Mathematical methods and economic theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Univ. Press
2011
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 312 S. graph. Darst. |
| ISBN: | 9780198069973 0198069979 |
Internformat
MARC
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| 020 | |a 9780198069973 |9 978-0-19-806997-3 | ||
| 020 | |a 0198069979 |9 0-19-806997-9 | ||
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| 100 | 1 | |a Mukherji, Anjan |d 1945- |e Verfasser |0 (DE-588)170297764 |4 aut | |
| 245 | 1 | 0 | |a Mathematical methods and economic theory |c Anjan Mukherji ; Subrata Guha |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Univ. Press |c 2011 | |
| 300 | |a XIV, 312 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 700 | 1 | |a Guha, Subrata |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-020772148 | ||
Datensatz im Suchindex
| _version_ | 1804143553384808448 |
|---|---|
| adam_text | Contents
Preface
xi
SECTION I
1
Introduction
3
LI The
Objectivo
:i
1.2
The Tools for Section
1 4
2
Basic Mathematical Logic
5
2.1
Introduction
5
2.2
Sentential Logic
7
2.2.1
Sentences, truth values, and notations
7
2.2.2
Truth rules and truth tables
11
2.2.3
Tautologies, contradictions, and contingent sentences
13
2.2.4
Logical consequence and the validity of arguments
15
2.2.5
Logical consistency and independence
19
2.3
Predicate Logic
20
2.3.1
Universe of discourse, universal and existential sentences
20
2.3.2
Individual constants, variables, quantifiers, and predicates
21
2.3.3
Well-formed formulas, scope of a quantifier, bound and
free variables
23
2.3.4
Truth rules of predicate logic
24
2.3.Ő
t sing multiple quantifiers
2-5
3
Set Theory
31
3.1
Operations with Sets
31
3.2
Binarv Relations
32
vi
CONTENTS
3.3
Even and Odd Integers 33
3.4
Real Numbers 33
3.5
Infimum and Suprernum 35
3.6
Functions 35
3.7
Countable Sets 36
3.8
Open and Closed Sets 38
3.9
Compactness 41
4
Functions of a Single Variable 46
4.1
Limits 46
4.2
Continuity 4T
4.2.1
Uniform continuity 4^
4.2.2
Existence of
extrema
50
4.3
Differentiability
51
4.3.1
Approximations
53
4.4
Integration
55
4.4.1
Introduction
56
4.4.2
Functions of bounded variation
56
4.4.3
Basic properties of the integral
57
4.4.4
Integration by parts
58
4.4.5
The Riemann-Stieltjes integral as a Riemann integral
59
4.4.6
The Riemann-Stieltjes integral as a finite Sum
60
4.4.7
The integral as a function
63
4.4.8
Improper integrals
66
5
Economic Applications I: Choice, Utility, and Aggregation
69
5.1
Introduction
69
5.2
Possibility of Choosing the Best
69
5.3
The Construction of a Continuous Utility Indicator Function
71
5.4
Arrow s Theorem
73
5.4.1
Notation and definitions
74
5.4.2
A lemma
75
5.4.3
The theorem
75
Further Readings for Section I
76
CONTENTS
vii
SECTION II
6
Introduction
79
6.1
The Objective of Section II
79
7
Real Linear Algebra
80
7.1
Preliminaries: Vector Spaces, Sub-spaces, Linear Dependence,
Rank of a Sub-space, Matrices
80
7.2
Solution to Equations and Inequalities
85
7.3
Determinants
89
7.4
Characteristic Roots and Vectors
91
7.5
Quadratic Forms
92
7.6
Dominant Diagonal Matrices
94
7.6.1
Non-negative square matrices
97
7.6.2
Stable matrices
100
8
Functions of Several Variables
103
8.1
Differentiability
103
8.2
Some Special Functions
107
8.3
Maps and Fixed Points
108
8.4
Separation Theorems
109
9
Static Optimization
112
9.1
Unconstrained Optimization
112
9.2
Constrained Optimization
113
9.3
Equality Constraints
113
9.4
Inequality Constraints
115
9.5
A Duality Theorem
117
10
Economic Applications II: Demand and Supply
122
10.1
Static Optimization I
122
10.2
The Hicks-Allen Theory
127
10.3
Producer Behaviour
130
10.3.1
Cost and profit functions
131
10.4
Market Equilibria
137
10.4.1
The excess demand function
137
10.4.2
The Existence Theorem and the Fixed Point Theorem
139
viii CONTENTS
10.5
Non-competitive Market Equilibria
141
10.6
Perfect Competition
142
10.7
Monopoly and Monopsony
142
10.8
Bilateral Monopoly
142
10.9
Social Welfare Maximization
144
10.10
Efficiency and Competitive Equilibria
144
11
Decision-making under Alternative Scenarios
149
11.1
Introduction
149
11.2
Decision-making under Uncertainty
149
11.2.1
Lotteries
149
11.2.2
Ranking over lotteries
150
11.2.3
The expected utility function
151
11.3
Risk Aversion
154
11.3.1
Preliminaries
154
11.3.2
Measures of risk aversion
154
11.3.3
Risk aversion and choice of risky assets
155
11.3.4
Global measures of risk aversion
160
11.3.5
Portfolio choice with more than one risky asset
162
11.4
Interactive Decision-making
163
11.4.1
Introduction
163
11.4.2
Games in normal form
164
11.4.3
Refinements of Nash equilibria
169
11.4.4
Bayesian-Nash equilibria
173
11.4.5
Repeated games
174
Further Readings for Section II
176
SECTION III
12
Introduction
181
13
Dynamical Systems
182
13.1
Continuous Time Processes
182
13.1.1
Introduction
182
13.1.2
Solutions to some standard forms
