Introduction
xi
A Note to the Reader
xvii
Sets and Spaces
1(144)
Sets
1(8)
Ordered Sets
9(36)
Relations
10(4)
Equivalence Relations and Partitions
14(2)
Order Relations
16(7)
Partially Ordered Sets and Lattices
23(9)
Weakly Ordered Sets
32(1)
Aggregation and the Pareto Order
33(12)
Metric Spaces
45(21)
Open and Closed Sets
49(7)
Convergence: Completeness and Compactness
56(10)
Linear Spaces
66(48)
Subspaces
72(5)
Basis and Dimension
77(6)
Affine Sets
83(5)
Convex Sets
88(16)
Convex Cones
104(6)
Sperner's Lemma
110(4)
Conclusion
114(1)
Normed Linear Spaces
114(16)
Convexity in Normed Linear Spaces
125(5)
Preference Relations
130(11)
Monotonicity and Nonsatiation
131(1)
Continuity
132(4)
Convexity
136(1)
Interactions
137(4)
Conclusion
141(1)
Notes
142(3)
Functions
145(118)
Functions as Mappings
145(41)
The Vocabulary of Functions
145(11)
Examples of Functions
156(15)
Decomposing Functions
171(3)
Illustrating Functions
174(3)
Correspondences
177(9)
Classes of Functions
186(1)
Monotone Functions
186(24)
Monotone Correspondences
195(3)
Supermodular Functions
198(7)
The Monotone Maximum Theorem
205(5)
Continuous Functions
210(22)
Continuous Functionals
213(3)
Semicontinuity
216(1)
Uniform Continuity
217(4)
Continuity of Correspondences
221(8)
The Continuous Maximum Theorem
229(3)
Fixed Point Theorems
232(27)
Intuition
232(1)
Tarski Fixed Point Theorem
233(5)
Banach Fixed Point Theorem
238(7)
Brouwer Fixed Point Theorem
245(14)
Concluding Remarks
259(1)
Notes
259(4)
Linear Functions
263(154)
Properties of Linear Functions
269(7)
Continuity of Linear Functions
273(3)
Affine Functions
276(1)
Linear Functionals
277(10)
The Dual Space
280(4)
Hyperplanes
284(3)
Bilinear Functions
287(8)
Inner Products
290(5)
Linear Operators
295(11)
The Determinant
296(3)
Eigenvalues and Eigenvectors
299(3)
Quadratic Forms
302(4)
Systems of Linear Equations and Inequalities
306(17)
Equations
308(6)
Inequalities
314(5)
Input-Output Models
319(1)
Markov Chains
320(3)
Convex Functions
323(28)
Properties of Convex Functions
332(4)
Quasiconcave Functions
336(6)
Convex Maximum Theorems
342(7)
Minimax Theorems
349(2)
Homogeneous Functions
351(7)
Homothetic Functions
356(2)
Separation Theorems
358(57)
Hahn-Banach Theorem
371(6)
Duality
377(11)
Theorems of the Alternative
388(10)
Further Applications
398(17)
Concluding Remarks
415(1)
Notes
415(2)
Smooth Functions
417(80)
Linear Approximation and the Derivative
417(12)
Partial Derivatives and the Jacobian
429(12)
Properties of Differentiable Functions
441(16)
Basic Properties and the Derivatives of Elementary Functions
441(6)
Mean Value Theorem
447(10)
Polynomial Approximation
457(19)
Higher-Order Derivatives
460(1)
Second-Order Partial Derivatives and the Hessian
461(6)
Taylor's Theorem
467(9)
Systems of Nonlinear Equations
476(7)
The Inverse Function Theorem
477(2)
The Implicit Function Theorem
479(4)
Convex and Homogeneous Functions
483(13)
Convex Functions
483(8)
Homogeneous Functions
491(5)
Notes
496(1)
Optimization
497(104)
Introduction
497(6)
Unconstrained Optimization
503(13)
Equality Constraints
516(33)
The Perturbation Approach
516(9)
The Geometric Approach
525(4)
The Implicit Function Theorem Approach
529(3)
The Lagrangean
532(10)
Shadow Prices and the Value Function
542(3)
The Net Benefit Approach
545(3)
Summary
548(1)
Inequality Constraints
549(49)
Necessary Conditions
550(18)
Constraint Qualification
568(13)
Sufficient Conditions
581(6)
Linear Programming
587(5)
Concave Programming
592(6)
Notes
598(3)
Comparative Statics
601(34)
The Envelope Theorem
603(6)
Optimization Models
609(13)
Revealed Preference Approach
610(4)
Value Function Approach
614(6)
The Monotonicity Approach
620(2)
Equilibrium Models
622(10)
Conclusion
632(1)
Notes
632(3)
References
635(6)
Index of Symbols
641(2)
General Index
643
Ik heb een vraag over het boek: ‘Foundations of Mathematical Economics - Michael (Universitat Hohenheim) Carter’.
Vul het onderstaande formulier in.
We zullen zo spoedig mogelijk antwoorden.