Mathematical Demoeconomy : Integrating Demographic and Economic Approaches

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. Preface Part I General principles of demoeconomics 1 The population-economy system 1.1 General characteristics of the population-economy system 1.2 Mathematical modeling of the PE system: specific features 1.2.1 Principles of mathematical modeling 1.2.2 Nonlinear processes 1.2.3 Temporal hierarchy 1.2.4 Spatial hierarchy 1.3 Forecasting of demoeconomic development 2 Probabilistic techniques in demoeconomic forecasting 2.1 Uncertainty in the PE system 2.2 Demoeconomic forecasting: the structure of probabilistic technique Part II Foundations of spatial demography 3 The population system 3.1 Key notions 3.2 State indicators of population 3.3 States evolution in a demographic process: general modeling principles 3.3.1 Structuring based on sex and space 3.3.2 Structuring based on sex, age and space 4 Demographic characteristics of fertility 4.1 Phenomenology of newborns distribution by maternal ages 4.2 Entropy model of age-specific fertility rate 4.3 Iterative method of age-specific fertility rate recovery 4.4 Dynamics of fertility rates 4.4.1 Dynamic model of total fertility rate 4.4.2 Dynamic model of age-specific fertility rate 5 Demographic characteristics of mortality 5.1 Phenomenology of mortality 5.2 Entropy model of sex-age distribution of mortality rate 5.2.1 Model construction 5.2.2 Model analysis 5.3 Parameter identification for the entropy model of mortality based on real data 5.4 Entropy decomposition of age-specific distribution of mortality by classes of diseases 5.5 Dynamic model of total mortality rate 6 Demographic characteristics of migration 6.1 General phenomenology of migration 6.2 Entropy-optimal distribution of migration flows 6.3 Optimality conditions for entropy models of migration 6.4 Parametric properties in entropy models of migration 6.4.1 Parametric properties of the B-model with complete consumption of resources 6.4.2 An example of analyzing the parametric properties of the B-model of migration flows 6.4.3 Parametric properties of the F-model with complete consumption of resources 7 Macrosystem models of population dynamics 7.1 Dynamics of isolated population 7.1.1 Deterministic functions of fertility and mortality 7.1.2 Random functions of fertility and mortality 7.2 Macrosystem dynamic model with linear reproduction of population and balanced emigration 7.2.1 Stationary states 7.2.2 Stability of stationary states 7.3 Stable stationary states of spatial distribution of population: an example of scenario forecasting 7.4 General macrosystem model of population size dynamics 7.4.1 Stationary states 7.4.2 Stability of stationary states Part III Foundations of spatial economics 8 Modeling economics 8.1 Political economy, micro- and macroeconomics, mathematical economics: objects and goals 8.2 Behavioral models for economic agents 8.2.1 Models of rational behavior 8.2.2 Models of compromise behavior 8.2.3 Models of stochastic behavior 9 Evolutionary economics 9.1 General principles of evolutionary economics 9.2 Market equilibriumand stability 9.3 Innovation activity of economic agents 9.3.1 External investments 9.3.2 Internal investments 9.4 Economic growth 10 Self-organization in economic systems 10.1 General notions 10.2 Phenomenology of the model of competitive firms. Determination of transitions 10.3 Construction of utility functions. Evaluation of transition rates 10.4 Equations of the model. Stationary states 10.5 Stability of stationary states 11 Spatial interaction of economic systems 11.1 Entropy model of spatial economic interaction 11.2 Economic system with triangular spatial structure 12 Selected models of spatial macroeconomics 12.1 Entropy decomposition 12.2 Spatial interaction of economic clusters 12.2.1 Static interaction 12.2.2 Dynamic interaction 12.3 Model of economic systems exchanging investments 12.3.1 Singular stationary states 12.3.2 Stability of singular stationary states 13 Fluctuations in models of spatial economics 13.1 Downturns and upturns in economic activity 13.2 The immersion method