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Table of Contents
                            Macroeconomic Analysis and Parametric Control of a National Economy
	Contents
	Chapter 1: Elements of Parametric Control Theory of Market Economic Development
		1.1 Components of Parametric Control Theory of Market Economic Development
		1.2 Methods of Analysis of the Stability and Structural Stability of Mathematical Models of National Economic Systems
			1.2.1 Development of the Methods for Evaluating Stability Indicators of Mathematical Models
			1.2.2 Development of Methods for Evaluating Weak Structural Stability of a Discrete-Time Dynamical System (Semi-cascade) Based...
		1.3 Approach to Synthesis and Choice (in the Environment of a Given Finite Set of Algorithms) of Optimal Laws of Parametric Co...
			1.3.1 Analysis of the Existence Conditions for a Solution of the Variational Calculus Problem of Synthesis and Choice (in the ...
				1.3.1.1 Statement of the Variational Calculus Problems of Synthesis and Choice of Parametric Control Laws for a Continuous-Tim...
				1.3.1.2 Solvability Conditions for the Variational Calculus Problem of Synthesis of the Optimal Control Law for a Continuous-T...
				1.3.1.3 Solvability Conditions for the Variational Calculus Problem of Choice (in the Environment of a Given Finite Set of Alg...
			1.3.2 Analysis of the Existence Conditions for a Solution of the Variational Calculus Problem of Synthesis and Choice (in the ...
				1.3.2.1 Statement of the Variational Calculus Problems of Synthesis and Choice of Parametric Control Laws for a Discrete-Time ...
				1.3.2.2 Solvability Conditions for the Variational Calculus Problem of Synthesis of the Optimal Control Law for a Discrete-Tim...
				1.3.2.3 Solvability Conditions for the Variational Calculus Problem of Choice (in the Environment of a Given Finite Set of Alg...
			1.3.3 Analysis of the Existence Conditions for a Solution of the Variational Calculus Problem of Synthesis and Choice (in the ...
				1.3.3.1 Statement of the Variational Calculus Problems of Synthesis and Choice of Parametric Control Laws for a Discrete -Time...
				1.3.3.2 Solvability Conditions for the Variational Calculus Problem of Synthesis of the Optimal Control Law for a Discrete-Tim...
				1.3.3.3 Solvability Conditions for the Variational Calculus Problem of Choice (in the Environment of a Given Finite Set of Alg...
			1.3.4 Analysis of the Influence of Uncontrolled Parameter Variations (Parametric Disturbances) on the Solution of the Variatio...
				1.3.4.1 Analysis of Continuous Dependence of Optimal Values of the Criteria of Variational Calculus Problems of Synthesis and ...
				1.3.4.2 Analysis of Bifurcation Points of the Variational Calculus Problems of Choice of Parametric Control Laws in the Enviro...
		1.4 Algorithm of Application of Parametric Control Theory and Rules of Interaction Between Persons Making Decisions on Elabora...
			1.4.1 Algorithm of the Application of Parametric Control Theory
			1.4.2 Rules of Interaction for Decision Makers on the Formulation and Implementation of an Effective Public Economic Policy Ba...
				1.4.2.1 Rules of Interaction Between the DM and IDSS at the Level of the Problem ``Evaluation of the National Economic Conditi...
				1.4.2.2 Rules of Interaction Between the DM and IDSS at the Level of Problem ``Choice of One or Several Econometric Models and...
				1.4.2.3 Rules of Interaction Between the DM and IDSS at the Level of Problem ``Statement and Solution of the Problem(s) of Est...
				1.4.2.4 Rules of Interaction Between the DM and IDSS at the Level of Problem ``Analysis of the Influence of Values of Exogenou...
				1.4.2.5 Rules of Interaction Between the DM and IDSS at the Level of Problem ``Formulation of Recommendations on the Choice of...
		1.5 Examples for Application of Parametric Control Theory
			1.5.1 Mathematical Model of the Neoclassical Theory of Optimal Growth
				1.5.1.1 Model Description
				1.5.1.2 Analysis of the Structural Stability from a Mathematical Model of the Neoclassic Theory of Optimal Growth Without Para...
