to shed light on the methodological nature of these consumption studies in economics. This book will be of great interest to scholars and students of methodology of economics and econometrics as well as anyone interested in the philosophy of science in an economic context. |
| euler equation in economics: Linear Algebra for Economists Fuad Aleskerov, Hasan Ersel, Dmitri Piontkovski, 2011-08-18 This textbook introduces students of economics to the fundamental notions and instruments in linear algebra. Linearity is used as a first approximation to many problems that are studied in different branches of science, including economics and other social sciences. Linear algebra is also the most suitable to teach students what proofs are and how to prove a statement. The proofs that are given in the text are relatively easy to understand and also endow the student with different ways of thinking in making proofs. Theorems for which no proofs are given in the book are illustrated via figures and examples. All notions are illustrated appealing to geometric intuition. The book provides a variety of economic examples using linear algebraic tools. It mainly addresses students in economics who need to build up skills in understanding mathematical reasoning. Students in mathematics and informatics may also be interested in learning about the use of mathematics in economics. |
| euler equation in economics: Introduction to Computational Economics Using Fortran Hans Fehr, Maurice Hofmann, Fabian Kindermann, 2020 This exercise and solutions manual accompanies the main edition of Introduction to Computational Economics Using Fortran. It enables students of all levels to practice the skills and knowledge needed to conduct economic research using Fortran. Introduction to Computational Economics Using Fortran is the essential guide to conducting economic research on a computer. Aimed at students of all levels of education as well as advanced economic researchers, it facilitates the first steps into writing programming language. This exercise and solutions manual is accompanied by a program database that readers are able to download. |
| euler equation in economics: The New Palgrave Dictionary of Economics , 2016-05-18 The award-winning The New Palgrave Dictionary of Economics, 2nd edition is now available as a dynamic online resource. Consisting of over 1,900 articles written by leading figures in the field including Nobel prize winners, this is the definitive scholarly reference work for a new generation of economists. Regularly updated! This product is a subscription based product. |
| euler equation in economics: Applied Stochastic Differential Equations Simo Särkkä, Arno Solin, 2019-05-02 With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice. |
| euler equation in economics: Recursive Macroeconomic Theory Lars Ljungqvist, Thomas J. Sargent, 2004 A significant new edition of a text that offers both tools and sample applications; extensive revisions and seven new chapters improve and expand upon the original treatment. |
| euler equation in economics: Dr. Euler's Fabulous Formula Paul J. Nahin, 2017-04-04 In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory. In some ways a sequel to Nahin's An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr. Euler's Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come. |
| euler equation in economics: Dynamic Programming in Economics Cuong Van, Rose-Anne Dana, 2003-04-30 Dynamic Programming in Economics is an outgrowth of a course intended for students in the first year PhD program and for researchers in Macroeconomics Dynamics. It can be used by students and researchers in Mathematics as well as in Economics. The purpose of Dynamic Programming in Economics is twofold: (a) to provide a rigorous, but not too complicated, treatment of optimal growth models in infinite discrete time horizon, (b) to train the reader to the use of optimal growth models and hence to help him to go further in his research. We are convinced that there is a place for a book which stays somewhere between the minimum tool kit and specialized monographs leading to the frontiers of research on optimal growth. |
| euler equation in economics: Optimal Control Theory with Applications in Economics Thomas A. Weber, 2011-09-30 A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models. |
