Mathematics for economists:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Norton
1994
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIV, 930 S. graph. Darst. |
| ISBN: | 0393957330 9780393957334 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematics for economists |c Carl P. Simon and Lawrence Blume |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Norton |c 1994 | |
| 300 | |a XXIV, 930 S. |b graph. Darst. | ||
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Record in the Search Index
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Contents
Preface xxi
part i Introduction
1
1.1
1.2
IWo-Dimensional Model of Consumer Choice
Multidimensional Model of Consumer Choice
2
2.1
Vocabulary of Functions
Polynomials
Graphs
Increasing and Decreasing Functions
Domain
Interval Notation
2.2
The Slope of a line in the Plane
The Equation of a line
Polynomials of Degree One Have linear Graphs
Interpreting the Slope of a linear Function
2.3
2.4
Rules for Computing Derivatives
VI
2.5
A Nondifferentiable Function
Continuous Functions
Continuously Differentiable Functions
2.6
2.7
3
3.1
Positive Derivative Implies Increasing Function
Using First Derivatives to Sketch Graphs
3.2
3.3
Hints for Graphing
3.4
Tails of Polynomials
Horizontal Asymptotes of Rational Functions
3.5
Local Maxima and Minima on the Boundary and in
the Interior
Second Order Conditions
Global Maxima and Minima
Functions with Only One Critical Point
Functions with Nowhere-Zero Second Derivatives
Functions with No Global Max or
Functions Whose Domains Are Closed Finite
Intervals
3.6
Production Functions
Cost Functions
Revenue and Profit Functions
Demand Functions and Elasticity
4
4.1
Composite Functions
Differentiating Composite Functions: The Chain Rule
4.2
Definition and Examples of the Inverse of a Function
The Derivative of the Inverse Function
The Derivative of ^ln
CONTENTS
Exponents and Logarithms
5.1
5.2
5.3
Base
Base
5.4
5.5
5.6
Present Value
Annuities
Optimal Holding Time
Logarithmic Derivative
part
6
6.1
6.2
Example
Example
Example
Example
Example
7
7.1
Substitution
Elimination of Variables
7.2
7.3
7.4
Application to Portfolio Theory
7.5
vili
8 Matrix Algebra 153
8.1 MATRIX ALGEBRA 153
Addition 153
Subtraction
Scalar Multiplication
Matrix
Laws of Matrix Algebra
Transpose
Systems of Equations in Matrix Form
8.2
8.3
8.4
8.5
Proof of Theorem
8.6
8.7
Mathematical Induction
Including Row Interchanges
9
9.1
Defining the Determinant
Computing the Determinant
Main Property of the Determinant
9.2
9.3
10
10.1
The Real line
The Plane
Three Dimensions and More
10.2
10.3
Addition and Subtraction
Scalar Multiplication
10.4
Length and Distance
The Inner Product
CONTENTS
10.5
10.6
Parametric
Nonparametric Equations
Hyperplanes 230
10.7
Budget
Input Space
Probability Simplex
The Investment Model
IS-LM Analysis
11
11.1
Definition
Checking linear Independence
11.2
11.3
Dimension
11.4
part iii Calculus of Several Variables
12
12.1
Definition
limit of a Sequence
Algebraic Properties of limits
12.2
12.3
Interior of a Set
12.4
Closure of a Set
Boundary of a Set
12.5
12.6
CONTENTS
13
13.1
Functions from Rn to R
Functions from Rk to Rm
13.2
Graphs of Functions of Two Variables
Level Curves
Drawing Graphs from Level Sets
Planar Level Sets in Economics
Representing Functions from Rk to R1 for k
Images of Functions from R1 to Rm
13.3
Linear Functions on Rk
Quadratic Forms
Matrix Representation of Quadratic Forms
Polynomials
13.4
13.5
Onto Functions and One-to-One Functions
Inverse Functions
Composition of Functions
14
14.1
14.2
Marginal Products
Elasticity
14.3
14.4-
Geometric Interpretation
Linear Approximation
Functions of More than Two Variables
14.5
Curves
Tangent Vector to a Curve
Differentiating along a Curve: The Chain Rule
14.6
Directional Derivatives
The Gradient Vector
CONTENTS
14.7
Approximation by Differentials
The Chain Rule
14.8
Continuously Differentiable Functions
Second Order Derivatives and Hessians
Young's Theorem
Higher-Order Derivatives
An Economic Application
14.9
15
15.1
Examples
The Implicit Function Theorem for R2
Several Exogenous Variables in an Implicit
