Download or read book Topological Methods in Walrasian Economics written by E. Dierker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: In winter 71/72 I held a seminar on general equilibrium theory for a jOint group of students in mathematics and in econo mics at the university of Bonn , w.Germany1~ The economists , how ever , had a mathematical background well above the average • Most of the material treated in that seminar is described in these notes. The connection between smooth preferences and smooth demand func tions [ see Debreu (1972) ] and regular economies based on agents with smooth preferences are not presented here • Some pedagogical difficulties arose from the fact that elementary knowledge of algebraic topology is not assumed although it is helpful and indeed necessary to make some arguments precise • It is only a minor restriction , at present , that functional ana lysis is not used • But with the development of the theory more economic questions will be considered in their natural infinite dimensional setting • Economic knowledge is not required , but especially a reader without economic background will gain much by reading Debreu's classic "Theory of Value" (1959) • Although the formulation of our economic problem uses a map between Euclidean spaces only , we shall also consider ma- folds • Manifolds appear in our situation because inverse images under differentiable mappings between Euclidean spaces are very often differentiable manifolds • ( Under differentiability assump tions , for instance , the graph of the equilibrium set correspon

Download or read book Multiple Criteria Decision Making Theory and Application written by G. Fandel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: He consider a cone dominance problem: given a "preference" cone lP and a set n X ~ R of available, or feasible, alternatives, the problem is to identify the non dominated elements of X. The nonzero elements of lP are assumed to model the do- nance structure of the problem so that y s X dominates x s X if Y = x + P for some nonzero p S lP. Consequently, x S X is nondominated if, and only if, ({x} + lP) n X = {x} (1.1) He will also refer to nondominated points as efficient points (in X with respect to lP) and we will let EF(XJP) denote the set of such efficient points. This cone dominance problem draws its roots from two separate, but related, ori gins. The first of these is multi-attribute decision making in which the elements of the set X are endowed with various attributes, each to be maximized or minimized.

Download or read book Temporary Monetary Equilibrium Theory written by Kuan-Pin Lin and published by Routledge. This book was released on 2017-04-28 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title, first published in 1984, considers a temporary monetary equilibrium theory under certainty in a differentiable framework. Using the techniques of differential topology the author investigates the structure of the set of temporary monetary equilibria. Temporary Monetary Equilibrium Theory: A Differentiable Approach will be of interest to students of monetary economics.

Download or read book Cost and Production Functions written by R.W. Shephard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study is the result of an interest in the economic theory of production intermittently pursued during the past three years. Over this period I have received substantial support from the Office of Naval Research, first from a personal service consulting contract directly with the Mathematics Division of the Office of Naval Research and secondly from Project N6 onr-27009 at Princeton Univer sity under the direction of Professor Oskar Morgenstern. Grateful acknowledgement is made to the ·Office of Naval Research for this support and to Professor Morgenstern, in particular, for his interest in the puolication of this research. The responsibility for errors and omissions, how ever, rests entirely upon the author. Professor G. C. Evans has given in terms of a simple total cost function, depending solely upon output rate, a treatment of certain aspects of the economic theory of production which has inherent generality and convenience of formulation. The classical approach of expressing the technology of production by means of a production function is potentially less restrictive than the use of a simple total cost function, but it has not been applied in a more general form other than to derive the familiar conditions between marginal productivities of the factors of produc tion and their market prices.

Download or read book Nonlinear Programming Codes written by Klaus Schittkowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Barriers to Entry written by C.C.v. Weizsäcker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: I was originally induced to think about barriers to entry by some re search done for Charles River Associates, Inc., Boston, on behalf of their client IBM Corporation, Armonk, N.Y. After the end of this re search project I continued to work on entry barriers and related is sues of market structure. The results of this effort are reported here. What I present is not a book in the traditional sense of the word. Due to other research and administrative obligations I could not, without substantial delay, present a more finished product. The rapid progress in the field of industrial organisation theory made me fear that my results could become obsolete if I further waited with their publica tion. I hope that the early presentation of a progress report rather than a much later publication of a finished product is not only in my interest but also in the interest of economics.

