Mathematics and methodology for economics: applications, problems and solutions
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham ; Heidelberg ; New York ; Dordrecht ; London
Springer
[2016]
|
| Series: | Springer texts in business and economics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xix, 630 Seiten Diagramme |
| ISBN: | 9783319233529 |
| ISSN: | 2192-4333 |
Staff View
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| 264 | 1 | |a Cham ; Heidelberg ; New York ; Dordrecht ; London |b Springer |c [2016] | |
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Record in the Search Index
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| adam_text | Contents
1 Sets, Numbers and Vectors............................................ 1
1.1 Introduction................................................. 1
1.2 Basics....................................................... 1
1.2.1 Exercises............................................ 7
1.2.2 Answers.............................................. 7
1.3 Subsets, Operations Between Sets ............................ 8
1.3.1 Exercises........................................... 11
1.3.2 Answers ............................................ 12
1.4 Cartesian Products of Sets, Rn, Vectors .................... 12
1.4.1 Exercises........................................... 18
1.4.2 Answers ............................................ 19
1.5 Operations for Vectors, Linear Dependence
and Independence ........................................... 19
1.5.1 Sums, Differences, Linear Combinations of Vectors_ 19
1.5.2 Linear Dependence, Independence..................... 21
1.5.3 Inner Product....................................... 24
1.5.4 Exercises........................................... 25
1.5.5 Answers ............................................ 26
1.6 Geometric Interpretations. Distance. Orthogonal Vectors... 26
1.6.1 Exercises......................................... 30
1.6.2 Answers ............................................ 30
1.7 Complex Numbers; the Cosine, Sine, Tangent
and Cotangent .............................................. 31
1.7.1 Multiplication of Complex Numbers................... 31
1.7.2 Trigonometric Form of Complex Numbers;
Sine, Cosine....................................... 34
1.7.3 Division of Complex Numbers; Equations.............. 40
1.7.4 Tangent, Cotangent.................................. 42
L7.5 Exercises........................................... 43
1.7.6 Answers ............................................ 43
vii
45
45
46
49
49
49
52
53
53
59
60
61
61
63
72
72
73
77
78
78
84
85
85
92
92
93
99
100
100
103
104
105
105
107
112
113
Production Systems Production Processes, Technologies,
Efficiency, Optimisation .....................................
2.1 Introduction...........................................
2.2 Basics.................................................
2.2.1 Exercises......................................
2.2.2 Answers .......................................
2.3 Linear Production Models, Linear Optimisation Problems
2.3.1 Exercises......................................
2.3.2 Answers .......................................
2.4 Simple Approaches to Linear Optimisation Problems......
2.4.1 Exercises......................................
2.4.2 Answers .......................................
Mappings, Functions...........................................
3.1 Introduction...........................................
3.2 Basics. Domains, Ranges, Images
(Codomains). Mappings (Binary Relations),
Functions, Injections, Surjections, Bijections. Graphs.
3.2.1 Exercises......................................
3.2.2 Answers .......................................
3.3 Functions of n Variables, n-Dimensional Intervals,
Composition of Functions...............................
3.3.1 Exercises......................................
3.3.2 Answers........................................
3.4 Monotonie and Linearly Homogeneous Functions.
Maxima and Minima......................................
3.4.1 Exercises......................................
3.4.2 Answers .......................................
3.5 Convex (Concave) Functions. Convex Sets................
3.5.1 Exercises......................................
3.5.2 Answers .......................................
3.6 Quasi-convex Functions.................................
3.6.1 Exercises......................................
3.6.2 Answers .......................................
3.7 Functions in the “Statistical Theory” of Price Indices_
3.7.1 Exercises......................................
3.7.2 Answers .......................................
Affine and Linear Functions and Transformations
(Matrices), Linear Economic Models, Systems of Linear
Equations and Inequalities....................................
4.1 Introduction...........................................
4.2 Proportionality, Linear and Affine Functions.
Additivity, Linear Homogeneity, Linearity..............
