Dynamic models of the firm: determining optimal investment, financing and production policies by computer
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin u.a.
Springer
1996
|
| Series: | Lecture notes in economics and mathematical systems
434 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 193 S. graph. Darst. |
| ISBN: | 3540608028 |
Staff View
MARC
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| 100 | 1 | |a Blok, Mark W. J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dynamic models of the firm |b determining optimal investment, financing and production policies by computer |c Mark W. J. Blok |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
2 Mathematical Background to Dynamic Optimization 5
2.1 Introduction 5
2.2 Analytical approach to the optimization problem 5
2.2.1 Problem formulation 5
2.2.2 Solving through path coupling 9
2.3 Numerical approach to the optimization problem 10
2.3.1 Discretization 11
2.3.2 Method 1 12
2.3.3 Method 2 14
2.4 Economic interpretation of the adjoint variables 15
2.5 General procedure 16
3 The Basic Model 17
3.1 Introduction 17
3.2 The model and its assumptions 17
3.3 Examination of the paths 20
3.3.1 Introducing the adjoint variables 20
3.3.2 Determining the feasible paths 21
3.3.3 Economic interpretation of paths 4, 8 and 10 22
3.4 Case study 23
3.4.1 The case of i (1 f)r 24
3.4.2 The case of i (1 f)r 29
3.5 Conclusions 32
4 A Model with Start up Costs 33
4.1 Introduction 33
4.2 The model and its assumptions 34
4.3 Examination of the paths 36
4.3.1 Introduction of the adjoint variables 36
4.3.2 Further examination of the stationary paths 38
4.4 Case study 43
CONTENTS
4.4.1 The case of i (1 f)r 43
4.4.2 The case of i (1 f)r 47
4.5 Conclusions 49
5 Models with a Business Cycle 51
5.1 Introduction 51
5.2 The basic model 51
5.2.1 Description of the model 51
5.2.2 Severe recession in the case of i (1 — f)r and m m* 54
5.2.3 Severe recession in the case of i (1 f)r and m m* 59
5.2.4 Severe recession in the case of i (1 f)r and m m° 62
5.2.5 Severe recession in the case of i (1 /)r and m m° 67
5.3 A model with a variable utilization rate 71
5.3.1 Description of the model 71
5.3.2 Moderate recession in the case of i (1 f)r 74
5.3.3 Moderate recession in the case of i (1 f)r 76
5.3.4 Severe recession in the case of i (1 — f)r 79
5.4 A model with a cash balance 84
5.4.1 Description of the model 84
5.4.2 Severe recession in the case of i (1 f)r and m m* 87
5.4.3 Severe recession in the case of i (1 f)r and m m* 92
5.4.4 Severe recession in the case of i (1 f)r and m m° 96
5.4.5 Severe recession in the case of i (1 f)r and m m° 96
5.5 A model with an inventory of finished goods 102
5.5.1 Description of the model 102
5.5.2 Severe recession in the case of i (1 f)r and m m* 106
5.5.3 Severe recession in the case of i (1 f)r and m m° 111
5.6 Conclusions 116
6 A Model with Increasing Returns to Scale, an Experience
Curve and a Production Life Cycle 119
6.1 Introduction 119
6.2 Description of the model 119
6.2.1 The production function 119
6.2.2 The price function 120
6.2.3 Problem formulation 124
6.3 Case study 126
6.4 Conclusions 131
Appendices ^33
A Mathematical Details for Chapter 3 135
A.I Problem formulation 135
CONTENTS vii
A.2 Necessary conditions for optimality 135
A.3 Elaborating the transversality conditions 137
A.4 Further examination of some paths 137
B Mathematical Details for Chapter 4 139
B.I Problem formulation 139
B.2 Necessary conditions for optimality 140
B.3 Elaborating the transversality conditions 141
B.4 Further examination of some paths 142
C Mathematical Details for Chapter 5 149
C.I The basic model 149
C.I.I Determining the coupling points for Subsection 5.2.2 . . 149
C.1.2 Determining the coupling points for Subsection 5.2.3 . . 150
C.1.3 Deriving relationships (5.22) and (5.27) 152
C.1.4 Determining the coupling points for Subsection 5.2.4 . . 153
C.I.5 Determining the coupling points for Subsection 5.2.5 . . 154
C.1.6 Deriving relationships (5.45) and (5.49) 156
C.2 A model with a variable utilization rate 157
C.2.1 Necessary conditions for optimality 157
C.2.2 Further examination of some paths 160
C.2.3 Determining the coupling points for Subsection 5.3.2 . . 162
C.2.4 Determining the coupling points for Subsection 5.3.3 . . 163
C.2.5 Determining the coupling points for Subsection 5.3.4 . . 163
C.3 A model with a cash balance 165
C.3.1 Necessary conditions for optimality 165
C.3.2 Further examination of some paths 167
C.3.3 Determining the coupling points for Subsection 5.4.2 . . 168
C.3.4 Determining the coupling points for Subsection 5.4.3 . . 169
C.3.5 Determining the coupling points for Subsection 5.4.5 . . 170
C.4 A model with an inventory of finished goods 171
C.4.1 Necessary conditions for optimality 171
C.4.2 Further examination of some paths 174
C.4.3 Determining the coupling points for Subsection 5.5.2 . . 177
C.4.4 Determining the coupling points for Subsection 5.5.3 . . 179
D Mathematical Details for Chapter 6 181
D.I Necessary conditions for optimality 181
Symbols and Notation 183
Bibliography 187
Summary 191
|
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| isbn | 3540608028 |
| language | German |
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| series2 | Lecture notes in economics and mathematical systems |
| spelling | Blok, Mark W. J. Verfasser aut Dynamic models of the firm determining optimal investment, financing and production policies by computer Mark W. J. Blok Berlin u.a. Springer 1996 VII, 193 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 434 Mathematisches Modell Industrial organization -- Mathematical models Mathematical optimization Dynamische Optimierung (DE-588)4125677-3 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Unternehmensmodell (DE-588)4201186-3 gnd rswk-swf Unternehmensmodell (DE-588)4201186-3 s Dynamische Optimierung (DE-588)4125677-3 s Optimale Kontrolle (DE-588)4121428-6 s DE-604 Optimierung (DE-588)4043664-0 s Lecture notes in economics and mathematical systems 434 (DE-604)BV000000036 434 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007080330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blok, Mark W. J. Dynamic models of the firm determining optimal investment, financing and production policies by computer Lecture notes in economics and mathematical systems Mathematisches Modell Industrial organization -- Mathematical models Mathematical optimization Dynamische Optimierung (DE-588)4125677-3 gnd Optimierung (DE-588)4043664-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Unternehmensmodell (DE-588)4201186-3 gnd |
| subject_GND | (DE-588)4125677-3 (DE-588)4043664-0 (DE-588)4121428-6 (DE-588)4201186-3 |
| title | Dynamic models of the firm determining optimal investment, financing and production policies by computer |
| title_auth | Dynamic models of the firm determining optimal investment, financing and production policies by computer |
| title_exact_search | Dynamic models of the firm determining optimal investment, financing and production policies by computer |
| title_full | Dynamic models of the firm determining optimal investment, financing and production policies by computer Mark W. J. Blok |
| title_fullStr | Dynamic models of the firm determining optimal investment, financing and production policies by computer Mark W. J. Blok |
| title_full_unstemmed | Dynamic models of the firm determining optimal investment, financing and production policies by computer Mark W. J. Blok |
| title_short | Dynamic models of the firm |
| title_sort | dynamic models of the firm determining optimal investment financing and production policies by computer |
| title_sub | determining optimal investment, financing and production policies by computer |
| topic | Mathematisches Modell Industrial organization -- Mathematical models Mathematical optimization Dynamische Optimierung (DE-588)4125677-3 gnd Optimierung (DE-588)4043664-0 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Unternehmensmodell (DE-588)4201186-3 gnd |
| topic_facet | Mathematisches Modell Industrial organization -- Mathematical models Mathematical optimization Dynamische Optimierung Optimierung Optimale Kontrolle Unternehmensmodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007080330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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