183
13.1.3
Definitions and propositions
187
13.1.4
The linear case
190
CONTENTS ix
13.1.5 Motion
on the
plane 192
13.1.6
Lotka-
Volterra
system
of equations
197
13.2
Discrete Processes
200
13.2.1
Preliminary definitions
200
13.3
Stability of Periodic Points
201
13.3.1
The logistic map
203
14
Dynamic Optimization
207
14.1
Introduction to the Optimal Control Theory
207
14.2
A Basic Optimal Control Problem
209
14.3
Necessary Conditions
211
14.3.1
Some special assumptions
211
14.3.2
A maximization condition
212
14.3.3
A differential equation
216
14.3.4
The backward value function
219
14.4
The Maximum Principle for the Basic Problem
221
14.4.1
The maximum principle for problem (A)
221
14.5
Sufficient Conditions for an Optimal Control
223
14.5.1
The Mangasarian sufficiency conditions for problem (A)
223
14.5.2
The Arrow sufficiency conditions for problem (A)
224
14.6
Variants of the Basic Problem
225
14.6.1
Alternative conditions on the terminal state
225
14.6.2
Addition of a salvage value function
227
14.6.3
An important note
229
14.6.4
Variable terminal time
229
14.6.5
Inequality constraints with control variables
232
14.7
Infinite Horizon Problems
237
14.7.1
Definition of an optimal control
238
14.7.2
Necessary conditions for optimality
240
14.7.3
Sufficient conditions for optimality
242
14.8
Infinite Horizon Problem: An Alternative Aproach
243
14.8.1
The value function and the Bellman equation 24S
14.8.2
The existence of the value function
250
14.8.3
Some properties of bounded continuous functions on X
250
14.8.4
Restrictions on
Γ
and application of the Contraction
Mapping Theorem
253
χ
CONTENTS
14.8.5
Differentiability of the value function and the
Euler
equation
256
15
Economic Applications III: Economic Dynamics
260
15.1
Introduction
260
15.2
The Stability of Competitive Equilibrium
260
15.2.1
Gross substitutes and the weak axiom of revealed
preference
263
15.2.2
Scarf example
267
15.2.3
Discrete price adjustment
271
15.2.4
Bifurcation and complex dynamics in a discrete
tâtonnement
273
15.3
Optimal Economic Growth
277
15.3.1
The outlines of the model
277
15.3.2
Solution to the optimal control problem for the household
282
15.3.3
The solution using Arrow-type sufficiency conditions
285
15.3.4
Aggregate dynamics in the model
287
15.4
The Social Planner s Problem
292
Further Readings for Section III
295
References
297
Index
302
|
| any_adam_object | 1 |
| author | Mukherji, Anjan 1945- Guha, Subrata |
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| dewey-ones | 330 - Economics |
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| dewey-search | 330.0151 |
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| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV036856282 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:49:29Z |
| institution | BVB |
| isbn | 9780198069973 0198069979 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020772148 |
| oclc_num | 699831663 |
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| owner | DE-355 DE-BY-UBR DE-M382 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-M382 DE-11 |
| physical | XIV, 312 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Univ. Press |
| record_format | marc |
| spelling | Mukherji, Anjan 1945- Verfasser (DE-588)170297764 aut Mathematical methods and economic theory Anjan Mukherji ; Subrata Guha 1. publ. Oxford [u.a.] Univ. Press 2011 XIV, 312 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Volkswirtschaftslehre (DE-588)4078943-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Volkswirtschaftslehre (DE-588)4078943-3 s Mathematische Methode (DE-588)4155620-3 s b DE-604 Guha, Subrata Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020772148&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mukherji, Anjan 1945- Guha, Subrata Mathematical methods and economic theory Mathematische Methode (DE-588)4155620-3 gnd Volkswirtschaftslehre (DE-588)4078943-3 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4078943-3 (DE-588)4123623-3 |
| title | Mathematical methods and economic theory |
| title_auth | Mathematical methods and economic theory |
| title_exact_search | Mathematical methods and economic theory |
| title_full | Mathematical methods and economic theory Anjan Mukherji ; Subrata Guha |
| title_fullStr | Mathematical methods and economic theory Anjan Mukherji ; Subrata Guha |
| title_full_unstemmed | Mathematical methods and economic theory Anjan Mukherji ; Subrata Guha |
| title_short | Mathematical methods and economic theory |
| title_sort | mathematical methods and economic theory |
| topic | Mathematische Methode (DE-588)4155620-3 gnd Volkswirtschaftslehre (DE-588)4078943-3 gnd |
| topic_facet | Mathematische Methode Volkswirtschaftslehre Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020772148&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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