Function
15.2
Geometric Interpretation of the Implicit Function
Theorem
Proof Sketch
Relationship to the Gradient
Tangent to the Level Set Using Differentials
Level Sets of Functions of Several Variables
15.3
Linear Systems
Nonlinear Systems
15.4
15.5
15.6
part iv Optimization
16
16.1
16.2
Definite Symmetric Matrices
XII
Application: Second Order Conditions and
Convexity
Application: Conic Sections
Principal Minors of a Matrix
The Deflniteness of Diagonal Matrices
The Deflniteness of
16.3
MATRICES
Deflniteness and Optimality
One Constraint
Other Approaches
16.4
17
17.1
17.2
17.3
Sufficient Conditions
Necessary Conditions
17.4
Global Maxima of Concave Functions
17.5
Profit-Maximizing Firm
Discriminating Monopolist
Least Squares Analysis
18
18.1
18.2
Two Variables and One Equality Constraint
Several Equality Constraints
18.3
One Inequality Constraint
Several Inequality Constraints
18.4
18.5
18.6
CONTENTS
18.7
Application: A Sales-Maximizing Firm with
Advertising
Application: The Averch-Johnson Effect
One More Worked Example
19
19.1
One Equality Constraint
Several Equality Constraints
Inequality Constraints
Interpreting the Multiplier
19.2
Unconstrained Problems
Constrained Problems
19.3
Constrained Maximization Problems
Minimization Problems
Inequality Constraints
Alternative Approaches to the Bordered Hessian
Condition
Necessary Second Order Conditions
19.4
19.5
19.6
Proof of Theorems
Proof of Theorems
Constraints
20
20.1
Definition and Examples
Homogeneous Functions in Economics
Properties of Homogeneous Functions
A Calculus Criterion for Homogeneity
Economic Applications of Euler's Theorem
20.2
Economic Applications of Homogenization
20.3
XIV
20.4
Motivation and Definition 500
Characterizing Homothetic Functions
21
21.1
Calculus Criteria for Concavity
21.2
Concave Functions in Economics
21.3
FUNCTIONS
Calculus Criteria
21.4
21.5
Unconstrained Problems
Constrained Problems
Saddle Point Approach
21.6
Proof of the Sufficiency Test of Theorem
Proof of Theorem
Proof of Theorem
Proof of Theorem
22
22.1
Utility Maximization
The Demand Function
The Indirect Utility Function
The Expenditure and Compensated Demand
Functions
The Slutsky Equation
22.2
The Profit-Maximizing Firm
The Cost Function
22.3
Necessary Conditions for
Sufficient Conditions for
22.4
Competitive Equilibrium
Fundamental Theorems of Welfare Economics
CONTENTS
part v Eigenvalues and Dynamics
23
23.1
23.2
One-Dimensional Equations
Two-Dimensional Systems: An Example
Conic Sections
The Leslie Population Model
Abstract Two-Dimensional Systems
k-Diinensional Systems
An Alternative Approach: The Powers of a Matrix
Stability of Equilibria
23.3
Trace as Sum of the Eigenvalues
23.4
2X2
3X3
Solving Nondiagonalizable Difference Equations
23.5
Diagonalizing Matrices with Complex Eigenvalues
Linear Difference Equations with Complex
Eigenvalues
Higher Dimensions
23.6
23.7
23.8
23.9
Proof of Theorem
Proof of Theorem
24
24.1
24.2
Linear First Order Equations
Separable Equations
24.3
Introduction
XVI
Real and Unequal Roots of
Equation
Real and Equal Roots of the Characteristic Equation
Complex Roots of the Characteristic Equation
The Motion of a Spring
Nonhomogeneous Second Order Equations
24.4
The Fundamental Existence and Uniqueness
Theorem
Direction Fields
24.5
Drawing Phase Portraits
Stability of Equilibria on the line
24.6
Indirect Money Metric Utility Functions
Converse of Euler's Theorem
25
Equations
25.1
Coupled Systems of Differential Equations
Vocabulary
Existence and Uniqueness
25.2
Distinct Real Eigenvalues
Complex Eigenvalues
Multiple Real Eigenvalues
25.3
25.4
Stability of Linear Systems via Eigenvalues
Stability of Nonlinear Systems
25.5
Vector Fields
Phase Portraits: Linear Systems
Phase Portraits: Nonlinear Systems
25.6
the Predator-Prey System
Conservative Mechanical Systems
25.7
25.8
CONTENTS
part
26
26.1
26.2
26.3
The Adjoint Matrix
26.4
Supply and Demand
26.5
Proof of Theorem
Proof of Theorem
Other Approaches to the Determinant
27
27.1
Rn as a Vector Space
Subspaces of R"
27.2
27.3
27.4
Dimension of the Column Space of A
The Role of the Column Space
27.5 NULLSPACE 765