4.2.1 Exercises......................................
4.2.2 Answers........................................
Contents
IX
4.3 Additivity, Linear Homogeneity, Linearity
of Vector-Vector Functions, Matrices........................ 113
4.3.1 Exercises .......................................... 117
4.3.2 Answers............................................. 117
4.4 Matrix Algebra.............................................. 118
4.4.1 Exercises .......................................... 124
4.4.2 Answers............................................. 125
4.5 Linear Economic Models: Leontief, von Neumann............... 126
4.5.1 Exercises........................................... 133
4.5.2 Answers............................................. 134
4.6 Systems of Linear Equations. Solution
by Elimination. Rank. Necessary and Sufficient Conditions . 135
4.6.1 Exercises........................................... 154
4.6.2 Answers............................................. 155
4.7 Determinant, Cramer’s Rule, Inverse Matrix.................. 156
4.7.1 Exercises........................................... 164
4.7.2 Answers............................................. 165
4.8 Applications of Functions of Vector Variables:
Aggregation in Economics.................................... 165
4.8.1 Exercises........................................... 174
4.8.2 Answers............................................. 176
5 Linear Optimisation, Duality: Zero-Sum Games....................... 177
5.1 Introduction................................................ 177
5.2 Linear Optimisation Problems ............................... 179
5.2.1 Exercises........................................... 192
5.2.2 Answers............................................. 192
5.3 Duality..................................................... 194
5.3.1 Exercises........................................... 200
5.3.2 Answers............................................. 201
5.4 Two-Person Zero-Sum Games .................................. 201
5.4.1 Exercises........................................... 207
5.4.2 Answers............................................. 207
6 Functions, Their Limits and Their Derivatives .................... 209
6.1 Introduction.............................................. 209
6.2 Limits, Infinity as Limit, Limit at Infinity, Sequences:
Trigonometric Functions, Polynomials, Rational Functions... 211
6.2.1 Exercises........................................... 220
6.2.2 Answers............................................. 221
6.3 Continuity, Sectional Continuity, Left and Right Limits..... 221
6.3.1 Exercises .......................................... 226
6.3.2 Answers ............................................ 227
6.4 Derivative, Derivation ..................................... 227
6.4.1 Exercises .......................................... 233
6.4.2 Answers ............................................ 234
X
Contents
6.5 Rules Which Make Derivation Easier.......................... 234
6.5.1 Exercises .......................................... 242
6.5.2 Answers ............................................ 243
6.6 An Application: Price-Elasticity of Demand.................. 243
6.6.1 Exercises ........................................ 245
6.6.2 Answers ............................................ 245
6.7 Laws of the Mean, Taylor Series,
Bernoulli—LHospital Rule ................................... 245
6.7.1 Exercises .......................................... 257
6.7.2 Answers............................................. 258
6.8 Mono tonicity, Local Maxima, Minima and Convexity
of Differentiable Functions................................. 258
6.8.1 Exercises .......................................... 262
6.8.2 Answers ............................................ 263
6.9 “Cobweb” Situations in Economics: Points
of Intersection of Graphs and Zeros of Functions............ 263
6.9.1 Exercises .......................................... 269
6.9.2 Answers............................................. 270
6.10 Newton’s Algorithm: Differentials (Linear Approximation)... 270
6.10.1 Exercises........................................... 275
6.10.2 Answers............................................. 275
6.11 Linear Approximation: Differentials and Derivatives
of Vector-Vector Functions—Partial Derivatives
of Higher Orders............................................ 277
6.11.1 Excercises ......................................... 286
6.11.2 Answers............................................. 287
6.12 Chain Rule: Euler’s Partial Differential Equation
for Homogeneous Functions ................................ 288
6.12.1 Excercises ......................................... 293
6.12.2 Answers............................................. 294
6.13 Implicit Functions.......................................... 294
6.13.1 Excercises ......................................... 298
6.13.2 Answers............................................. 299
7 Nonlinear Functions of Interest to Economics. Systems
of Nonlinear Equations ........................................... 301
7.1 Introduction................................................ 301
7.2 Exponential and Logarithm Functions. Powers
with Arbitrary Real Exponents. Conditions
for Convexity and Applications.............................. 302
7.2.1 Exercises........................................... 318
7.2.2 Answers............................................. 318
Contents xi
7.3 Applications: “Discrete” and “Continuous”
Compounding, “Effective Interest Rate”, Doubling
Time, Discounting........................................... 319
7.3.1 Exercises........................................... 324
7.3.2 Answers............................................. 324
7.4 Some Interesting Scalar Valued Nonlinear Functions
in Several Variables. Homothetic Functions.................. 325
7.4.1 Exercises........................................... 339
7.4.2 Answers............................................. 340
7.5 Fundamental Notions in Production Theory.
Production Functions. Elasticity of Substitution............ 341
7.5.1 Exercises........................................... 356
7.5.2 Answers............................................. 356
