Foundations Of Mathematical And Computational Economics

This is a book on the basics of mathematics and computation and their uses in economics for modern day students and practitioners. The reader is introduced to the basics of numerical analysis as well as the use of computer programs such as Matlab and Excel in carrying out involved computations. Sections are devoted to the use of Maple in mathematical analysis. Examples drawn from recent contributions to economic theory and econometrics as well as a variety of end of chapter exercises help to illustrate and apply the presented concepts.

Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.

The ability to conceptualize an economic problem verbally, to formulate it as a mathematical model, and then represent the mathematics in software so that the model can be solved on a computer is a crucial skill for economists. Computational Economics contains well-known models--and some brand-new ones--designed to help students move from verbal to mathematical to computational representations in economic modeling. The authors' focus, however, is not just on solving the models, but also on developing the ability to modify them to reflect one's interest and point of view. The result is a book that enables students to be creative in developing models that are relevant to the economic problems of their times. Unlike other computational economics textbooks, this book is organized around economic topics, among them macroeconomics, microeconomics, and finance. The authors employ various software systems--including MATLAB, Mathematica, GAMS, the nonlinear programming solver in Excel, and the database systems in Access--to enable students to use the most advantageous system. The book progresses from relatively simple models to more complex ones, and includes appendices on the ins and outs of running each program. The book is intended for use by advanced undergraduates and professional economists and even, as a first exposure to computational economics, by graduate students. Organized by economic topics Progresses from simple to more complex models Includes instructions on numerous software systems Encourages customization and creativity

This book provides a comprehensive introduction to the mathematical foundations of economics, from basic set theory to fixed point theorems and constrained optimization. Rather than simply offer a collection of problem-solving techniques, the book emphasizes the unifying mathematical principles that underlie economics. Features include an extended presentation of separation theorems and their applications, an account of constraint qualification in constrained optimization, and an introduction to monotone comparative statics. These topics are developed by way of more than 800 exercises. The book is designed to be used as a graduate text, a resource for self-study, and a reference for the professional economist.

In the field of economic analysis, computability in the formation of economic hypotheses is seen as the way forward. In this book, Professor Velupillai implements a theoretical research program along these lines. Choice theory, learning rational expectations equlibria, the persistence of adaptive behavior, arithmetical games, aspects of production theory, and economic dynamics are given recursion theoretic (i.e. computable) interpretations.

What is Computational Economics Computer science, economics, and management science are all branches of study that are included in the field of computational economics, which is an interdisciplinary research field. This topic includes the modeling of economic processes through the use of computer methods. There are some of these fields that are not found anywhere else, while others have established themselves as areas of economics by enabling robust data analytics and solutions to problems that would be difficult to investigate without the use of computers and the numerical methods that are connected with them. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Computational economics Chapter 2: Econometrics Chapter 3: Experimental economics Chapter 4: Representative agent Chapter 5: Macroeconomic model Chapter 6: Formal epistemology Chapter 7: Evolutionary economics Chapter 8: Economics education Chapter 9: Agent-based computational economics Chapter 10: Dynamic stochastic general equilibrium Chapter 11: Microfoundations Chapter 12: Adaptive Modeler Chapter 13: Mathematical economics Chapter 14: Methodology of econometrics Chapter 15: ACEGES Chapter 16: Anil K. Bera Chapter 17: Heterogeneity in economics Chapter 18: Criticisms of econometrics Chapter 19: Causal inference Chapter 20: Michael Keane (economist) Chapter 21: John Rust (II) Answering the public top questions about computational economics. (III) Real world examples for the usage of computational economics in many fields. (IV) Rich glossary featuring over 1200 terms to unlock a comprehensive understanding of computational economics. (eBook only). Who will benefit Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of computational economics.

This book presents a variety of computational methods used to solve dynamic problems in economics and finance. It emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. The examples are drawn from a wide range of subspecialties of economics and finance, with particular emphasis on problems in agricultural and resource economics, macroeconomics, and finance. The book also provides an extensive Web-site library of computer utilities and demonstration programs. The book is divided into two parts. The first part develops basic numerical methods, including linear and nonlinear equation methods, complementarity methods, finite-dimensional optimization, numerical integration and differentiation, and function approximation. The second part presents methods for solving dynamic stochastic models in economics and finance, including dynamic programming, rational expectations, and arbitrage pricing models in discrete and continuous time. The book uses MATLAB to illustrate the algorithms and includes a utilities toolbox to help readers develop their own computational economics applications.