				1.5.1.3 Choosing Optimal Laws of Parametric Control of Market Economic Development Based on a Mathematical Model of the Neocla...
				1.5.1.4 Analysis of the Structural Stability of the Mathematical Model of the Neoclassical Theory of Optimal Growth with Param...
				1.5.1.5 Finding Bifurcation Points for the Extremals of the Variational Calculus Problem Based on the Mathematical Model of th...
			1.5.2 One-Sector Solow Model of Economic Growth
				1.5.2.1 Model Description
				1.5.2.2 Estimation of the Model Parameters
				1.5.2.3 Analysis of the Structural Stability of the One-Sector Solow Model of Economic Growth Without Parametric Control
				1.5.2.4 Choosing Optimal Laws of Parametric Control of Market Economic Development Based on the Solow Mathematical Model
				1.5.2.5 Analysis of the Structural Stability of the One-Sector Solow Model of Economic Growth with Parametric Control
				1.5.2.6 Analysis of the Dependence of the Optimal Value of Criterion K on the Parameter for the Variational Calculus Problem B...
			1.5.3 Richardson Model for the Estimation of Defense Costs
				1.5.3.1 Model Description
				1.5.3.2 Estimation of Model Parameters
				1.5.3.3 Analysis of the Structural Stability of the Richardson Mathematical Model Without Parametric Control
				1.5.3.4 Choosing Optimal Laws of Parametric Control of Market Economies on the Basis of the Richardson Mathematical Model
				1.5.3.5 Analysis of Structural Stability of the Richardson Mathematical Model with Parametric Control
				1.5.3.6 Analysis of the Dependence of the Optimal Value of Criterion K on the Parameter for the Variational Calculus Problem B...
			1.5.4 Mathematical Model of a National Economic System Subject to the Influence of the Share of Public Expense and the Interes...
				1.5.4.1 Model Description
				1.5.4.2 Analysis of the Structural Stability of the Mathematical Model of the National Economic System Subject to the Influenc...
				1.5.4.3 Choosing the Optimal Laws of Parametric Control of Market Economic Development on the Basis of the Mathematical Model ...
				1.5.4.4 Parametric Control of Market Economic Development with Varying Objectives on the Basis of a Mathematical Model Subject...
				1.5.4.5 Analysis of the Structural Stability of the Mathematical Model of the Country Subject to the Influence of the Share of...
				1.5.4.6 Finding the Bifurcation Points of the Extremals of the Variational Calculus Problem on the Basis of the Mathematical M...
			1.5.5 Mathematical Model of the National Economic System Subject to the Influence of International Trade and Currency Exchange...
				1.5.5.1 Model Description
				1.5.5.2 Analysis of the Structural Stability of the Mathematical Model of the National Economic System Subject to the Influenc...
				1.5.5.3 Choosing Optimal Laws of Parametric Control of Market Economic Development on the Basis of the Mathematical Model of t...
				1.5.5.4 Analysis of the Structural Stability of the Mathematical Model of the Country Subject to the Influence of Internationa...
				1.5.5.5 Finding the Bifurcation Points of the Extremals of the Variational Calculus Problem on the Basis of the Mathematical M...
			1.5.6 Forrester´s Mathematical Model of Global Economy
				1.5.6.1 Model Description
				1.5.6.2 Analysis of the Structural Stability of Forrester´s Mathematical Model Without Parametric Control
				1.5.6.3 Choosing Optimal Laws of Parametric Control on Basis of the Forrester Model
				1.5.6.4 Analysis of the Structural Stability of Forrester´s Mathematical Model Subject to Parametric Control
				1.5.6.5 Finding Bifurcation Points of Extremals of the Variational Calculus Problem on the Basis of Forrester´s Mathematical M...
