Introduction to Mathematical Economics

ISBN-13: 9781461262800 / Angielski / Miękka / 2011 / 249 str.

M. C. Kemp; Y. Kimura

Opis

Our objectives may be briefly stated. They are two. First, we have sought to provide a compact and digestible exposition of some sub-branches of mathematics which are of interest to economists but which are underplayed in mathematical texts and dispersed in the journal literature. Second, we have sought to demonstrate the usefulness of the mathematics by providing a systematic account of modern neoclassical economics, that is, of those parts of economics from which jointness in production has been excluded. The book is introductory not in the sense that it can be read by any high-school graduate but in the sense that it provides some of the mathematics needed to appreciate modern general-equilibrium economic theory. It is aimed primarily at first-year graduate students and final-year honors students in economics who have studied mathematics at the university level for two years and who, in particular, have mastered a full-year course in analysis and calculus. The book is the outcome of a long correspondence punctuated by periodic visits by Kimura to the University of New South Wales. Without those visits we would never have finished. They were made possible by generous grants from the Leverhulme Foundation, Nagoya City University, and the University of New South Wales. Equally indispensible were the expert advice and generous encouragement of our friends Martin Beckmann, Takashi Negishi, Ryuzo Sato, and Yasuo Uekawa.

Spis treści

1 Linear Inequalities.- 1 Some Fundamental Theorems.- 2 Linear Programming and Matrix Games.- 3 Convex Sets and Convex Cones.- 4 Nonlinear Programming.- 2 Nonnegative Matrices.- 1 The Perron-Frobenius Theorem.- 2 Power-Nonnegative Matrices.- 3 Some Special Matrices.- 1 P-, NP-, PN-, and Semi-PN Matrices.- 2 Fundamental Properties of P-, N-, PN-, and NP Matrices.- 3 Fundamental Properties of Semi-PN Matrices.- 4 Matrices with the Minkowski or Metzler Property.- 4 Stability Analysis of Some Dynamic Systems.- 1 Systems of Linear Differential Equations: Solutions, Stability, and Saddle-Point Property.- 2 Systems of Linear tâtonnement Processes.- 3 An Existence Theorem for Systems of Ordinary Differential Equations.- 4 Liapunov’s Stability Theorems for Systems of Ordinary Differential Equations.- 5 Stability Theorems for Systems of Difference Equations.- 5 Neoclassical Economies—Statics.- 1 Neoclassical Technologies.- 2 Mapping from Factor-Rentals and Primary-Factor Endowments to Commodity Prices and Outputs.- 3 Mapping from Commodity Prices and Own-Rates of Return to Primary-Factor Rentals.- 4 Mapping from Commodity Prices and Own-Rates of Return to Gross and Net Outputs.- 6 Neoclassical Economies—Dynamics.- 1 Introduction.- 2 Stability of Market Equilibrium.- 3 A Dynamic Heckscher-Ohlin Model.- Appendix A.- Appendix B.- References.- Name Index.- List of Symbols.