Popkov Mathematical Demoeconomy

Integrating Demographic and Economic Approaches
1. Auflage 2014
ISBN: 978-3-11-033916-1
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 514 Seiten

This monograph aspires to lay the foundations of a new scientific discipline, demoeconomics, representing the synthesis of demography and spatial economics. This synthesis is performed in terms of interaction between population and its economic activity. The monograph appears a unique research work having no analogs in scientific literature. Demoeconomic systems are studied involving the macrosystems approach which combines the generalized entropy maximization principle and the local equilibria principle. Demoeconomic systems operate in an uncertain environment; thus and so, the monograph develops the methodology and technique of probabilistic modeling and forecasting of their evolution.

Zielgruppe

Scientific researches in demographic and economic fields, Academi

Autoren/Hrsg.

Popkov, Yuri S.

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftstheorie, Wirtschaftsphilosophie
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftsstatistik, Demographie
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie

Inhaltsverzeichnis

1;Preface;5
2;Part I General principles of demoeconomics;15
2.1;1 The population-economy system;17
2.1.1;1.1 General characteristics of the population-economy system;17
2.1.2;1.2 Mathematical modeling of the PE system: specific features;21
2.1.2.1;1.2.1 Principles of mathematical modeling;22
2.1.2.2;1.2.2 Nonlinear processes;23
2.1.2.3;1.2.3 Temporal hierarchy;23
2.1.2.4;1.2.4 Spatial hierarchy;24
2.1.3;1.3 Forecasting of demoeconomic development;25
2.2;2 Probabilistic techniques in demoeconomic forecasting;30
2.2.1;2.1 Uncertainty in the PE system;30
2.2.2;2.2 Demoeconomic forecasting: the structure of probabilistic technique;33
3;Part II Foundations of spatial demography;37
3.1;3 The population system;39
3.1.1;3.1 Key notions;39
3.1.2;3.2 State indicators of population;43
3.1.3;3.3 States evolution in a demographic process: general modeling principles;46
3.1.3.1;3.3.1 Structuring based on sex and space;47
3.1.3.2;3.3.2 Structuring based on sex, age and space;48
3.2;4 Demographic characteristics of fertility;50
3.2.1;4.1 Phenomenology of newborns distribution by maternal ages;50
3.2.2;4.2 Entropy model of age-specific fertility rate;53
3.2.3;4.3 Iterative method of age-specific fertility rate recovery;58
3.2.4;4.4 Dynamics of fertility rates;63
3.2.4.1;4.4.1 Dynamic model of total fertility rate;63
3.2.4.2;4.4.2 Dynamic model of age-specific fertility rate;71
3.3;5 Demographic characteristics of mortality;74
3.3.1;5.1 Phenomenology of mortality;74
3.3.2;5.2 Entropy model of sex-age distribution of mortality rate;76
3.3.2.1;5.2.1 Model construction;76
3.3.2.2;5.2.2 Model analysis;79
3.3.3;5.3 Parameter identification for the entropy model of mortality based on real data;81
3.3.4;5.4 Entropy decomposition of age-specific distribution of mortality by classes of diseases;90
3.3.5;5.5 Dynamic model of total mortality rate;96
3.4;6 Demographic characteristics of migration;101
3.4.1;6.1 General phenomenology of migration;102
3.4.2;6.2 Entropy-optimal distribution of migration flows;106
3.4.3;6.3 Optimality conditions for entropy models of migration;118
3.4.4;6.4 Parametric properties in entropy models of migration;122
3.4.4.1;6.4.1 Parametric properties of the B-model with complete consumption of resources;126
3.4.4.2;6.4.2 An example of analyzing the parametric properties of the B-model of migration flows;130
3.4.4.3;6.4.3 Parametric properties of the F-model with complete consumption of resources;140
3.5;7 Macrosystem models of population dynamics;146
3.5.1;7.1 Dynamics of isolated population;146
