Handbook of Computational Economics, Volume 2: Agent-Based Computational Economics (Handbook of Computational Economics)
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  • An Invaluable Resource for Practicing and Novice Agent-based Modelers
Handbook of Computational Economics, Volume 2: Agent-Based Computational Economics (Handbook of Computational Economics)

Manufacturer: North Holland
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Binding: Hardcover

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ASIN: 0444512535

Book Description

The explosive growth in computational power over the past several decades offers new tools and opportunities for economists. This handbook volume surveys recent research on Agent-based Computational Economics (ACE), the computational study of economic processes modeled as dynamic systems of interacting agents. Empirical referents for "agents" in ACE models can range from individuals or social groups with learning capabilities to physical world features with no cognitive function. Topics covered include: learning; empirical validation; network economics; social dynamics; financial markets; innovation and technological change; organizations; market design; automated markets and trading agents; political economy; social-ecological systems; computational laboratory development; and general methodological issues.

*Every volume contains contributions from leading researchers
*Each Handbook presents an accurate, self-contained survey of a particular topic
*The series provides comprehensive and accessible surveys

Customer Reviews:

5 out of 5 stars An Invaluable Resource for Practicing and Novice Agent-based Modelers.......2006-12-29

This excellent volume should be entitled "Explorations in Agent-Based Modeling," as a comparison with Volume I of the Handbook of Computational Economics should make clear. The earlier volume is an extremely mature product summarizing the application of computer-intensive mathematical techniques to traditional economic problems--a subject the history of which goes back to the earliest applications of computers during World War II. The volume under review, Volume II, has a completely different character. Agent-based modeling is a young and vigorous, rather than a mature and technically plodding science. Mathematics, rather than being the central focus, tends to be rather a simple-minded tool, and the programming, rather than being of the number-crunching variety, tends to be a versatile and imaginative mirroring of real-world processes in silicon life-forms and object-oriented structures. The subject matter, moreover, is not limited to the bread and butter of traditional economics (computable general equilibrium, solving for Nash equilibria, macroeconomic modeling, parallel computation, dynamic programming, and the like), but rather explores novel themes in the interface between economics and the other behavioral sciences--especially in this volume politics, biology, and ecology. The chapters do accomplish fairly comprehensive literature reviews (but beware--in this fast-moving field some of the most important contributions are likely to be the most recent, and hence not referenced), but they are rarely technically detailed summaries of the state-of-the-art. Rather, chapters tend to develop themes that are particularly interesting to the author. This makes for a very readable volume, but I am not sure the appellation "Handbook" is truly appropriate.

Tesfatsion's first sentence in her introductory essay to the volume gets right to the point. "Economies," she asserts, "are complex dynamic systems." What, we may ask, makes an economy a complex dynamic system? For one thing, the complex economy is never in equilibrium, but is constantly subjected to shocks, both exogenous and endogenous, that affect its short-term movements. There are frequent local nonlinear resonances that lead to significant deviations of economic variables (prices, quantities, wages, asset prices) from their equilibrium values even in the absence of strong or systematic perturbations to the system. We see such deviations in many economic time series, which often have the "fat tails" characteristics of the power laws of complex systems, as opposed to the Gaussian distributions of Neoclassical theory. Second, in a complex (a.k.a. real-world) economy, the Law of One Price fails. For instance, in the European Union, the standard deviation of prices rose from 12.3% in 1998 to 13.8% in 2003, despite the extensive dropping of trade barriers and movement to a common currency over this period. A third characteristic of the complex economy is that it rarely, if ever, achieves the sort of optimality that can be attained in simple engineered systems. For instance, since economies are rarely in equilibrium, most production, trade, and consumption takes place out of equilibrium, and hence is Pareto-suboptimal, at least when measured against a complete information Walrasian economy that has somehow attained equilibrium.