Download or read book Stochastic Dynamic Properties of Linear Econometric Models written by J. Wolters and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Test Examples for Nonlinear Programming Codes written by W. Hock and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: ................................................................. The performance of a nonlinear programming algorithm can only be ascertained by numerical experiments requiring the collection and implementation of test examples in dependence upon the desired performance criterium. This book should be considered as an assis tance for a test designer since it presents an extensive collec tion of nonlinear programming problems which have been used in the past to test or compare optimization programs. He will be in formed about the optimal solution, about the structure of the problem in the neighbourhood of the solution, and, in addition, about the usage of the corresp,onding FORTRAN subroutines if he is interested in obtaining them -ofi a magnetic tape. Chapter I shows how the test examples are documented. In par ticular, the evaluation of computable information about the solu tion of a problem is outlined. It is explained how the optimal solution, the optimal Lagrange-multipliers, and the condition number of the projected Hessian of the Lagrangian are obtained. Furthermore, a classification number is defined allowing a formal description of a test problem, and the documentation scheme is described which is used in Chapter IV to present the problems.

Download or read book Optimization with Disjunctive Constraints written by H.D. Sherali and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The disjunctive cut principle of Balas and Jeroslow, and the related polyhedral annexation principle of Glover, provide new insights into cutting plane theory. This has resulted in its ability to not only subsume many known valid cuts but also improve upon them. Originally a set of notes were written for the purpose of putting together in a common terminology and framework significant results of Glover and others using a geometric approach, referred to in the literature as convexity cuts, and the algebraic approach of Balas and Jeroslow known as Disjunctive cuts. As it turned out subsequently the polyhedral annexation approach of Glover is also closely connected with the basic disjunctive principle of Balas and Jeroslow. In this monograph we have included these results and have also added several published results which seem to be of strong interest to researchers in the area of developing strong cuts for disjunctive programs. In particular, several results due to Balas [4,5,6,7], Glover [18,19] and Jeroslow [23,25,26] have been used in this monograph. The appropriate theorems are given without proof. The notes also include several results yet to be published [32,34,35] obtained under a research contract with the National Science Foundation to investigate solution methods for disjunctive programs. The monograph is self-contained and complete in the sense that it attempts to pool together existing results which the authors viewed as important to future research on optimization using the disjunctive cut approach.

Download or read book Optimal Decisions under Uncertainty written by J.K. Sengupta and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of optimal decisions in a stochastic environment has seen many new developments in recent years. The implications of such theory for empirical and policy applications are several. This book attempts to analyze some of the impor tant applied aspects of this theory and its recent developments. The stochastic environment is considered here in specific form, e.g., (a) linear programs (LP) with parameters subject to a probabilistic mechanism, (b) decision models with risk aversion, (c) resource allocation in a team, and (d) national economic planning. The book attempts to provide new research insights into several areas, e.g., (a) mixed strategy solutions and econometric tests of hypotheses of LP models, (b) the dual problems of efficient estimation and optimal regulation, (c) input-output planning under imperfect competition, and (d) linear programs viewed as constrained statistical games. Methods of optimal decision rules developed here for quadratic and linear decision problems are applicable in three broad areas: (a) applied economic models in resource allocation, planning and team decision, (b) operations research models in management decisions involving portfolio analysis and stochastic programming, and (c) systems science models in stochastic control and adaptive behavior. Some results reported here have been published in professional journals be-. fore, and I would like to thank the following journals in particular: Inter national Journal of Systems Science, Journal of Optimization Theory and Applica tions and Journal of Mathematical Analysis and Applications.