3.5.1.1;7.1.1 Deterministic functions of fertility and mortality;146
3.5.1.2;7.1.2 Random functions of fertility and mortality;153
3.5.2;7.2 Macrosystem dynamic model with linear reproduction of population and balanced emigration;156
3.5.2.1;7.2.1 Stationary states;158
3.5.2.2;7.2.2 Stability of stationary states;161
3.5.3;7.3 Stable stationary states of spatial distribution of population: an example of scenario forecasting;167
3.5.4;7.4 General macrosystem model of population size dynamics;171
3.5.4.1;7.4.1 Stationary states;175
3.5.4.2;7.4.2 Stability of stationary states;176
4;Part III Foundations of spatial economics;181
4.1;8 Modeling economics;183
4.1.1;8.1 Political economy, micro- and macroeconomics, mathematical economics: objects and goals;184
4.1.2;8.2 Behavioral models for economic agents;190
4.1.2.1;8.2.1 Models of rational behavior;191
4.1.2.2;8.2.2 Models of compromise behavior;194
4.1.2.3;8.2.3 Models of stochastic behavior;201
4.2;9 Evolutionary economics;205
4.2.1;9.1 General principles of evolutionary economics;205
4.2.2;9.2 Market equilibriumand stability;206
4.2.3;9.3 Innovation activity of economic agents;210
4.2.3.1;9.3.1 External investments;213
4.2.3.2;9.3.2 Internal investments;216
4.2.4;9.4 Economic growth;220
4.3;10 Self-organization in economic systems;225
4.3.1;10.1 General notions;225
4.3.2;10.2 Phenomenology of the model of competitive firms. Determination of transitions;227
4.3.3;10.3 Construction of utility functions. Evaluation of transition rates;231
4.3.4;10.4 Equations of the model. Stationary states;234
4.3.5;10.5 Stability of stationary states;240
4.4;11 Spatial interaction of economic systems;246
4.4.1;11.1 Entropy model of spatial economic interaction;246
4.4.2;11.2 Economic system with triangular spatial structure;257
4.5;12 Selected models of spatial macroeconomics;262
4.5.1;12.1 Entropy decomposition;262
4.5.2;12.2 Spatial interaction of economic clusters;270
4.5.2.1;12.2.1 Static interaction;272
4.5.2.2;12.2.2 Dynamic interaction;275
4.5.3;12.3 Model of economic systems exchanging investments;278
4.5.3.1;12.3.1 Singular stationary states;281
4.5.3.2;12.3.2 Stability of singular stationary states;283
4.6;13 Fluctuations in models of spatial economics;295
4.6.1;13.1 Downturns and upturns in economic activity;295
4.6.2;13.2 The immersion method for periodic solutions;296
4.6.3;13.3 Periodic solutions to generating system: application of the Laplace transform;300
5;Part IV Macrosystem models of demoeconomics;311
5.1;14 Macrosystems concept in demoeconomics;313
5.1.1;14.1 Phenomenology of demoeconomics;313
5.1.1.1;14.1.1 The systems character of demoeconomic processes;314
5.1.1.2;14.1.2 The individual and the collective;315
5.1.1.3;14.1.3 Time scales;315
5.1.2;14.2 Macrosystems concept of demoeconomics: model representation;317
5.1.3;14.3 The Monte Carlo method in probabilisticmacrosystem modeling of demoeconomic processes;319
5.2;15 One-sector macrosystem demoeconomic model (MSDEM );324
5.2.1;15.1 Structure and basic variables of the model;324
5.2.2;15.2 Equations of one-sector MSDEM;327
5.2.2.1;15.2.1 The block 1sEM;327
5.2.2.2;15.2.2 The block MSDM;330
5.2.3;15.3 An example of one-sector MSDEM;334
5.2.3.1;15.3.1 Equations of the model;335
5.2.3.2;15.3.2 Analytic treatment of the simplified one-sector MSDEM;338
5.2.3.3;15.3.3 Computer experiments with the one-sector MSDEM;341
5.2.3.4;15.3.4 Analytic treatment and computer experiments with the one-sector PMSDEM;347
5.3;16 Macrosystem demoeconomic model with regional localization of sectors (branches) Ns-MSDEM;353
5.3.1;16.1 Structure and basic variables of the model;353
5.3.2;16.2 Equations of Ns - MSDEM with resource exchange on regional markets;358
5.3.2.1;16.2.1 The block NsEM;358
5.3.2.2;16.2.2 The block MSDM;363
5.3.2.3;16.2.3 The block TRM;365