| euler equation in economics: Open Economy Macroeconomics Martín Uribe, Stephanie Schmitt-Grohé, 2017-04-04 A cutting-edge graduate-level textbook on the macroeconomics of international trade Combining theoretical models and data in ways unimaginable just a few years ago, open economy macroeconomics has experienced enormous growth over the past several decades. This rigorous and self-contained textbook brings graduate students, scholars, and policymakers to the research frontier and provides the tools and context necessary for new research and policy proposals. Martín Uribe and Stephanie Schmitt-Grohé factor in the discipline's latest developments, including major theoretical advances in incorporating financial and nominal frictions into microfounded dynamic models of the open economy, the availability of macro- and microdata for emerging and developed countries, and a revolution in the tools available to simulate and estimate dynamic stochastic models. The authors begin with a canonical general equilibrium model of an open economy and then build levels of complexity through the coverage of important topics such as international business-cycle analysis, financial frictions as drivers and transmitters of business cycles and global crises, sovereign default, pecuniary externalities, involuntary unemployment, optimal macroprudential policy, and the role of nominal rigidities in shaping optimal exchange-rate policy. Based on courses taught at several universities, Open Economy Macroeconomics is an essential resource for students, researchers, and practitioners. Detailed exploration of international business-cycle analysis Coverage of financial frictions as drivers and transmitters of business cycles and global crises Extensive investigation of nominal rigidities and their role in shaping optimal exchange-rate policy Other topics include fixed exchange-rate regimes, involuntary unemployment, optimal macroprudential policy, and sovereign default and debt sustainability Chapters include exercises and replication codes |
| euler equation in economics: Neuroeconomics Paul W. Glimcher, 2013-08-13 In the years since it first published, Neuroeconomics: Decision Making and the Brain has become the standard reference and textbook in the burgeoning field of neuroeconomics. The second edition, a nearly complete revision of this landmark book, will set a new standard. This new edition features five sections designed to serve as both classroom-friendly introductions to each of the major subareas in neuroeconomics, and as advanced synopses of all that has been accomplished in the last two decades in this rapidly expanding academic discipline. The first of these sections provides useful introductions to the disciplines of microeconomics, the psychology of judgment and decision, computational neuroscience, and anthropology for scholars and students seeking interdisciplinary breadth. The second section provides an overview of how human and animal preferences are represented in the mammalian nervous systems. Chapters on risk, time preferences, social preferences, emotion, pharmacology, and common neural currencies—each written by leading experts—lay out the foundations of neuroeconomic thought. The third section contains both overview and in-depth chapters on the fundamentals of reinforcement learning, value learning, and value representation. The fourth section, The Neural Mechanisms for Choice, integrates what is known about the decision-making architecture into state-of-the-art models of how we make choices. The final section embeds these mechanisms in a larger social context, showing how these mechanisms function during social decision-making in both humans and animals. The book provides a historically rich exposition in each of its chapters and emphasizes both the accomplishments and the controversies in the field. A clear explanatory style and a single expository voice characterize all chapters, making core issues in economics, psychology, and neuroscience accessible to scholars from all disciplines. The volume is essential reading for anyone interested in neuroeconomics in particular or decision making in general. - Editors and contributing authors are among the acknowledged experts and founders in the field, making this the authoritative reference for neuroeconomics - Suitable as an advanced undergraduate or graduate textbook as well as a thorough reference for active researchers - Introductory chapters on economics, psychology, neuroscience, and anthropology provide students and scholars from any discipline with the keys to understanding this interdisciplinary field - Detailed chapters on subjects that include reinforcement learning, risk, inter-temporal choice, drift-diffusion models, game theory, and prospect theory make this an invaluable reference - Published in association with the Society for Neuroeconomics—www.neuroeconomics.org - Full-color presentation throughout with numerous carefully selected illustrations to highlight key concepts |
| euler equation in economics: Mathematical Modeling in Economics, Ecology and the Environment N.V. Hritonenko, Yuri P. Yatsenko, 2013-04-17 The problems of interrelation between human economics and natural environment include scientific, technical, economic, demographic, social, political and other aspects that are studied by scientists of many specialities. One of the important aspects in scientific study of environmental and ecological problems is the development of mathematical and computer tools for rational management of economics and environment. This book introduces a wide range of mathematical models in economics, ecology and environmental sciences to a general mathematical audience with no in-depth experience in this specific area. Areas covered are: controlled economic growth and technological development, world dynamics, environmental impact, resource extraction, air and water pollution propagation, ecological population dynamics and exploitation. A variety of known models are considered, from classical ones (Cobb Douglass production function, Leontief input-output analysis, Solow models of economic dynamics, Verhulst-Pearl and Lotka-Volterra models of population dynamics, and others) to the models of world dynamics and the models of water contamination propagation used after Chemobyl nuclear catastrophe. Special attention is given to modelling of hierarchical regional economic-ecological interaction and technological change in the context of environmental impact. Xlll XIV Construction of Mathematical Models ... |
| euler equation in economics: Monetary Policy, Inflation, and the Business Cycle Jordi Galí, 2015-06-09 The classic introduction to the New Keynesian economic model This revised second edition of Monetary Policy, Inflation, and the Business Cycle provides a rigorous graduate-level introduction to the New Keynesian framework and its applications to monetary policy. The New Keynesian framework is the workhorse for the analysis of monetary policy and its implications for inflation, economic fluctuations, and welfare. A backbone of the new generation of medium-scale models under development at major central banks and international policy institutions, the framework provides the theoretical underpinnings for the price stability–oriented strategies adopted by most central banks in the industrialized world. Using a canonical version of the New Keynesian model as a reference, Jordi Galí explores various issues pertaining to monetary policy's design, including optimal monetary policy and the desirability of simple policy rules. He analyzes several extensions of the baseline model, allowing for cost-push shocks, nominal wage rigidities, and open economy factors. In each case, the effects on monetary policy are addressed, with emphasis on the desirability of inflation-targeting policies. New material includes the zero lower bound on nominal interest rates and an analysis of unemployment’s significance for monetary policy. The most up-to-date introduction to the New Keynesian framework available A single benchmark model used throughout New materials and exercises included An ideal resource for graduate students, researchers, and market analysts |
| euler equation in economics: The Master Equation and the Convergence Problem in Mean Field Games Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry, Pierre-Louis Lions, 2019-08-13 This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics. |
| euler equation in economics: Economic Growth, second edition Robert J. Barro, Xavier I. Sala-I-Martin, 2003-10-10 The long-awaited second edition of an important textbook on economic growth—a major revision incorporating the most recent work on the subject. This graduate level text on economic growth surveys neoclassical and more recent growth theories, stressing their empirical implications and the relation of theory to data and evidence. The authors have undertaken a major revision for the long-awaited second edition of this widely used text, the first modern textbook devoted to growth theory. The book has been expanded in many areas and incorporates the latest research. After an introductory discussion of economic growth, the book examines neoclassical growth theories, from Solow-Swan in the 1950s and Cass-Koopmans in the 1960s to more recent refinements; this is followed by a discussion of extensions to the model, with expanded treatment in this edition of heterogenity of households. The book then turns to endogenous growth theory, discussing, among other topics, models of endogenous technological progress (with an expanded discussion in this edition of the role of outside competition in the growth process), technological diffusion, and an endogenous determination of labor supply and population. The authors then explain the essentials of growth accounting and apply this framework to endogenous growth models. The final chapters cover empirical analysis of regions and empirical evidence on economic growth for a broad panel of countries from 1960 to 2000. The updated treatment of cross-country growth regressions for this edition uses the new Summers-Heston data set on world income distribution compiled through 2000. |
| euler equation in economics: Mathematical Economics Akira Takayama, 1985-08-30 This systematic exposition and survey of mathematical economics emphasizes the unifying structures of economic theory. |