It is evident, then, that standard Neoclassical economic theory, as taught in the college and graduate textbooks and developed in the mainstream economics journals, does not recognize that the economy is a complex dynamic system. If the first volume of this pair of Handbooks might be called "how to do traditional economics better with computers," the volume under consideration could be called "How to transform economic theory using agent based modeling." We can chart the following characteristics of the complex economy: (a) The complex economy is thermodynamically open, dynamic, nonlinear, and generally far from equilibrium, whereas the Walrasian economy is thermodynamically closed, static, and linear in the sense that it can be understood using algebraic geometry and manifold theory; (b) In the complex economy, agents have limited information and face high costs of information processing. However, under appropriate conditions, they evolve non-optimal but highly effective heuristics for operating in complex environments. There is no assurance that when faced with novel environments, individuals will shift efficiently to new heuristics. In the Neoclassical economy, by contrast, agents have perfect information and can costlessly optimize; (c) Agents in the complex economy participate in sophisticated overlapping networks that allow them to compensate for having limited information and facing formidable information processing costs. In the Walrasian economy, agents do not interact at all. Rather, each agent faces an impersonal price structure; (d) In the complex economy, macroeconomic patterns are emergent properties of micro-level interactions and behaviors, in the same sense as the chemical properties of a complex molecule, such as carbon, is an emergent property of its nuclear and electronic structure, or that thermodynamics is an emergent property of many-particle systems. In such cases we cannot analytically derive the properties of the macro system from those of its component parts, although we can apply novel mathematical techniques to model the behavior of the emergent properties. In the case of the complex economy, these higher level modeling constructs are currently largely absent, although agent-based modeling may provide the data needed to develop the appropriate mathematical tools. By contrast, the Walrasian economy has no macro properties that cannot be derived from its micro properties (for instance, the First and Second Welfare Theorems); (e) In the complex economy, the evolutionary process of differentiation, selection, and amplification provides the system with novelty and is responsible for the growth in order and complexity. In the Walrasian economy there is no mechanism for creating novelty or growth in complexity. In his chapter in this book, Axel Leijonhufvud develops the insight that many contributions to economic theory from the Marshallian tradition, effectively eclipsed by the influence of Edgeworth, Walras, and their general equilibrium successors, are echoed and developed in the agent-based simulations of economic dynamics.

Several authors address the question as to the epistemological status of agent-based models. It is indicative of the youth of this brand of research that widely divergent answers are offered. One such view is that agent-based modeling is an alternative to formal analytical economic theory. It strikes me that this is not at all the case. Rather, an agent-based model is a set of empirical data, and building such models is akin to laboratory experimentation. One can use the results of such experimentation to inspire theorists to construct analytical models in which one can derive logically the properties of the system observed in the laboratory. Or, if the complexity of the system precludes analytical modeling, one can make broad generalizations based on a comparative study of different agent-based systems. In principle, an agent-based model could provide an existence theorem for a particular emergent phenomenon, but in general there are sufficient differences between a mathematical model of a process and its agent-based implementation (for instance, real numbers are approximated by fixed-precision floating point numbers, and random numbers are approximated by deterministic algorithms with long periods), that the two models could have substantively different properties.

Representing ABM models as empirical rather than theoretical contributions is likely to improve the chances for publication in mainstream journals, and hence improve the communication among economists. Economic theorists often make the point to me that in reading an analytical paper, the assumptions and the method of proof are completely transparent, while an agent-based model must be taken on faith, since the model itself is not presented in a journal article, nor would it make much sense if it were, except to an expert in the computer language used. If the ABM is presented as a contribution to theory, it is easy to see why it is rejected by respectable journals: it is asking the reader to take the authors' assertions on faith alone. If the ABM results are represented as empirical data, this problem disappears.

When agent-based models are not accepted in mainstream economics journals, modelers tend to place the blame on the closed-mindedness and traditionalistic mentality of the reviewers. I consider this a very serious error, because it gives the agent-based modeler no means of correcting the problem. I think that it is almost always good advice to blame yourself when a paper is rejected, because the you is the only one with an incentive to change to meet the reviewers' criteria the next time around. The authors in this volume do not make this mistake, and several have valuable suggestions as to how agent-based models must be crafted to increase their scientific value (Robert Axelrod's suggestions are particularly incisive).

It is interesting that none of the authors appears to have noticed the inverse problem: agent-based models are all the rage in some circles, and many faulty models get past reviewers and are published in top journals, including Science and Nature. The fact is that if two researchers are given the same specifications and write the computer code independently, there is a very good chance their models will differ in substantial ways. There is simply no way for a reviewer to assess the quality of a simulation without spending a considerable amount of time going over the code. Moreover, I have found that researchers often bias code generation in such a way as to support their pet theories. The nature of this bias often cannot be revealed without a thorough inspection of the computer code. This sort of author behavior is not not necessarily due to our dishonesty, but rather due to our capacity to self-delude. If the ABM behaves the way we want it to, we leave the code alone. If it does not, we work over it to find out why. The resulting code is thus virtually certain to be self-serving and biased.