5.3.3;16.3 An example of analytic treatment of Ns - MSDEM;366
5.3.3.1;16.3.1 Equations of the model;366
5.3.3.2;16.3.2 Stationary states;368
5.3.4;16.4 Computer analysis of Ns - MSDEM;372
5.3.4.1;16.4.1 Equations of the model;372
5.4;17 Macrosystem model of labour market;385
5.4.1;17.1 Quantitative state indicators of labour market;385
5.4.2;17.2 Structure and equations of the model;387
5.4.3;17.3 Competition among cohorts;389
5.4.3.1;17.3.1 Intrinsic competitive ability;390
5.4.3.2;17.3.2 The comparative competitive ability;393
5.4.3.3;17.3.3 Labour force requirement and supply of labour force;394
5.4.4;17.4 Identification algorithm for model parameters;395
5.4.5;17.5 Identification of model parameters based on real data;397
5.5;18 Probabilistic macrosystem demoeconomic model;406
5.5.1;18.1 Aggregated structure of PMSDEM and its spatiotemporal characteristics;406
5.5.2;18.2 Realization of PMSDEM: the Monte Carlo methods;411
5.5.2.1;18.2.1 Average computing;411
5.5.2.2;18.2.2 Random search;412
5.5.2.3;18.2.3 Generation of random variables with given properties;413
5.5.3;18.3 The POPULATION block;414
5.5.3.1;18.3.1 Classification of population;414
5.5.3.2;18.3.2 Biological reproduction of population (the R module);416
5.5.3.3;18.3.3 Migration (theMmodule);419
5.5.3.4;18.3.4 Dynamics of population (the DP module);425
5.5.3.5;18.3.5 Outputs of the POPULATION block;425
5.5.4;18.4 The economy block;426
5.5.4.1;18.4.1 Production economy (the PE module);426
5.5.4.2;18.4.2 Exchange of products (the Ex module);430
5.5.4.3;18.4.3 Prices (the Pr module);432
5.5.4.4;18.4.4 The output variable of the ECONOMY block;434
5.5.5;18.5 The interaction block;435
5.5.5.1;18.5.1 Migration (the MPP module);435
5.5.5.2;18.5.2 Fertility (the TFR module and the AFRR module);439
5.5.5.3;18.5.3 Mortality (the TMR module and the ASMR module);445
6;Part V Mathematical appendices;453
6.1;A Some theorems of implicit functions;455
6.1.1;A.1 Introduction;455
6.1.2;A.2 Local properties;455
6.1.2.1;A.2.1 Existence and continuity;455
6.1.2.2;A.2.2 Homogeneous forms and posinomials;457
6.1.2.3;A.2.3 Differentiability;461
6.1.3;A.3 Global properties;464
6.1.3.1;A.3.1 Existence;464
6.1.3.2;A.3.2 Differentiability;467
6.2;B Estimating the local Lipschitz Constant of the entropy operator Bv,q;468
6.2.1;B.1 Introduction;468
6.2.2;B.2 Definitions;468
6.2.2.1;B.2.1 The operator Bv,q;468
6.2.2.2;B.2.2 The normal operator B0v,q;469
6.2.2.3;B.2.3 The relation between Bv,q and B0v,q;469
6.2.3;B.3 Properties of the entropy operator B0v,q;471
6.2.3.1;B.3.1 Existence and uniqueness;471
6.2.3.2;B.3.2 Majorant construction;473
6.2.4;B.4 Estimating the norm of derivative of the entropy operator B0v,q;475
6.2.5;B.5 Estimating the spectral norm of the matrix [I0?]-1;478
6.3;C Estimating the local Lipschitz Constant of the entropy operator Fv,q;481
6.3.1;C.1 Definitions;481
6.3.2;C.2 Properties of the normal entropy operator F0v,q;482
6.3.3;C.3 Majorants of the operator F0v,q;484
6.3.4;C.4 Estimate lF;487
6.4;D Zero-order multiplicative algorithms for positive solutions to nonlinear equations;489
6.4.1;D.1 Introduction;489
6.4.2;D.2 Auxiliary estimates;490
6.4.3;D.3 Convergence analysis by continuous analogs of iterative algorithms;493
6.4.4;D.4 Convergence of zero-order multiplicative algorithms withm-active variables: nonlinear equations;494
6.4.5;D.5 Convergence of zero-order multiplicative algorithms withm-active variables: convex programming;496
6.5;E Multiplicative algorithms for positive solutions to entropy-quadratic programming problems;503
6.5.1;E.1 Problem statement;503
6.5.2;E.2 Optimality conditions;504
6.5.3;E.3 Multiplicative algorithm;506
7;Bibliography;507
8;Index;512

Über Autor(innen)

Yuri S. Popkov, Institute for Systems Analysis of the Russian academy of sciences, Moscow, Russia.