| euler equation in economics: Macroeconomic Analysis Dirk Niepelt, 2019-12-31 A concise but rigorous and thorough introduction to modern macroeconomic theory. This book offers an introduction to modern macroeconomic theory. It is concise but rigorous and broad, covering all major areas in mainstream macroeconomics today and showing how macroeconomic models build on and relate to each other. The self-contained text begins with models of individual decision makers, proceeds to models of general equilibrium without and with friction, and, finally, presents positive and normative theories of economic policy. After a review of the microeconomic foundations of macroeconomics, the book analyzes the household optimization problem, the representative household model, and the overlapping generations model. It examines risk and the implications for household choices and macroeconomic outcomes; equilibrium asset returns, prices, and bubbles; labor supply, growth, and business cycles; and open economy issues. It introduces frictions and analyzes their consequences in the labor market, financial markets, and for investment; studies money as a unit of account, store of value, and medium of exchange; and analyzes price setting in general equilibrium. Turning to government and economic policy, the book covers taxation, debt, social security, and monetary policy; optimal fiscal and monetary policies; and sequential policy choice, with applications in capital income taxation, sovereign debt and default, politically motivated redistribution, and monetary policy biases. Macroeconomic Analysis can be used by first-year graduate students in economics and students in master's programs, and as a supplemental text for advanced courses. |
| euler equation in economics: Euler's Gem David S. Richeson, 2019-07-23 How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author. |
| euler equation in economics: Dynamic Macroeconomic Theory Thomas J. Sargent, 2009-06-01 The tasks of macroeconomics are to interpret observations on economic aggregates in terms of the motivations and constraints of economic agents and to predict the consequences of alternative hypothetical ways of administering government economic policy. General equilibrium models form a convenient context for analyzing such alternative government policies. In the past ten years, the strengths of general equilibrium models and the corresponding deficiencies of Keynesian and monetarist models of the 1960s have induced macroeconomists to begin applying general equilibrium models. This book describes some general equilibrium models that are dynamic, that have been built to help interpret time-series of observations of economic aggregates and to predict the consequences of alternative government interventions. The first part of the book describes dynamic programming, search theory, and real dynamic capital pricing models. Among the applications are stochastic optimal growth models, matching models, arbitrage pricing theories, and theories of interest rates, stock prices, and options. The remaining parts of the book are devoted to issues in monetary theory; currency-in-utility-function models, cash-in-advance models, Townsend turnpike models, and overlapping generations models are all used to study a set of common issues. By putting these models to work on concrete problems in exercises offered throughout the text, Sargent provides insights into the strengths and weaknesses of these models of money. An appendix on functional analysis shows the unity that underlies the mathematics used in disparate areas of rational expectations economics. This book on dynamic equilibrium macroeconomics is suitable for graduate-level courses; a companion book, Exercises in Dynamic Macroeconomic Theory, provides answers to the exercises and is also available from Harvard University Press. |
| euler equation in economics: Handbook of Computational Economics Karl Schmedders, Kenneth L. Judd, 2013-12-31 Handbook of Computational Economics summarizes recent advances in economic thought, revealing some of the potential offered by modern computational methods. With computational power increasing in hardware and algorithms, many economists are closing the gap between economic practice and the frontiers of computational mathematics. In their efforts to accelerate the incorporation of computational power into mainstream research, contributors to this volume update the improvements in algorithms that have sharpened econometric tools, solution methods for dynamic optimization and equilibrium models, and applications to public finance, macroeconomics, and auctions. They also cover the switch to massive parallelism in the creation of more powerful computers, with advances in the development of high-power and high-throughput computing. Much more can be done to expand the value of computational modeling in economics. In conjunction with volume one (1996) and volume two (2006), this volume offers a remarkable picture of the recent development of economics as a science as well as an exciting preview of its future potential. - Samples different styles and approaches, reflecting the breadth of computational economics as practiced today - Focuses on problems with few well-developed solutions in the literature of other disciplines - Emphasizes the potential for increasing the value of computational modeling in economics |
| euler equation in economics: Inframarginal Economics Xiaokai Yang, Wai-Man Liu, 2009 This monograph resurrects the spirit of classical economic thinking on network effects of division of labor and general equilibrium mechanisms that simultaneously determine the interdependent benefits of specialization and the number of participants in the network of division of labor (extent of the market) in a modern body of inframarginal economics. Inframarginal economics applies inframarginal analysis (nonclassical mathematical programming which allows corner solution) to studies of network effects of division of labor, individuals' networking decisions in choosing their levels of specialization, mechanisms that endogenously determine the network size and pattern of division of labor, increasing returns, and the relationship between transaction costs, evolution in institutions, property rights, contracts, organization, and the network size and pattern of division of labor. Here, inframarginal analysis is total cost-benefit analysis across different network patterns of trade and division of labor in addition to marginal analysis of resource allocation for a given pattern of organization. It provides an overarching framework that encompasses many areas of the discipline that have customarily been treated as separate branches. These include microeconomics, macroeconomics, development economics, international economics, urban economics, growth theory, industrial organization. applications of game theory in economics, economics of property rights, economics of transaction costs, economics of institutions and contracts, economics of organization, managerial economics, theory of hierarchy, new theory of the firm, theory of money, theory of insurance, theory of the network and reliability, and so on. |
| euler equation in economics: Mathematics for Stability and Optimization of Economic Systems Yasuo Murata, 2014-05-10 Economic Theory and Mathematical Economics: Mathematics for Stability and Optimization of Economic Systems provides information pertinent to the stability aspects and optimization methods relevant to various economic systems. This book presents relevant mathematical theorems sufficient to develop important economic systems, including Leontief input–output systems, Keynesian dynamic models, the Ramsey optimal accumulation systems, and von Neumann expanding economic systems. Organized into two parts encompassing nine chapters, this book begins with an overview of useful theorems on matrices, eigenvalue problems, and matrices with dominant diagonals and P-matrices. This text then explores the linear transformations on vector spaces. Other chapters consider the Hawkins–Simon theorem concerning non-negative linear systems. This book discusses as well the dual linear relations and optimization methods applicable to inequality economic systems. The final chapter deals with powerful optimal control method for dynamical systems. This book is a valuable resource for mathematicians, economists, research workers, and graduate students. |
| euler equation in economics: Structural Econometric Models Eugene Choo, Matthew Shum, 2013-12-18 This volume focuses on recent developments in the use of structural econometric models in empirical economics. The first part looks at recent developments in the estimation of dynamic discrete choice models. The second part looks at recent advances in the area empirical matching models. |
| euler equation in economics: Variational Principles in Classical Mechanics Douglas Cline, 2018-08 Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York. |
| euler equation in economics: Shocks, Stocks and Socks Martin Browning, Thomas F. Crossley, 1999 |
| euler equation in economics: Handbook of Behavioral Economics - Foundations and Applications 1 , 2018-09-27 Handbook of Behavioral Economics: Foundations and Applications presents the concepts and tools of behavioral economics. Its authors are all economists who share a belief that the objective of behavioral economics is to enrich, rather than to destroy or replace, standard economics. They provide authoritative perspectives on the value to economic inquiry of insights gained from psychology. Specific chapters in this first volume cover reference-dependent preferences, asset markets, household finance, corporate finance, public economics, industrial organization, and structural behavioural economics. This Handbook provides authoritative summaries by experts in respective subfields regarding where behavioral economics has been; what it has so far accomplished; and its promise for the future. This taking-stock is just what Behavioral Economics needs at this stage of its so-far successful career. - Helps academic and non-academic economists understand recent, rapid changes in theoretical and empirical advances within behavioral economics - Designed for economists already convinced of the benefits of behavioral economics and mainstream economists who feel threatened by new developments in behavioral economics - Written for those who wish to become quickly acquainted with behavioral economics |
| euler equation in economics: Mathematica for Microeconomics John Robert Stinespring, 2002-01-10 Accompanying CD-ROM contains ... the Mathematica programs discussed in the book and MathReader software (a viewing program from Wolfram, Inc.).--Page 4 of cover. |
| euler equation in economics: Reconstruction of Macroeconomics: Methods of Statistical Physics, and Keynes' Principle of Effective Demand Hiroshi Yoshikawa, 2022-10-29 This book explains how standard micro-founded macroeconomics is misguided and proposes an alternative method based on statistical physics. The Great Recession following the bankruptcy of Lehman Brothers in September 2015 amply demonstrated that mainstream micro-founded macroeconomics was in trouble. The new approach advanced in this book reasonably explains important macro-problems such as employment, business cycles, growth, and inflation/deflation. The key concept is demand failures, which modern micro-founded macroeconomics has ignored. “It (Chapter 3) captures analytically a good part of the intuition that underlies the Keynesian economics of people like Tobin and me.” Robert Solow, Emeritus Institute Professor of Economics, Massachusetts Institute of Technology, Nobel Laureate in Economics, 1987 “Professor Hiroshi Yoshikawa provides a unique synthesis of statistical physics and macro-economic theory in order to confront the dismal failure in economics and in finance to understand how an economy or a financial market works, given the heterogeneous decision making of many different individual interacting actors. Economics has failed in this regard with the naive and often misleading concept of “representative agents.” The author presents many insights on the historical development, concepts, and errors made by the most illustrious economists in the past. This book should be essential readings for any economics students as well as academic researchers and policy makers, who should learn to bring back good-sense thinking in their impactful decisions.” Didier Sornette, Professor on the Chair of Entrepreneurial Risks at the Swiss Federal Institute of Technology Zurich (ETH Zurich) |
| euler equation in economics: Advances in Economics and Econometrics Econometric Society. World Congress, 2003-01-20 Sample Text |
| euler equation in economics: Quantitative Financial Economics Keith Cuthbertson, Dirk Nitzsche, 2005-05-05 This new edition of the hugely successful Quantitative Financial Economics has been revised and updated to reflect the most recent theoretical and econometric/empirical advances in the financial markets. It provides an introduction to models of economic behaviour in financial markets, focusing on discrete time series analysis. Emphasis is placed on theory, testing and explaining ‘real-world’ issues. The new edition will include: Updated charts and cases studies. New companion website allowing students to put theory into practice and to test their knowledge through questions and answers. Chapters on Monte Carlo simulation, bootstrapping and market microstructure. |
| euler equation in economics: The Routledge Handbook of Environmental Economics in Asia Shunsuke Managi, 2015-02-11 Problems of climate change, biodiversity and air pollution are clearly growing globally, but more particularly in Asia because of its economic importance and richness in nature. The increasing interest in environmental and resource economics applied in regions of Asia will make this book an outstanding resource to the existing literature, particularly in the fields of environmental and resource economics and the integration of applied content in traditional and agricultural development. At present there is no single handbook or text on the state of current knowledge in environmental economics in Asia or one which offers a comprehensive guide to students and academics on the subjects of environmental economics research. This book will help to fill the gap in the existing literature. |
How to prove Euler's formula: $e^{it}=\\cos t +i\\sin t$?
Aug 28, 2010 · Euler's formula is quite a fundamental result, and we never know where it could have been used. I don't expect one to know the proof of every dependent theorem of a given result.
Euler Product formula for Riemann zeta function proof
Apr 15, 2016 · A formal proof based on the sieving method described in Proof of the Euler product formula for the Riemann zeta function is given below, along with a 'heuristic' proof - ie a non …
What is the geometrical importance of the Euler Line?
Jul 23, 2021 · What is the geometrical importance of the Euler Line (ie, the line through the centroid, orthocenter, and circumcenter (and other points) of a non-equilateral triangle)? What is …
The interconnection between Hyperbolic functions and Euler's …
Jul 16, 2018 · There is one difference that arises in solving Euler's identity for standard trigonometric functions and hyperbolic trigonometric functions. The difference is that the …
Why is it Euler's 'Totient' Function? - Mathematics Stack Exchange
Dec 13, 2018 · The function ϕ(n) ϕ (n) calculates the number of positive integers k ⩽ n , gcd(k, n) = 1 k ⩽ n , gcd (k, n) = 1. It was found by mathematician Leonhard Euler. In 1879, mathematician …
rotations - Are Euler angles the same as pitch, roll and yaw ...