I do not know how to get around this problem. It is reminiscent of a similar problem with econometric research with complex data sets, where it is virtually impossible for reviewers to ascertain the significance of the results, especially in the case of economic time series. In the case of econometric analysis, the problem is attenuated if researchers are obligated to place the data in the public domain, making replication feasible. In the case of agent-based models, there is usually no "data" different from the model itself. It would be a step forward to require researchers to place their code in the public domain, so that the threat of public scrutiny might serve to attenuate the temptation to torture the code whose results one does not like, while coddling the code that reinforces our prejudices and expectations.

Another important issue not systematically addressed in this Handbook is the mechanics of producing an agent-based model. If the researcher does not do his or her own programming, clearly the researcher should generated a completely unambiguous set of specifications for programming the model. However, if the research does not know computer programming, this is impossible in all but the most simple cases. Even if the researcher is an expert programmer, he or she cannot pre-envision exactly how the model should function, since often one tries several alteratives for each piece of code, and one often does not know what the real dynamics of the model are until one has done considerable hands-on programming. For this reason, if I had my way, I would never accept a paper for publication that was not programmed by the researchers themselves, except for the simplest sort of models. Therefore, I believe training in ABM should include training in computer programming to the point of professional proficiency. I do not even accept using canned ABM software, because it is difficult to tell what the software is doing, the implementation is always painfully slow compared to a real computer language, and there are strict limits as to what can be accomplished with such software. However, I know that many leading ABM researchers disagree with this, and happily teach their students to use Swarm, StarLogo, and the like. Until this issue is thoroughly investigated and the truth sorted out from the myth, ABM will remain of limited value to the economic research community.

I commend the Editors for doing a fine job in addressing the needs of the ABM community, while producing a volume that can be profitably read by those new to the field. Nevertheless, there remain hard problems that must be soberly addressed before ABM becomes a standard part of the repertoire of economic researchers, and ABM results appear widely in top economics journals.
Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era (International Series in Operations Research & Management Science)
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    Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era (International Series in Operations Research & Management Science)

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    Over the past two decades, not only has supply chain analysis become a strategic focus of leading firms, it has also spawned an impressive array of research that brings together diverse research communities. Adding to this diversity and intellectual energy is the emergence of E-Business. E-Business creates new competitive dimensions that are fast-paced, ever-changing, and risk-prone, dimensions where innovation, speed, and technological savvy often define success. Most importantly, E-Business challenges the premises and expands the scope of supply chain analysis. The Handbook is a comprehensive research reference that is essential for anyone interested in conducting research in supply chain. Unique features include:

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    -Coverage of most state-of-the-art business practices in supply chain management.

    Audience: This volume is suitable for researchers, faculty, graduate students, and practitioners in the following areas: supply chain management, operations research, management science, decision science, industrial engineering, operations management, civil engineering/transportation, logistics management, risk management, applied mathematics, economics, computer science, industrial management, and other related areas.

    Handbook of Metaheuristics (International Series in Operations Research & Management Science)
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      ASIN: 1402072635

      Book Description

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      Handbook on Modelling for Discrete Optimization (International Series in Operations Research & Management Science)
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        Handbook on Modelling for Discrete Optimization (International Series in Operations Research & Management Science)

        Manufacturer: Springer
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        The primary objective underlying the Handbook on Modelling for Discrete Optimization is to demonstrate and detail the pervasive nature of Discrete Optimization. While its applications cut across an incredibly wide range of activities, many of the applications are only known to specialists. It is the aim of this handbook to correct this.

        It has long been recognized that "modelling" is a critically important mathematical activity in designing algorithms for solving these discrete optimization problems. Nevertheless solving the resultant models is also often far from straightforward. In recent years it has become possible to solve many large-scale discrete optimization problems. However, some problems remain a challenge, even though advances in mathematical methods, hardware, and software technology have pushed the frontiers forward. This handbook couples the difficult, critical-thinking aspects of mathematical modelling with the hot area of discrete optimization. It will be done in an academic handbook treatment outlining the state-of-the-art for researchers across the domains of the Computer Science, Math Programming, Applied Mathematics, Engineering, and Operations Research. Included in the handbook's treatment are results from Graph Theory, Logic, Computer Science, and Combinatorics.