7.6 Nonlinear Vector-Valued Functions, Systems
of Equations. Banach’s Fixed Point Theorem.................. 357
7.6.1 Exercises........................................... 370
7.6.2 Answers............................................. 371
8 Nonlinear Optimisation with One or Several Objectives:
Kuhn-Tucker Conditions............................................. 373
8.1 Introduction.............................................. 373
8.2 Convexity of Differentiable Functions of Several
Variables, Matrix-Conditions for Convexity,
Eigenvalues, Eigenvectors................................... 375
8.2.1 Exercises........................................... 388
8.2.2 Answers............................................. 389
8.3 Quadratic Approximation. Maxima and Minima of
Functions of Several Variables.............................. 389
8.3.1 Exercises........................................... 405
8.3.2 Answers............................................. 406
8.4 Bellman’s Principle of Dynamic Optimisation;
Application to a Maximum Problem............................ 407
8.4.1 Exercises........................................... 413
8.4.2 Answers............................................. 414
8.5 Linear Regression; the “Method of Least Squares”.......... 414
8.5.1 Exercises........................................... 420
8.5.2 Answers............................................. 421
8.6 Extrema of an Objective Function Under Equality
Constraints ................................................ 422
8.6.1 Exercises........................................... 431
8.6.2 Answers............................................. 432
8.7 Extrema of an Objective Function Depending on
Parameters. Envelope Theorems. LeChatelier Principle........ 435
8.7.1 Exercises........................................... 447
8.7.2 Answers............................................. 448
XII
Contents
8.8 Extrema of an Objective Function Under Inequality
Constraints................................................. 449
8.8.1 Exercises........................................... 463
8.8.2 Answers............................................. 464
8.9 The Kuhn-Tucker Conditions................................... 465
8.9.1 Exercises........................................... 468
8.9.2 Answers............................................. 468
8.10 Optimisation with Several Objective Functions................ 470
8.10.1 Exercises........................................... 473
8.10.2 Answers............................................. 474
9 Set Valued Functions: Equilibria—Games.............................. 477
9.1 Introduction................................................. 477
9.2 Set Valued Functions (Correspondences): Shephard’s Axioms... 479
9.2.1 Exercises........................................... 483
9.2.2 Answers............................................. 484
9.3 Competitive Equilibria: Kakutani’s Fixed Point Theorem...... 485
9.3.1 Exercises........................................... 492
9.3.2 Answers............................................. 493
9.4 Applications in the Theory of Games: Nash Equilibrium........ 493
9.4.1 Exercises........................................... 505
9.4.2 Answers............................................. 506
10 Integrals .......................................................... 509
10.1 Introduction: Definite Integral.............................. 509
10.2 Properties of Definite Integrals............................. 512
10.2.1 Exercises........................................... 513
10.2.2 Answers............................................. 513
10.3 Indefinite Integrals (Antiderivatives)....................... 513
10.3.1 Exercises........................................... 517
10.3.2 Answers............................................. 518
10.4 Methods to Calculate Integrals............................. 518
10.4.1 Exercises........................................... 522
10.4.2 Answers............................................. 523
10.5 An Application: Calculating Present Values................... 524
10.5.1 Exercises........................................... 528
10.5.2 Answers........................................... 529
10.6 Improper Integrals (Integrals on Infinite Intervals or
on Intervals Containing Points Where the Function
Tends to Infinity).......................................... 530
10.6.1 Exercises........................................... 533
10.6.2 Answers............................................. 533
11 Differential Equations.............................................. 535
11.1 Introduction................................................. 535
11.1.1 Exercises........................................... 539
11.1.2 Answers............................................. 539
Contents
xiii
11.2 Basics........................................................ 539
11.2.1 Exercises............................................ 541
11.2.2 Answers.............................................. 542
11.3 Linear Differential Equations of First Order.................. 542
11.3.1 Exercises............................................ 549
11.3.2 Answers.............................................. 549
11.4 An Application: Saturation of Markets: “Logistic Growth”.... 549
11.5 Linear Second Order Differential Equations
with Constant Coefficients .................................. 552
11.5.1 Exercises............................................ 559
11.5.2 Answers.............................................. 559
11.6 The Predator-Prey Model....................................... 559
11.6.1 Exercise............................................. 562
11.6.2 Answer............................................... 563
12 Difference Equations............................................... 565
12.1 Introduction.................................................. 565
12.1.1 Exercises............................................ 570
12.1.2 Answers.............................................. 571
12.2 Linear Difference Equations................................... 571
12.2.1 Exercises............................................ 581
12.2.2 Answers.............................................. 582
12.3 Some Applications of Linear Difference Equations.............. 582
12.3.1 The Growth Model of Roy Forbes Harrod
(1900-1978).......................................... 582
12.3.2 Settlement of Bond Issues ........................... 583
12.3.3 Distribution of Wealth .............................. 585
12.3.4 The Multi-sector Multiplier Model.................... 586
12.4 Systems of Linear Difference Equations........................ 586
12.5 Nonlinear Difference Equations, Chaos ........................ 592
12.5.1 Exercises............................................ 596
12.5.2 Answers.............................................. 596
13 Methodology: Models and Theories in Economics...................... 597
13.1 Introduction................................................ 597
13.2 Models in Engineering, Natural Sciences and Mathematics..... 598
13.3 Models in Economics......................................... 600
13.4 Systems of Assumptions........................................ 607
13.5 Theories in the Sciences, in Particular in Economics.......... 609
13.6 Why Construct Models and Theories? Types of
Models and Theories.......................................... 616
13.7 Control, Correction and Applicability of Models
and Theories................................................. 619
13.8 Concluding Remarks............................................ 622
xiv Contents
13.9 Exercises ................................................. 622
13.10 Answers.................................................... 623
Index.................................................................. 627
|
| any_adam_object | 1 |
| author | Eichhorn, Wolfgang 1933- Gleißner, Winfried 1948- |
| author_GND | (DE-588)119133288 (DE-588)142823457 |
| author_facet | Eichhorn, Wolfgang 1933- Gleißner, Winfried 1948- |
| author_role | aut aut |
| author_sort | Eichhorn, Wolfgang 1933- |
| author_variant | w e we w g wg |
| building | Verbundindex |
| bvnumber | BV043463830 |
| classification_rvk | QH 110 |
| ctrlnum | (OCoLC)945013721 (DE-599)BVBBV043463830 |
| dewey-full | 330.1 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330.1 |
| dewey-search | 330.1 |
| dewey-sort | 3330.1 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV043463830 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:26:28Z |
| institution | BVB |
| isbn | 9783319233529 |
| issn | 2192-4333 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028880997 |
| oclc_num | 945013721 |
| open_access_boolean | |
| owner | DE-1050 DE-19 DE-BY-UBM DE-703 DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-1050 DE-19 DE-BY-UBM DE-703 DE-355 DE-BY-UBR DE-11 |
| physical | xix, 630 Seiten Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in business and economics |
| spelling | Eichhorn, Wolfgang 1933- Verfasser (DE-588)119133288 aut Mathematics and methodology for economics applications, problems and solutions Wolfgang Eichhorn, Winfried Gleißner Cham ; Heidelberg ; New York ; Dordrecht ; London Springer [2016] © 2016 xix, 630 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer texts in business and economics 2192-4333 Game theory Economic history Economic theory Economics Economic Theory/Quantitative Economics/Mathematical Methods Methodology/History of Economic Thought Game Theory, Economics, Social and Behav. Sciences Wirtschaft Wirtschaft. Geschichte Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Mittelstufe (DE-588)4130953-4 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematikunterricht (DE-588)4037949-8 s Mittelstufe (DE-588)4130953-4 s Bildverarbeitung (DE-588)4006684-8 s Algorithmus (DE-588)4001183-5 s DE-604 Gleißner, Winfried 1948- Verfasser (DE-588)142823457 aut Erscheint auch als Online-Ausgabe 978-3-319-23353-6 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028880997&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eichhorn, Wolfgang 1933- Gleißner, Winfried 1948- Mathematics and methodology for economics applications, problems and solutions Game theory Economic history Economic theory Economics Economic Theory/Quantitative Economics/Mathematical Methods Methodology/History of Economic Thought Game Theory, Economics, Social and Behav. Sciences Wirtschaft Wirtschaft. Geschichte Mathematikunterricht (DE-588)4037949-8 gnd Bildverarbeitung (DE-588)4006684-8 gnd Mittelstufe (DE-588)4130953-4 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4037949-8 (DE-588)4006684-8 (DE-588)4130953-4 (DE-588)4001183-5 (DE-588)4123623-3 |
| title | Mathematics and methodology for economics applications, problems and solutions |
| title_auth | Mathematics and methodology for economics applications, problems and solutions |
| title_exact_search | Mathematics and methodology for economics applications, problems and solutions |
| title_full | Mathematics and methodology for economics applications, problems and solutions Wolfgang Eichhorn, Winfried Gleißner |
| title_fullStr | Mathematics and methodology for economics applications, problems and solutions Wolfgang Eichhorn, Winfried Gleißner |
| title_full_unstemmed | Mathematics and methodology for economics applications, problems and solutions Wolfgang Eichhorn, Winfried Gleißner |
| title_short | Mathematics and methodology for economics |
| title_sort | mathematics and methodology for economics applications problems and solutions |
| title_sub | applications, problems and solutions |
| topic | Game theory Economic history Economic theory Economics Economic Theory/Quantitative Economics/Mathematical Methods Methodology/History of Economic Thought Game Theory, Economics, Social and Behav. Sciences Wirtschaft Wirtschaft. Geschichte Mathematikunterricht (DE-588)4037949-8 gnd Bildverarbeitung (DE-588)4006684-8 gnd Mittelstufe (DE-588)4130953-4 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Game theory Economic history Economic theory Economics Economic Theory/Quantitative Economics/Mathematical Methods Methodology/History of Economic Thought Game Theory, Economics, Social and Behav. Sciences Wirtschaft Wirtschaft. Geschichte Mathematikunterricht Bildverarbeitung Mittelstufe Algorithmus Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028880997&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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