Download or read book Organizations Multiple Agents with Multiple Criteria written by J.N. Morse and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourth International MCDM Conference follows a tradition that began with an exploratory gathering at the University of South Carolina in 1973. The First International Conference was held in Jouy-en-Josas in 1975. The second and third were held in Buffalo (1977) and KOnigswinter (1979). We are grateful to the Office of Naval Research for years of advice and funding, and to Springer-Verlag for providing a widely dispersed series of proceedings volumes. In the case of the Delaware Conference we gratefully acknowledge new support from the corporate sector, coordinated by the University of Delaware's Development Office. Now that I have attended to the formal recognitions, I wish to place my recollection of the human side of the conference into the record. This is justi fiable because multiple criteria problem solving has been nurtured by a close-knit group of people whose interactions are not fully captured by the standard journal format. This was the conference in which an animated discussion between Dave,Bell and Paul Schoemaker caused Mathilde Stephenson to stand up and say, "Don't stop it; this is the best part of the conference. " Another sort of moment occurred when Lucas Pun was asked to explain a certain Chinese character in one of his transpar encies. He replied, "No alcohol allowed. " From Erick Duesing, speaking with an historical perspective, we had the insight that multiple criteria methods lan guished because "McCarthyism had made planning suspect.

Download or read book Information Structures in Economics written by M. Nermuth and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a contribution to the theory of markets with imperfect information. The subject being nearly limitless, only certain selected topics are discussed. These are outlined in the Introduction (Ch. 0). The remainder of the book is divided into three parts. All results of economic significance are contained in Parts II & III. Part I introduces the main tools for the analysis, in particular the concept of an information structure. Although most of the material presented in Part I is not original, it is hoped that the detailed and self-contained exposition will help the reader to understand not only the following pages, but also the existing technical and variegated literature on markets with imperfect information. The mathematical prerequisites needed, but not explained in the text rarely go beyond elementary calculus and probability theory. Whenever more advanced concepts are used, I have made an effort to give an intuitive explanation as well, so that the argument can also be followed on a non-technical level (cf. e.g. the treatment of the "generic" viewpoint in Ch. 9). In the same spirit, discussion of mathematical assumptions is limited to those which have economic sig- ficance, whereas purely "technical" assumptions (like differentiability or integrability of certain functions) are usually made without comment whenever convenient. The logical interdependence of chapters is as follows: Ch. 3 . Ch. 1 /~I--=---- Ch. 4 Ch. 2 Ch. 8 ~I -=--- /"'-.... Ch.

Download or read book Disequilibrium and Self Organisation written by C.W. Kilmister and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Chif1ese 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 sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit 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.

Download or read book Parallel Genetic Algorithms written by Joachim Stender and published by IOS Press. This book was released on 1993 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Equilibrium Analysis written by W. Hildenbrand and published by Elsevier. This book was released on 2014-07-22 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Textbooks in Economics, Volume 6: Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras focuses on the approaches developed and instituted by Edgeworth and Walras in the study of equilibrium analysis. The book first underscores exchange economies, core of a game, and large economies. Discussions focus on economies with a continuum of agents, Walras equilibrium, prices and demand, balancedness, and commodity space. The manuscript then ponders on limit theorems for the core and existence of competitive equilibria. Topics include equilibria without convexity of preferences, existence of equilibria for economies with convex preferences, individual demand, emergence of prices, asymptotic equal treatment for most, uniform boundedness of core allocations, and limit theorems for type and replica economies. The publication examines continuous, upper, and lower hemi-continuous correspondences, fixed point theorems, and separation of convex sets. The book is a vital source of data for economists and researchers interested in equilibrium analysis.

Download or read book Core and Equilibria of a Large Economy PSME 5 written by Werner Hildenbrand and published by Princeton University Press. This book was released on 2015-03-08 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Can every allocation in the core of an economy be decentralized by a suitably chosen price system? Werner Hildenbrand shows that the answer is yes if the economy has "many" participating agents and if the influence of every individual agent on collective actions is "negligible." To give a general and precise definition of economics with this property he considers both economies with a continuum of agents, and a sequence of economies with an increasing number of participants. In both cases this leads to a measure theoretic formulation of economic equilibrium analysis. In the first part of the book the relevant mathematics is developed. In the second part the continuity and convexity properties of the total demand of a consumption sector are investigated. An important result is the equivalence between the core and the set of Walras equilibria for an exchange economy with a continuum of agents. The author then deals with limit theorems on the core for purely competitive sequences of exchange economies. In the last chapter the core and the set of Walras equilibria for a coalition production economy and the relation between these two equilibrium concepts are studied. Originally published in 1974. 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.

Download or read book Fixed Point Theory written by Andrzej Granas and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS