Introduction to Mathematical Economics

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.