        The chapters of this book are divided into two parts: (1) one dealing with general methods in the modelling of discrete optimization problems and (2) the other with specific applications. The first chapter of this volume, written by H. Paul Williams, can be regarded as a basic introduction of how to model discrete optimization problems as mixed integer problems, and outlines the main methods of solving them. In the second part of the book various real life applications are presented, most of them formulated as mixed integer linear or nonlinear programming problems. These applications include network problems, constant logic problems, many engineering problems, computer design, finance problems, medical diagnosis and medical treatment problems, applications of the Genome project, an array of transportation scheduling problems, and other applications.

        Further information including a detailed Table of Contents and Preface can be found and examined on the Handbook's web page at http://www.springer.com/0-387-32941-2.

        Handbook of Economic Growth, Volume 1 (Set) (Handbooks in Economics)
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          The Handbook of Portfolio Mathematics: Formulas for Optimal Allocation & Leverage (Wiley Trading)
          Average customer rating: 3.5 out of 5 stars
          • High level Mathematics but not useful for real life applications.
          • The greatest book in the history of trading!
          The Handbook of Portfolio Mathematics: Formulas for Optimal Allocation & Leverage (Wiley Trading)
          Ralph Vince
          Manufacturer: Wiley
          ProductGroup: Book
          Binding: Hardcover

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          The Handbook of Portfolio Mathematics

          "For the serious investor, trader, or money manager, this book takes a rewarding look into modern portfolio theory. Vince introduces a leverage-space portfolio model, tweaks it for the drawdown probability, and delivers a superior model. He even provides equations to maximize returns for a chosen level of risk. So if you're serious about making money in today's markets, buy this book. Read it. Profit from it."
          —Thomas N. Bulkowski, author, Encyclopedia of Chart Patterns

          "This is an important book. Though traders routinely speak of their 'edge' in the marketplace and ways of handling 'risk,' few can define and measure these accurately. In this book, Ralph Vince takes readers step by step through an understanding of the mathematical foundations of trading, significantly extending his earlier work and breaking important new ground. His lucid writing style and liberal use of practical examples make this book must reading."
          —Brett N. Steenbarger, PhD, author, The Psychology of Trading and Enhancing Trader Performance

          "Ralph Vince is one of the world's foremost authorities on quantitative portfolio analysis. In this masterly contribution, Ralph builds on his early pioneering findings to address the real-world concerns of money managers in the trenches-how to systematically maximize gains in relation to risk."
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          "Gambling and investing may make strange bedfellows in the eyes of many, but not Ralph Vince, who once again demonstrates that an open mind is the investor's most valuable asset. What does bet sizing have to do with investing? The answer to that question and many more lie inside this iconoclastic work. Want to make the most of your investing skills Open this book."
          —John Bollinger, CFA, CMT, www.BollingerBands.com

          Customer Reviews:

          2 out of 5 stars High level Mathematics but not useful for real life applications........2007-09-11

          Ok. To begin with I am giving only 2 stars for this book , and the reason for this high rating is some good mathematics it covers.

          Part 1 of the book covers statistics, normal distribution, binomial distribution and all other concepts applied to trading systems. However this has been covered inadequately. Author should have either presumed that people reading this book are already aware of this and avodied it altogether or he should have covered it in enough details. Some 150 pages are lost on this but again 150 pages are not enough for covering all this material. The examples given are kind of weird, one page author speaks of coin toss examples and immediately after that he goes to example of horse racing and its probabilities. Instead it would have been great had he taken single example of a trading system and evolved his work around it.

          Part 2 of the book comes back to Vince favourite concept of optimal F. Another 100 pages are spent on this. The problem is nobody in real life is going to trade optimal F as it is too risky to trade in real life. The whole discussion rounds on optimal f, its characteristics etc.

          These two sections (part 1 & 2 ) are straight from Ralph Vince previous books. So in case you have read those books then there is nothing new here.

          Part 3 is where it becomes slightly interesting. Author speaks about portfolio management, space leveraged model, and gives overview of what professionals have done. But all the computations on this are presuming that you are trading optimal F. In case you have already decided not to trade optimal f as it is too risky, then there is not much advise here for you on how to adjust your portfolio. The section on "What professionals have done" is slightly interesting though.

