Mainstream Mathematical Economics in the 20th Century Book

Prolegomena: Cournot, Walras, and Edgeworth.- Preliminary.- Courno&tgrave;s Main Contributions.- Walra&sgrave; Contributions to General Equilibrium.- Edgewort&hgrave;s Theory of the Core.- The Founding Years: 1900 - 1949: Pareto and General Equilibrium.- Preliminary.- General Equilibrium.- Monopolies into General Equilibrium.- Paretòs Efficiency.- Paretòs Italian Main Followers.- Classical General Equilibrium.- Preliminary.- Technologies.- Firms.- Utilities.- Households.- Classical General Equilibrium.- Wald and Existence Proofs.- Preliminary.- Wal&dgrave;s Equations.- Wal&dgrave;s Proof.- Wal&dgrave;s Subsequent Elaborations.- Early Game Theory.- Introduction.- Defining a Game.- Subsequent Elaborations.- Early Multisectoral Growth.- Introduction.- Von Neuman&ngrave;s Balanced Growth Model.- The Existence of Solutions.- Properties of Solutions.- Conclusion.- Dynamic Modelling.- Introduction.- Eva&ngrave;s Dynamic Monopoly.- Ramse&ygrave;s Macroeconomic Model.- Ezekie&lgrave;s Cobweb Model.- Volterràs Struggle for Life.- Mathematical Appendix.- Irving Fisher and Interest Theory.- Introduction.- Individual Wantability or Utility.- Determining Interest Rates.- Fishe&rgrave;s Second Approximation.- Conclusion.- Widening General Equilibrium Theory.- Introduction.- Temporary Equilibrium.- A Temporary Equilibrium Model.- Expectations and Stability.- La Volpès Contribution.- Stability Analysis.- Applied General Equilibrium.- Introduction.- An Open Leontie&fgrave;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-Leontie&fgrave;s Economy.- Sraffàs Contribution.- Mathematical Appendix.- From Classical to Modern Analysis.- Introduction.- Linear Spaces.- Topological Spaces and Metric Spaces.- Linear Topological Spaces.- Normed Spaces and Banac&hgrave;s Spaces.- Hilber&tgrave;s Spaces.- Convexity.- Multifunctions.- Degree Theory and Fixed Points.- Linear Programming and Extensions.- Introduction.- Linear Programming.- Lagrangian Functions.- Convex Programming.- Consume&rgrave;s Analysis.- Preliminary.- Consumption Sets.- Preference Relations.- Ordinal Utility Functions.- Budget Set.- The Consume&rgrave;s Problem.- Differentiability of u.- Expenditure and Indirect Utility.- Comparative Statics Analysis.- Observed Demand and Utility.- N&Mgrave;s Expected Utility.- Fir&mgrave;s Analysis.- Preliminary.- Production Sets.- Production Relations and Functions.- The Competitive Fir&mgrave;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.- Walra&sgrave; Multifunction.- Properties of Walra&sgrave; Multifunction.- The Projection Map.- Mathematical Appendix.- Efficiency and Core. Large Economies.- Introduction.- Paretòs Efficiency.- Core of an Economy.- Large Economies.- Mathematical Appendix.- Game Theory and Oligopoly.- Preliminary.- Classifying Games.- Nas&hgrave;s Solution.- Non-Dynamic Oligopoly Theory.- The Dynamic Oligopoly Theory.- Oligopoly and General Equilibrium.- Cooerative Games.- Social Choice and Welfare Economics.- Preliminary.- The Paradox of Voting.- Social Choice.- Aggregation of Individual Orderings.- Arro&wgrave;s Impossibility Theorem.- Possibility Theorems.- Welfare Economics.- Central Planning.- Implementation Mechanisms and Incentives.- Macroeconomic Growth Theory.- Preliminary.- Solo&wgrave;s Macroeconomic Model.- Exogenous Technical Progress.- Optimal Growth.- Endogenous Growth.- Concluding Remarks.- Multisectoral Growth Models.- Introduction.- Linear Production Models.- General Production Models.- Intertemporal Production Efficiency.- The Turnpike Theory.- Individual Consumption.- Optimal Growth.- Preliminary.- The Discrete Time Model.- The Continuous Time Model.- Mathematical Appendix.- Intertemporal Individual Choices.- Introduction.- Intertemporal Consume&rgrave;s Choices.- Intertemporal Fir&mgrave;s Choices.- Dynamic General Equilibrium.- Preliminary.- Temporary General Equilibrium.- Overlapping Generations.- Rational Expectations.- Equilibria with Sunspots.- Infinite Dimensional Economies.- Imperfect General Equilibrium.- Mathematical Appendix.- Money in Dynamic General Equilibrium.- Preliminary.- The Quantity Theory of Money.- Money in a Production of OLG Model.- Money and Price Fluctuations.- Macroeconomic Asset Pricing.- Preliminary.- Luca&sgrave; Asset Price Model.- Asset Prices and Bubbles.- Conclusion.- Incomplete Markets and Finance.- Preliminary.- Good-Event, and Date-Event, Pairs.- Contingent Markets and Spot Markets.- Real and Nominal Assets.- Exchange Economies.- Production Economies.- Conclusion.- Deterministic Chaos.- Introduction.- Chaotic Trajectories.- Multidimensional Economic Models.- Conclusion.- A Look to the Future.- Some Conjectures.- Directions for Research.- Finale.