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In a wide number of economic problems the equilibrium values of the variables can be regarded as solutions of a parametrized constrained maximization problem. This occurs in static as well as dynamic models; in the latter case the choice variables are often paths in certain function spaces and thus can be regarded as points in infinite dimensional spaces. It is sometimes possible to determine qualitative properties of the solutions with respect to changes in the parameters of the model. The study of such properties is often called comparative statics; [15], [2], and [10]. Certain comparative static properties of the maxima have proven to be of particular importance for economic theory, since the works of Slutsky, Hicks, and Samuelson [15]: they have been for- lated in terms of synunetry and negative semidefiniteness of a matrix, called the Slutsky-Hicks-Samuelson matrix. A discussion of this matrix and its applications is given in Section 1. The study of these properties in economic theory, however, has so far been restricted to static models where the choice variable and the parameters are elements in Euclidean spaces, and where there is only one constraint.
Organization design has been discussed by many authors in management and organization theory. They have obtained intuitive and prescriptive propositions appealing that the best organization design is contingent on the environmental conditions. But their studies, called contingency theory, are mostly based on empirical research. Most of the "propositions" are drawn as only inferences from the results of them. On the other hand, decision theoretic models of "organizations" in the stochastic environment have been studied by some economists and management scientists independently of contingency theory. In this book, important aspects of organization design problems are formulated as statistical decision problems in the framework of management and organization theory. Part One of this book analyzes a short-run adaptive problems of the organization design. Part One contains an expanded exposition of the ideas and results published in the professional journals, and I would like to thank the anonymous reviewers of the following journals: Behaviormetrika, Human Relations, Behavioral Science. Part Two of this book considers a long-run adaptive process in the organization, and has not previously been published in its IV present form, although a version of this part is to appear in Journal of the Department of Liberal Arts, March 1987, The University of Tokyo. The resul ts of Part One and Part Two are supported by the empirical research on Japanese firms in Part Three. This research was financially supported by Nippon Telegraph and Telephone Public Corporation (NTT). I acknowledge this gratefully.
This research was supported by the World Bank and the Social Sciences and Humanities R~search Council of Canada. Neither institution is responsible for the views expressed in this paper. The author is indebted to V. Corbo, A. Haymer, Y. Kanemoto, K. Lee, K. Mera, Hal Varian and A. Walters for helpful comments and to Elizabeth Lambert, Shehnaz Motani', and Jeanette Leigh Paisley for excellent typing services. I would like to dedicate this book to my wife, Virginia. TABLE OF CONTENTS 1. Introduction . . . •. . ••. . •. ••. •••. . . . •. . . . . •. •. . . •. . . •. •. •. . •. . . •. ••. • 2. A Simple Producer Benefit Measure . . ••. •••. ••••. •••••••••••. ••••••. • 8 3. Willingness to P~v Functions and Marginal Cost Functions ••••••••••• 15 4. Approximate Benefit Measures 30 5. Problems with the Producer Benefit Measure ••••••••••••• ! ••••••••••• 41 5. 1. Static versus Dynamic Benefit Measures ••••••••••••••••••• 41 5. 2. The Problem of Endogenous Prices for Local Goons ••••••••• 48 5. 3. The Neglect of Consumer Benefits' ••••••••••••••••••••••••• 56 6. Alternative Approaches to Benefit Measurement •••••••••••••••••••••• 70 6. 1. The Questionnaire or Sample Survey Approach •••••••••••••• 70 6. 2. Ex Post Accounting Approaches •••••••••••••••••••••••••••• 72 6. 3. Engineering and Mathematical Programming Approaches •••••• 74 6. 4. The Applied General Equilibrium Modelling Approach ~ •••••• 75 6. 5. The Differential Approach •••••••••••••••••••••••••••••••• 77 6. 6. The Econometric Approach . . •••••••••. •. ••••••. •••••••••. •• 79 7.
Introducing his book "The Theory of UnemPloyment Reconsidered", Professor Malinvaud expressed several years ago his hope "to convey [his] strong belief that the reconsideration is a major step in the development of our science". In view of the stimulating effect this approach has on economic research, it seems now that many economists do indeed share Malinvaud's belief and are ready to devote their time and their skill to ensure the realization of that progress. This book, grown out of a Ph. D. thesis presented at the Universit~ Catholique de Louvain, aims at contributing in its own way to that venture. Looking towards econometric applications, it illustrates that a framework h la Malinvaud (i. e. based on the theory of temporary equilibrium with rationing) provides the means of improving macro econometric modelling. There has been so far a wide and pervasive fear that, despite its analytical and theoretical usefulness, the quantity rationing approach would be much too complex to be successfully implemented into econometric models. The research the interested reader will discover in the subsequent pages should convince him that the difficulty faced by econometricians is essentially (I am tempted to say merely) one of developing an adequate methodology; it should thus disappear once is made the initial research investment. The empirical results presented towards the end of the book, though prelim inary, already suggests that the effort is rewarding and should be continued. My debts are many.
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.
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.