" Affine
Fundamental Theorem of Linear Algebra
Conclusion
27.6
27.7
Proof of Theorem
Proof of Theorem
28
28.1
Two Equations in Two Unknowns
Two Equations in Three Unknowns
Three Equations in Three Unknowns
XVIII
28.2
28.3
Three Alternatives
Four Alternatives
Consequences of the Existence of Cycles
Other Voting Paradoxes
Rankings of the Quality of Firms
28.4
Activity Analysis
Simple linear Models and Productive Matrices
28.5
Leontief
part
29
29.1
29.2
29.3
29.4
Three Norms on Rn
Equivalent Norms
Norms on Function Spaces
29.5
Finite Covering Property
Heine-Borel Theorem
Summary
30
30.1
Existence of Global Maxima on Compact Sets
Rolle's Theorem and the Mean Value Theorem
30.2
Functions of One Variable
30.3
30.4
Second Order Sufficient Conditions for
Optimization
Indefinite Hessian
CONTENTS
Second
Optimization
30.5
part vim Appendices
A1 Sets, Numbers, and Proofs
A1.1 SETS
Vocabulary of Sets
Operations with Sets
Al
Vocabulary
Properties of Addition and Multiplication
Least Upper Bound Property
A1.3 PROOFS
Direct Proofs
Converse and
Indirect Proofs
Mathematical Induction
A2 Trigonometric Functions
A2.1 DEFINITIONS OF THE TRIG FUNCTIONS
A2.2 GRAPHING TRIG FUNCTIONS
A2.3 THE PYTHAGOREAN THEOREM
A2.4 EVALUATING TRIGONOMETRIC FUNCTIONS
A2.5 MULTIANGLE FORMULAS
A2.6 FUNCTIONS OF REAL NUMBERS
A2.7 CALCULUS WITH TRIG FUNCTIONS
A2.8 TAYLOR SERIES
A2.9 PROOF OF THEOREM A2.3
A3
A3.1 BACKGROUND
Definitions
Arithmetic Operations
A3.2
XX
A3.3
A3.4 COMPLEX NUMBERS AS EXPONENTS
A3.5 DIFFERENCE EQUATIONS
A4
A4.1
Integration by Parts
A4.2 THE FUNDAMENTAL THEOREM OF CALCULUS
A4.3 APPLICATIONS
Area under a Graph
Consumer Surplus
Present Value of a Flow
A5 Introduction to Probability
A5.1 PROBABILITY OF AN EVENT
A5.2 EXPECTATION AND VARIANCE
A5.3 CONTINUOUS RANDOM VARIABLES
A6 Selected Answers
Index |
| any_adam_object | 1 |
| author | Simon, Carl P. 1945- Blume, Lawrence E. |
| author_GND | (DE-588)170767981 (DE-588)170098389 |
| author_facet | Simon, Carl P. 1945- Blume, Lawrence E. |
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| bvnumber | BV011224125 |
| callnumber-first | H - Social Science |
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| callnumber-raw | HB135.S545 1994 |
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| callnumber-subject | HB - Economic Theory and Demography |
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| dewey-full | 510/.2433920 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV011224125 |
| illustrated | Illustrated |
| indexdate | 2025-01-27T09:00:29Z |
| institution | BVB |
| isbn | 0393957330 9780393957334 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007530677 |
| oclc_num | 263552967 |
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| physical | XXIV, 930 S. graph. Darst. |
| publishDate | 1994 |
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| spelling | Simon, Carl P. 1945- Verfasser (DE-588)170767981 aut Mathematics for economists Carl P. Simon and Lawrence Blume 1. ed. New York [u.a.] Norton 1994 XXIV, 930 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wirtschaftsmathematik (DE-588)4066472-7 s DE-604 Blume, Lawrence E. Verfasser (DE-588)170098389 aut Digitalisierung UBPassau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007530677&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simon, Carl P. 1945- Blume, Lawrence E. Mathematics for economists Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4123623-3 |
| title | Mathematics for economists |
| title_auth | Mathematics for economists |
| title_exact_search | Mathematics for economists |
| title_full | Mathematics for economists Carl P. Simon and Lawrence Blume |
| title_fullStr | Mathematics for economists Carl P. Simon and Lawrence Blume |
| title_full_unstemmed | Mathematics for economists Carl P. Simon and Lawrence Blume |
| title_short | Mathematics for economists |
| title_sort | mathematics for economists |
| topic | Economics, Mathematical Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | Economics, Mathematical Wirtschaftsmathematik Lehrbuch |
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