          The whole book is full of complex mathematics (You must have done majors in mathematics at graduation level in your college), and author presumes that you know most of that mathematics so there is little explaination for those notations.

          The book may be interesting for a large futures fund who can afford to employ an army of mathematicians and programmers to try all those concepts. However if you trade for yourself, or have a small fund then you are not likely to gain much from the book. If you have read any of Ralph Vince previous books then I will suggest not to go for this one.

          I will rate Ryan Jones "The number Game" much higher on subject of money management for its ease of application in real life.

          5 out of 5 stars The greatest book in the history of trading!.......2006-01-19

          The greatest book in the history of trading!
          Handbook of Mathematical Economics Volume 4 (Handbooks in Economics)
          Average customer rating: Not rated
            Handbook of Mathematical Economics Volume 4 (Handbooks in Economics)

            Manufacturer: North Holland
            ProductGroup: Book
            Binding: Hardcover

            EconometricsEconometrics | Economics | Business & Investing | Subjects | Books
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            1. Handbook of Industrial Organization Handbook of Industrial Organization

            ASIN: 0444874615

            Book Description

            The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field.
            The emphasis of this fourth volume of the Handbook of Mathematical Economics is on choice under uncertainty, general equilibrium analysis under conditions of uncertainty, economies with an infinite number of consumers or commodities, and dynamical systems. The book thus reflects some of the ideas that have been most influential in mathematical economics since the appearance of the first three volumes of the Handbook.

            Researchers, students, economists and mathematicians will all find this Handbook to be an indispensable reference source. It surveys the entire field of mathematical economics, critically reviewing recent developments. The chapters (which can be read independently) are written at an advanced level suitable for professional, teaching and graduate-level use.

            For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes
            Handbook of Asset and Liability Management
            Average customer rating: 3 out of 5 stars
            • Good but quite confuse
            Handbook of Asset and Liability Management

            Manufacturer: North Holland
            ProductGroup: Book
            Binding: Hardcover

            GeneralGeneral | Popular Economics | Business & Investing | Subjects | Books
            Banks & BankingBanks & Banking | Industries & Professions | Business & Investing | Subjects | Books
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            Similar Items:
            1. The Stochastic Programming Approach to Asset, Liability, and Wealth Management The Stochastic Programming Approach to Asset, Liability, and Wealth Management
            2. Asset and Liability Management Tools: A Handbook for Best Practice Asset and Liability Management Tools: A Handbook for Best Practice
            3. Stochastic Optimization Models in Finance 2006 Stochastic Optimization Models in Finance 2006
            4. Handbook of Asset and Liability Management, Volume 2: Applications and Case Studies (Handbook of Asset and Liability Management) (Handbook of Asset and Liability Management) Handbook of Asset and Liability Management, Volume 2: Applications and Case Studies (Handbook of Asset and Liability Management) (Handbook of Asset and Liability Management)
            5. Bank Asset & Liability Management: Strategy, Trading, Analysis (Wiley Finance) Bank Asset & Liability Management: Strategy, Trading, Analysis (Wiley Finance)

            ASIN: 0444508759

            Book Description

            This first volume of the Handbook of Asset and Liability Management presents the theories and methods supporting models that align a firm's operations and tactics with its uncertain environment. Detailing the symbiosis between optimization tools and financial decision-making, its original articles cover term and volatility structures, interest rates, risk-return analysis, dynamic asset allocation strategies in discrete and continuous time, the use of stochastic programming models, bond portfolio management, and the Kelly capital growth theory and practice. They effectively set the scene for Volume Two by showing how the management of risky assets and uncertain liabilities within an integrated, coherent framework remains the core problem for both financial institutions and other business enterprises as well.

            *Each volume presents an accurate survey of a sub-field of finance
            *Fills a substantial gap in this field
            *Broad in scope

            Customer Reviews:

            3 out of 5 stars Good but quite confuse.......2007-09-18

            This book has a good summary of the new challenges in the Enterprise Wide Risk Management and ALM. But when applying some concepts and theories it complicates itself. Focuses too little in the issues related to the appropriate mapping of Assets and Liabilities and too much in those of the optimization.
            Handbook of Game Theory with Economic Applications Volume 1 (Handbooks in Economics)
            Average customer rating: Not rated
              Handbook of Game Theory with Economic Applications Volume 1 (Handbooks in Economics)

