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The Economics and Mathematics of Aggregation provides a general characterization of group behavior in a market environment. A crucial feature of the authors' approach is that they do not restrict the form of individual preferences or the nature of individual consumptions. The authors allow for public as well as private consumption, for intragroup production, and for any type of consumption externalities across group members. The main questions addressed are: what restrictions (if any) on the aggregate demand function characterize the efficient behavior of the group and when is it possible to recover the underlying structure - namely, individual preferences, the decision process and the resulting intragroup transfers - from the group's aggregate behavior? The Economics and Mathematics of Aggregation takes an alternative, axiomatic perspective -- the 'collective' approach -- and assumes that the group always reaches Pareto efficient decisions. The authors view efficiency as a natural assumption in many contexts and as a natural benchmark in all cases. Finally, even in the presence of asymmetric information, first best efficiency is a natural benchmark. However, it is important to note that no restriction is placed on the form of the decision process beyond efficiency.
Professor Green discusses the definition of consistent aggregation and the problem of grouping variables in a single equation; he deals with the aggregation of equations and the probable errors; and summarizes, with reference to the text, the considerations involved in selecting an appropriate form of aggregation. The author's survey presents a well-balanced overview and analysis of aggregation, and makes readily accessible for the first time much material otherwise difficult to obtain. Originally published in 1964. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
In order to solve a given problem, economic analysis is com pelled to concentrate on the interaction of selected factors while disregarding a multitude of other influences. This book offers a discussion of certain central premises involved here and draws some analytical consequences. The argument is fo cused on process analysis, i.e., on the analysis of economic processes within a given institutional setting, although certain corollaries for institutional analysis are patent. Many colleagues and students have helped me, for many years, to develop the views presented here, and it seems im possible to trace individual influences. Thus I can only ex press my indebtedness in a macro sense. I wish to thank the Westdeutscher Verlag for its kind per mission to use material from my Grundlagen der okonomi schen Analyse. The results of Chap. 4 were presented at the Econometric Society European Meeting in Pisa, 1983. Dr. W.A. MUller from Springer-Verlag has encouraged me to write this book and has been helpful in many ways.
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 44. Chapters: Agent-based computational economics, Aggregation problem, Brander-Spencer model, Comparative statics, Confrontation analysis, Convexity in economics, DNSS point, Elasticity of a function, Foundations of Economic Analysis, Game theory, Historical simulation, Isoelastic function, Kakutani fixed-point theorem, Maximum theorem, Non-convexity (economics), Perfect competition, Qualitative economics, Recursive economics, Sethi model, Shadow price, Shapley-Folkman lemma, Social Choice and Individual Values, St. Petersburg paradox, Topkis's theorem, Transportation theory (mathematics).
A rigorous and self-contained exposition of aggregation functions and their properties.
Through careful methodological analysis, this book argues that modern macroeconomics has completely overlooked the aggregate nature of the data. In Part I, the authors test and reject the homogeneity assumption using disaggregate data. In Part II, they demonstrate that apart from random flukes, cointegration unidirectional Granger causality and restrictions on parameters do not survive aggregation when heterogeneity is introduced. They conclude that the claim that modern macroeconomics has solid microfoundations is unwarranted. However, some important theory-based models that do not fit aggregate data well in their representative-agent version can be reconciled with aggregate data by introducing heterogeneity.
Professor Green discusses the definition of consistent aggregation and the problem of grouping variables in a single equation; he deals with the aggregation of equations and the probable errors; and summarizes, with reference to the text, the considerations involved in selecting an appropriate form of aggregation. The author's survey presents a well-balanced overview and analysis of aggregation, and makes readily accessible for the first time much material otherwise difficult to obtain. Originally published in 1964. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Judgment aggregation is a mathematical theory of collective decision-making. It concerns the methods whereby individual opinions about logically interconnected issues of interest can, or cannot, be aggregated into one collective stance. Aggregation problems have traditionally been of interest for disciplines like economics and the political sciences, as well as philosophy, where judgment aggregation itself originates from, but have recently captured the attention of disciplines like computer science, artificial intelligence and multi-agent systems. Judgment aggregation has emerged in the last decade as a unifying paradigm for the formalization and understanding of aggregation problems. Still, no comprehensive presentation of the theory is available to date. This Synthesis Lecture aims at filling this gap presenting the key motivations, results, abstractions and techniques underpinning it. Table of Contents: Preface / Acknowledgments / Logic Meets Social Choice Theory / Basic Concepts / Impossibility / Coping with Impossibility / Manipulability / Aggregation Rules / Deliberation / Bibliography / Authors' Biographies / Index
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were. thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various Isciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geom. eJry interacts with I physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and rpathematical programminglprofit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.