			1.5.7 Turnovsky´s Monetary Model
				1.5.7.1 Model Description
				1.5.7.2 Estimation of Turnovsky´s Model Parameters and Retrospective Forecast
				1.5.7.3 Analysis of the Structural Stability of Turnovsky´s Monetary Model
				1.5.7.4 Estimation of the Parametric Sensitivity of Turnovsky´s Model
				1.5.7.5 Finding Optimal Values of the Adjusted Parameters Based on Turnovsky´s Model
				1.5.7.6 Analysis of the Dependence of Optimal Values of the Parametric Control Criterion on the Values of the Uncontrolled Par...
			1.5.8 Endogenous Jones´s Model
				1.5.8.1 Model Description
				1.5.8.2 Evaluation of the Exogenous Parameters of the Jones´s Model and Retrospective Forecast
				1.5.8.3 Analysis of the Structural Stability of the Mathematical Jones´s Model
				1.5.8.4 Estimation of the Parametric Sensitivity of Jones´s Model
				1.5.8.5 Finding the Optimal Values of the Adjusted Parameters Based on Jones´s Model
				1.5.8.6 Analysis of the Dependence of the Optimal Values of the Parametric Control Criterion on the Values of Uncontrolled Par...
				1.5.8.7 Appendix. Proof of Statements Given in Chapter 1
	Chapter 2: Methods of Macroeconomic Analysis and Parametric Control of Equilibrium States in a National Economy
		2.1 Macroeconomic Analysis of a National Economic State Based on IS, LM, and IS-LM Models, Keynesian All-Economy Equilibrium. ...
			2.1.1 Construction of the IS Model and Analysis of the Influence of Economic Instruments
			2.1.2 Macroeconomics of Equilibrium Conditions in the Money Market
			2.1.3 Macroestimation of the Mutual Equilibrium State in Wealth and Money Markets. Analysis of the Influence of Economic Instr...
			2.1.4 Macroestimation of the Equilibrium State on the Basis of the Keynesian Model of Common Economic Equilibrium. Analysis of...
			2.1.5 Parametric Control of an Open Economic State Based on the Keynesian Model
		2.2 Macroeconomic Analysis and Parametric Control of the National Economic State Based on the Model of a Small Open Country
			2.2.1 Construction of the Model of an Open Economy of a Small Country and Estimation of Its Equilibrium Conditions
			2.2.2 Influence of Economic Instruments on Equilibrium Solutions and Payment Balance States
			2.2.3 Parametric Control of an Open Economy State Based on a Small Country Model
	Chapter 3: Parametric Control of Cyclic Dynamics of Economic Systems
		3.1 Mathematical Model of the Kondratiev Cycle
			3.1.1 Model Description
			3.1.2 Estimating the Robustness of the Kondratiev Cycle Model Without Parametric Control
			3.1.3 Parametric Control of the Evolution of Economic Systems Based on the Kondratiev Cycle Model
			3.1.4 Estimating the Structural Stability of the Kondratiev Cycle Mathematical Model with Parametric Control
			3.1.5 Analysis of the Dependence of the Optimal Value of Criterion K on the Parameter for the Variational Calculus Problem Bas...
		3.2 Goodwin Mathematical Model of Market Fluctuations of a Growing Economy
			3.2.1 Model Description
			3.2.2 Analysis of the Structural Stability of the Goodwin Mathematical Model Without Parametric Control
			3.2.3 Problem of Choosing Optimal Parametric Control Laws on the Basis of the Goodwin Mathematical Model
			3.2.4 Analysis of the Structural Stability of the Goodwin Mathematical Model with Parametric Control
			3.2.5 Analysis of the Dependence of the Optimal Parametric Control Law on Values of the Uncontrolled Parameter of the Goodwin ...
	Chapter 4: Macroeconomic Analysis and Parametric Control of Economic Growth of a National Economy Based on Computable Models o...
