Full Description
To write everything about nothing, or to write nothing about everything: this is the problem. (Anonym, circa 1996-97) The first idea to write a book on M athematical Economics, more or less ordered in a historical sequence, occurred to me in 1995, when I was asked, by Istituto delta Enciclopedia Italiana, to write the entry "Storia dell'economia 1 2 matematica" , for the collective work "Storia deI XX Secolo". I thought that it would be interesting to elaborate on the text presented to the editors, to turn it into a book aiming at giving a panorama of what, in my opinion, are the main 20th century contributions to mathematical eco nomics. Of course, only a narrow set of the contributions made by economic theorists could be included, both for space limitations and necessity, because 3 of the limited competence of any single author. For instance, I have paid very limited attention to what is now called Macroeconomics, and also to Game Theory, which actually has grown so much as to acquire scientific in dependence as a living branch of applied mathematics. For the same reason, I have also left completely untouched such fields as Mathematical Finance, Public Economics, Theory of Taxation, etc. I have always based my presentation on published material only, assuming that what is contained in working papers still waits to be confirmed, possibly in the first years of the 21th century.
Contents
Prolegomena: Cournot, Walras, and Edgeworth.- Preliminary.- Cournot`s Main Contributions.- Walras` Contributions to General Equilibrium.- Edgeworth`s Theory of the Core.- The Founding Years: 1900 - 1949: Pareto and General Equilibrium.- Preliminary.- General Equilibrium.- Monopolies into General Equilibrium.- Pareto`s Efficiency.- Pareto`s Italian Main Followers.- Classical General Equilibrium.- Preliminary.- Technologies.- Firms.- Utilities.- Households.- Classical General Equilibrium.- Wald and Existence Proofs.- Preliminary.- Wald`s Equations.- Wald`s Proof.- Wald`s Subsequent Elaborations.- Early Game Theory.- Introduction.- Defining a Game.- Subsequent Elaborations.- Early Multisectoral Growth.- Introduction.- Von Neumann`s Balanced Growth Model.- The Existence of Solutions.- Properties of Solutions.- Conclusion.- Dynamic Modelling.- Introduction.- Evan`s Dynamic Monopoly.- Ramsey`s Macroeconomic Model.- Ezekiel`s Cobweb Model.- Volterra`s Struggle for Life.- Mathematical Appendix.- Irving Fisher and Interest Theory.- Introduction.- Individual Wantability or Utility.- Determining Interest Rates.- Fisher`s Second Approximation.- Conclusion.- Widening General Equilibrium Theory.- Introduction.- Temporary Equilibrium.- A Temporary Equilibrium Model.- Expectations and Stability.- La Volpe`s Contribution.- Stability Analysis.- Applied General Equilibrium.- Introduction.- An Open Leontief`s Model.- Prices, Profits and the Wage Rate.- Some Accountancy.- Compatibility of Exogenous Data.- Extensions, Finesses, and Formalism: 1950 on: Walras 'cum' Leontief.- Introduction.- Positivity of Input-Output Solutions.- The non Substitution Theorem.- A Walras-Leontief`s Economy.- Sraffa`s Contribution.- Mathematical Appendix.- From Classical to Modern Analysis.- Introduction.- Linear Spaces.- Topological Spaces and Metric Spaces.- Linear Topological Spaces.- Normed Spaces and Banach`s Spaces.- Hilbert`s Spaces.- Convexity.- Multifunctions.- Degree Theory and Fixed Points.- Linear Programming and Extensions.- Introduction.- Linear Programming.- Lagrangian Functions.- Convex Programming.- Consumer`s Analysis.- Preliminary.- Consumption Sets.- Preference Relations.- Ordinal Utility Functions.- Budget Set.- The Consumer`s Problem.- Differentiability of u.- Expenditure and Indirect Utility.- Comparative Statics Analysis.- Observed Demand and Utility.- NM`s Expected Utility.- Firm`s Analysis.- Preliminary.- Production Sets.- Production Relations and Functions.- The Competitive Firm`s Problem.- Differentiable Techniques.- Comparative Statics.- Cost-Production Duality.- Monopoly and Monopsony.- Other Market Forms.- The Principal-Agent Problem.- General Competitive Equilibrium.- Introduction.- Some 'Meta-Assumptions'.- Goods.- Agents.- General Competitive Equilibrium.- Boundedness of the Economy.- The Existence of a General Equilibrium.- The Law of Demand and Supply.- Non Convexity and Approximate Equilibrium.- On Excess Demand Functions.- More on the Law of Demand.- Rationing.- Conclusion.- Stability and More.- Introduction.- Discrete versus Continuous Time.- The Stability Problem.- Stability Properties.- Other Adjustment Processes.- Excess Demand Multifunctions.- Computation of Equilibria.- Applied General Equilibrium.- Mathematical Appendix.- Regular Economies.- Introduction.- Differentiability Again.- Walras` Multifunction.- Properties of Walras` Multifunction.- The Projection Map.- Mathematical Appendix.- Efficiency and Core. Large Economies.- Introduction.- Pareto`s Efficiency.- Core of an Economy.- Large Economies.- Mathematical Appendix.- Game Theory and Oligopoly.- Preliminary.- Classifying Games.- Nash`s Solution.- Non-Dynamic Oligopoly Theory.- The Dynamic Oligopoly Theory.- Oligopoly and General Equilibrium.