for periodic solutions 13.3 Periodic solutions to generating system: application of the Laplace transform Part IV Macrosystem models of demoeconomics 14 Macrosystems concept in demoeconomics 14.1 Phenomenology of demoeconomics 14.1.1 The systems character of demoeconomic processes 14.1.2 The individual and the collective 14.1.3 Time scales 14.2 Macrosystems concept of demoeconomics: model representation 14.3 The Monte Carlo method in probabilisticmacrosystem modeling of demoeconomic processes 15 One-sector macrosystem demoeconomic model (MSDEM ) 15.1 Structure and basic variables of the model 15.2 Equations of one-sector MSDEM 15.2.1 The block 1sEM 15.2.2 The block MSDM 15.3 An example of one-sector MSDEM 15.3.1 Equations of the model 15.3.2 Analytic treatment of the simplified one-sector MSDEM 15.3.3 Computer experiments with the one-sector MSDEM 15.3.4 Analytic treatment and computer experiments with the one-sector PMSDEM 16 Macrosystem demoeconomic model with regional localization of sectors (branches) Ns-MSDEM 16.1 Structure and basic variables of the model 16.2 Equations of Ns - MSDEM with resource exchange on regional markets 16.2.1 The block NsEM 16.2.2 The block MSDM 16.2.3 The block TRM 16.3 An example of analytic treatment of Ns - MSDEM 16.3.1 Equations of the model 16.3.2 Stationary states 16.4 Computer analysis of Ns - MSDEM 16.4.1 Equations of the model 17 Macrosystem model of labour market 17.1 Quantitative state indicators of labour market 17.2 Structure and equations of the model 17.3 Competition among cohorts 17.3.1 Intrinsic competitive ability 17.3.2 The comparative competitive ability 17.3.3 Labour force requirement and supply of labour force 17.4 Identification algorithm for model parameters 17.5 Identification of model parameters based on real data 18 Probabilistic macrosystem demoeconomic model 18.1 Aggregated structure of PMSDEM and its spatiotemporal characteristics 18.2 Realization of PMSDEM: the Monte Carlo methods 18.2.1 Average computing 18.2.2 Random search 18.2.3 Generation of random variables with given properties 18.3 The POPULATION block 18.3.1 Classification of population 18.3.2 Biological reproduction of population (the R module) 18.3.3 Migration (theMmodule) 18.3.4 Dynamics of population (the DP module) 18.3.5 Outputs of the POPULATION block 18.4 The economy block 18.4.1 Production economy (the PE module) 18.4.2 Exchange of products (the Ex module) 18.4.3 Prices (the Pr module) 18.4.4 The output variable of the ECONOMY block 18.5 The interaction block 18.5.1 Migration (the MPP module) 18.5.2 Fertility (the TFR module and the AFRR module) 18.5.3 Mortality (the TMR module and the ASMR module) Part V Mathematical appendices A Some theorems of implicit functions A.1 Introduction A.2 Local properties A.2.1 Existence and continuity A.2.2 Homogeneous forms and posinomials A.2.3 Differentiability A.3 Global properties A.3.1 Existence A.3.2 Differentiability B Estimating the local Lipschitz Constant of the entropy operator Bv,q B.1 Introduction B.2 Definitions B.2.1 The operator Bv,q B.2.2 The normal operator B0v,q B.2.3 The relation between Bv,q and B0v,q B.3 Properties of the entropy operator B0v,q B.3.1 Existence and uniqueness B.3.2 Majorant construction B.4 Estimating the norm of derivative of the entropy operator B0v,q B.5 Estimating the spectral norm of the matrix [I0?]-1 C Estimating the local Lipschitz Constant of the entropy operator Fv,q C.1 Definitions C.2 Properties of the normal entropy operator F0v,q C.3 Majorants of the operator F0v,q C.4 Estimate lF D Zero-order multiplicative algorithms for positive solutions to nonlinear equations D.1 Introduction D.2 Auxiliary estimates D.3 Convergence analysis by continuous analogs of iterative algorithms D.4 Convergence of zero-order multiplicative algorithms withm-active variables: nonlinear equations D.5 Convergence of zero-order multiplicative algorithms withm-active variables: convex programming E Multiplicative algorithms for positive solutions to entropy-quadratic programming problems E.1 Problem statement E.2 Optimality conditions E.3 Multiplicative algorithm Bibliography Index