		4.1 National Economic Evolution Control Based on a Computable Model of General Equilibrium of Economic Branches
			4.1.1 Model Description, Parametric Identification, and Retrospective Prediction
				4.1.1.1 Model Agents
				4.1.1.2 Exogenous Variables of the Model
				4.1.1.3 Endogenous Variables of the Model
				4.1.1.4 The Model Markets
				4.1.1.5 Economic Agent Nos. 1-16 Producing Products and Services
				4.1.1.6 Economic Agent No. 17: Aggregate Consumer
				4.1.1.7 Economic Agent No. 18 Government
				4.1.1.8 Integral Indexes of the Model
				4.1.1.9 Parametric Identification of the Model and Retrospective Prediction
			4.1.2 Macroeconomic Analysis on the Basis of the Computable Model of General Equilibrium of Economic Branches
				4.1.2.1 Retrospective and Perspective Analysis of the Economic Agents´ Indicators and National Economy on the Basis of the Com...
				4.1.2.2 Analysis of Elasticity Coefficients of Endogenous Variables of Computable Model of General Equilibrium of Economic Bra...
				4.1.2.3 Analysis of Economic Growth Sources on the Basis of the Computable Model of General Equilibrium of Economic Branches
				4.1.2.4 Estimation of the Macroeconomic Theory Provisions on the Basis of the Computable Model of General Equilibrium of Econo...
			4.1.3 Finding Optimal Parametric Control Laws on the Basis of the CGE Model of Economic Branches
				4.1.3.1 Attenuation of Cyclic Oscillations of Macroeconomic Indicators by Parametric Control Methods
				4.1.3.2 Finding Optimal Parametric Control Laws on the Basis of the Stochastic CGE Model of Economic Branches
		4.2 National Economic Evolution Control Based on the Computable Model of General Equilibrium with the Knowledge Sector
			4.2.1 Model Description, Parametric Identification, and Retrospective Prediction
				4.2.1.1 Model Agents
				4.2.1.2 Exogenous Parameters of Model
				4.2.1.3 Endogenous Variables of the Model
				4.2.1.4 Model Markets
				4.2.1.5 Economic Agent No. 1: Science and Education Sector
				4.2.1.6 Economic Agent No. 2: Innovation Sector
				4.2.1.7 Economic Agent No. 3: Other Branches of the Economy
				4.2.1.8 Economic Agent No. 4: The Aggregate Consumer (Households)
				4.2.1.9 Economic Agent No. 5: Government
				4.2.1.10 Integral Indices of Model
			4.2.2 Estimation of the Macroeconomic Theory Provisions on the Basis of the Computable Model of General Equilibrium with the K...
			4.2.3 Finding Optimal Parametric Control Laws Based on the CGE Model with the Knowledge Sector
				4.2.3.1 Attenuation of Cyclic Oscillations of Macroeconomic Indicators by Parametric Control Methods
				4.2.3.2 Finding Optimal Parametric Control Laws on the Basis of the Stochastic CGE Model with the Knowledge Sector
		4.3 National Economic Evolution Control Based on the Computable Model of General Equilibrium with the Shady Sector
			4.3.1 Model Description, Parametric Identification, and Retrospective Prediction
				4.3.1.1 Economic Agents of the Model
				4.3.1.2 Exogenous Parameters of the Model
				4.3.1.3 Endogenous Variables of the Model
				4.3.1.4 Model Markets
				4.3.1.5 Economic Agent No. 1: The State Sector
				4.3.1.6 Economic Agent No. 2: The Market Sector
				4.3.1.7 Economic Agent No. 3: The Shady Sector
				4.3.1.8 Economic Agent No. 4: The Aggregate Consumer (Households)
				4.3.1.9 Economic Agent No. 5: Government
				4.3.1.10 Economic Agent No. 6: The Banking Sector
				4.3.1.11 Economic Agent No. 7: The Outer World
				4.3.1.12 Integral Indices of the Model
				4.3.1.13 Parametric Identification of the CGE Model with the Shady Sector
			4.3.2 Finding the Optimal Values of the Adjusted Parameters on the Basis of the CGE Model in the Shady Sector
	Chapter 5: Conclusion
	References
	About the Authors
	Index
                        

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