Mathematical Systems Theory and Economics I/II: Proceeding of an International Summer School Held in Varenna, Italy, June 1-12, 1967

ISBN-13: 9783540046356 / Angielski / Miękka / 1969 / 487 str.

H. W. Kuhn; G. P. Szega

Opis

The International Summer School on Mathematical Systems Theory and Economics was held at the Villa Monastero in Varenna, Italy, from June 1 through June 12, 1967. The objective of this Summer School was to review the state of the art and the prospects for the application of the mathematical theory of systems to the study and the solution of economic problems. Particular emphasis was given to the use of the mathematical theory of control for the solution of problems in economics. It was felt that the publication of a volume collecting most of the lectures given at the school would show the current status of the application of these methods. The papers are organized into four sections arranged into two volumes: basic theories and optimal control of economic systems which appear in the first volume, and special mathematical problems and special applications which are contained in the second volume. Within each section the papers follow in alphabetical order by author. The seven papers on basic theories are a rather complete representative sample of the fundaments of general systems theory, of the theory of dynamical systems and the theory of control. The five papers on the application of optimal control to economic systems present a broad spectrum of applications.

Spis treści

I Basic Theories.- Dynamical Systems.- Economic Equilibrium.- Control as Programming in General Normed Linear Spaces.- to the Algebraic Theory of Linear Dynamical Systems.- Duality in Mathematical Programming.- Mathematical Theory of General Systems and some Economic Problems.- Convex Functions and Duality in Optimization Problems and Dynamics.- II Optimal Control of Economic Systems.- Optimal Investment Policy.- On the Inverse Optimal Problem.- Dynamic Keynesian Economic Systems: Control and Identification.- On the Controllability of Decentralized Macroeconomic Systems: The Assignment Problem.- Application of Pontriagin’s Maximum Principle to Economics.- III Special Mathematical Problems.- Control Vector Fields on Manifolds and Attainability.- Semi-Dynamical Systems.- Some Theorems in Measure Theory and Generalized Dynamical Systems Defined by Contingent Equations.- On the Controllability of Linear Difference-Differential Systems.- The Core and Competitive Equilibria.- Geometric Theory of Linear Controlled Systems.- Stability of Sets with Respect to Abstract Processes.- Invariance of Contingent Equations.- Space of Solutions.- IV Special Applications.- Feedback and the Dynamics of Market Stability.- Investigations of Organization of Production Processes with Tree Structure.- Testing Econometric Models by Means of Time Series Analysis.- Optimum Control and Synthesis of Organizational Structure of Large Scale Systems.- Optimal Accumulation in a Listian Model.- Multi-level Approach to the Large-scale Control Problem.