The 3 3 Euler angles (usually denoted by α, β α, β and γ γ) are often used to represent the current orientation of an aircraft. Starting from the "parked on the ground with nose pointed North" …
Does Euler's formula give $e^{-ix}=\\cos(x) -i\\sin(x)$?
Apr 13, 2018 · Does Euler's formula give e − ix = cos(x) − isin(x)? Ask Question Asked 7 years, 2 months ago Modified 6 years, 11 months ago
algebraic topology - Euler characteristic of a covering space ...
The fact that the Euler characteristic of a sensible space with coefficients on a local system of coefficients which locally looks like Zn Z n is n n times that of the space should be written down …
How can I prove Euler's formula using mathematical induction
Mar 18, 2019 · Using Euler's formula in graph theory where r − e + v = 2 r − e + v = 2 I can simply do induction on the edges where the base case is a single edge and the result will be 2 vertices. A …
Euler characteristic of torus - Mathematics Stack Exchange
Jun 1, 2021 · We know that the euler characteristic of the torus is 0 0. Let´s say I have a torus which has a quadratic hole. As far as I understood the shape of the hole doesn't make any difference in …
How to prove Euler's formula: $e^{it}=\\cos t +i\\sin t$?
Aug 28, 2010 · Euler's formula is quite a fundamental result, and we never know where it could have been used. I don't expect one to know the proof of every dependent theorem of a given …
Euler Product formula for Riemann zeta function proof
Apr 15, 2016 · A formal proof based on the sieving method described in Proof of the Euler product formula for the Riemann zeta function is given below, along with a 'heuristic' proof - ie a non …
What is the geometrical importance of the Euler Line?
Jul 23, 2021 · What is the geometrical importance of the Euler Line (ie, the line through the centroid, orthocenter, and circumcenter (and other points) of a non-equilateral triangle)? What …
The interconnection between Hyperbolic functions and Euler's …
Jul 16, 2018 · There is one difference that arises in solving Euler's identity for standard trigonometric functions and hyperbolic trigonometric functions. The difference is that the …
Why is it Euler's 'Totient' Function? - Mathematics Stack Exchange
Dec 13, 2018 · The function ϕ(n) ϕ (n) calculates the number of positive integers k ⩽ n , gcd(k, n) = 1 k ⩽ n , gcd (k, n) = 1. It was found by mathematician Leonhard Euler. In 1879, …
rotations - Are Euler angles the same as pitch, roll and yaw ...
The 3 3 Euler angles (usually denoted by α, β α, β and γ γ) are often used to represent the current orientation of an aircraft. Starting from the "parked on the ground with nose pointed North" …
Does Euler's formula give $e^{-ix}=\\cos(x) -i\\sin(x)$?
Apr 13, 2018 · Does Euler's formula give e − ix = cos(x) − isin(x)? Ask Question Asked 7 years, 2 months ago Modified 6 years, 11 months ago
algebraic topology - Euler characteristic of a covering space ...
The fact that the Euler characteristic of a sensible space with coefficients on a local system of coefficients which locally looks like Zn Z n is n n times that of the space should be written down …
How can I prove Euler's formula using mathematical induction
Mar 18, 2019 · Using Euler's formula in graph theory where r − e + v = 2 r − e + v = 2 I can simply do induction on the edges where the base case is a single edge and the result will be 2 …
Euler characteristic of torus - Mathematics Stack Exchange
Jun 1, 2021 · We know that the euler characteristic of the torus is 0 0. Let´s say I have a torus which has a quadratic hole. As far as I understood the shape of the hole doesn't make any …