              Manufacturer: North Holland
              ProductGroup: Book
              Binding: Hardcover

              GeneralGeneral | Popular Economics | Business & Investing | Subjects | Books
              TheoryTheory | Economics | Business & Investing | Subjects | Books
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              GeneralGeneral | Applied | Mathematics | Science | Subjects | Books
              Game TheoryGame Theory | Applied | Mathematics | Science | Subjects | Books
              Probability & StatisticsProbability & Statistics | Applied | Mathematics | Science | Subjects | Books
              GeneralGeneral | Mathematics | Science | Subjects | Books
              Game TheoryGame Theory | Applied | Mathematics | Professional Science | Professional & Technical | Subjects | Books
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              ASIN: 0444880984

              Book Description

              This is the first volume of the Handbook of Game Theory with Economic Applications, to be followed by two additional volumes. Game Theory has developed greatly in the last decade, and today it is an essential tool in much of economic theory. The three volumes will cover the fundamental theoretical aspects, a wide range of applications to economics, several chapters on applications to political science, and individual chapters on relations with other disciplines.
              The topics covered in the present volume include chess-playing computers, an introduction to the non-cooperative theory, repeated games, bargaining theory, auctions, location, entry deterrence, patents, the cooperative theory and its applications, and the relation between Game Theory and ethics.
              For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes
              Theory of International Trade: A Dual, General Equilibrium Approach (Cambridge Economic Handbooks)
              Average customer rating: 4 out of 5 stars
              • A good book for international trade, but not perfect
              Theory of International Trade: A Dual, General Equilibrium Approach (Cambridge Economic Handbooks)
              Avinash Dixit , and Victor Norman
              Manufacturer: Cambridge University Press
              ProductGroup: Book
              Binding: Paperback

              Exports & ImportsExports & Imports | Economics | Business & Investing | Subjects | Books
              InternationalInternational | Economics | Business & Investing | Subjects | Books
              MacroeconomicsMacroeconomics | Economics | Business & Investing | Subjects | Books
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              Similar Items:
              1. Advanced International Trade: Theory and Evidence Advanced International Trade: Theory and Evidence
              2. Market Structure and Foreign Trade: Increasing Returns, Imperfect Competition, and the International Economy Market Structure and Foreign Trade: Increasing Returns, Imperfect Competition, and the International Economy
              3. Innovation and Growth in the Global Economy Innovation and Growth in the Global Economy
              4. The Spatial Economy: Cities, Regions, and International Trade The Spatial Economy: Cities, Regions, and International Trade
              5. International Economics: Worth Series in Outstanding Contributions International Economics: Worth Series in Outstanding Contributions

              ASIN: 0521299691

              Book Description

              This book expounds trade theory emphasizing that a trading equilibrium is general rather than partial, and is often best modelled using dual or envelope functions. This yields a compact treatment of standard theory, clarifies some errors and confusions, and produces some new departures. In particular, the book (i) gives unified treatments of comparative statics and welfare, (ii) sheds new light on the factor-price equalization issue, (iii) treats the modern specific-factor model in parallel with the usual Heckscher-Ohlin one, (iv) analyses the balance of payments in general equilibrium with flexible and fixed prices, (v) studies imperfect competition and intra-industry trade.

              Customer Reviews:

              4 out of 5 stars A good book for international trade, but not perfect.......2004-02-02

              The book gets into rather good discusion of basic models, equilibrium and more advanced topics. The math level of the book is at a graduate level and many of the results are done with enough details, discussion and algebra. However, the book suffers from lack of algebra and enough reasoning in the first chapters where it is describing basic models. The notation of the book is sometimes confusing too (I think this problem exists in all of the books about international trade). Besides, the book is rather old and may be missing some topics. A complementarity text for this book is recommended.

              Books:

              1. History: Fiction or Science? (Chronology, No. 1)
              2. History: Fiction or Science? (Chronology, No. 1)
              3. History: Fiction or Science? (Chronology, No. 1)
              4. History: Fiction or Science? (Chronology, No. 1)
              5. History: Fiction or Science? (Chronology, No. 1)
              6. History: Fiction or Science? (Chronology, No. 1)
              7. Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit (Springer Finance)
              8. Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit (Springer Finance)
              9. International Monetary and Financial Economics (with Printed Access Card)
              10. International Trotskyism, 1929-1985: A Documented Analysis of the Movement

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