Elements of Numerical Mathematical Economics with Excel ; Static and Dynamic Optimization

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ELEMENTS OF NUMERICAL MATHEMATICAL ECONOMICS WITH EXCEL: STATIC AND DYNAMIC OPTIMIZATION
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Contents
P A R T I:
 Excel and fundamental mathematics for economics
	1. Excel VBA, solver, and other advanced worksheet tools
		1.1 VBA introduction and main statements The VBA Editor and the modules
		1.2 The Excel Solver: simplex LP, Generalized Reduced Gradient, and evolutionary
		1.3 What-if analysis: scenario manager, Goal Seek, Data Table, and contour lines
		1.4 Scatter charts and trendlines
	2. Univariate and multivariate calculus
		2.1 Numerical methods for univariate differentiation
		2.2 Numerical methods for univariate integration
		2.3 Numerical partial differentiation
		2.4 Applications in economics
	3. Elements of linear algebra
		3.1 Built-in Excel matrix functions and basic operations
		3.2 Linear systems and resolution methods in Excel: Cramer, Solver, Inverse
		3.3 Eigenvalues and eigenvectors search: analytical and graphical approach
		3.4 Quadratic forms and definiteness of a symmetric matrix
		3.5 Leontief open model
		3.6 Equilibrium in n markets
		3.7 Economic policy modeling: objectives and instruments
	4. Mathematics for dynamic economic models
		4.1 Ordinary differential equations and numerical methods: Euler and Runge-Kutta
		4.2 Force of interest, Walrasian stability, utility functions, and capital formation with ordinary differential equation
		4.3 Difference equations and phase diagrams
		4.4 Cobweb model of price adjustment and other economic models with difference equations Cobweb model (price adjustment model in
		4.5 Systems of linear differential equations
		4.6 Tourism
		4.7 Walrasian adjustment with entry
P A R T II:  Static optimization
	5. Classical static nonlinear optimization theory
		5.1 Classical unconstrained optimization of a univariate function
		5.2 Classical unconstrained optimization of a multivariate function
		5.3 Some economic applications of the nonlinear unconstrained optimization
		5.4 Numerical steepest descent method applied to the unconstrained optimization with VBA
		5.5 Nonlinear problems in Rn with equality constraints: Lagrange multipliers and Solver
		5.6 Nonlinear problems in R2 with equality constraints: contour lines
		5.7 Nonlinear problems with inequality constraints
	6. Microeconomic theory in a static environment
		6.1 The consumer problem: cardinal versus ordinal utility approach
		6.2 Consumer optimization and derivation of the demand curve in the cardinal approach
		6.3 Consumer optimization and derivation of the demand curve in the ordinal approach
		6.4 The firm problem
		6.5 One-input classical production function
		6.6 Two-inputs production functions 1. CobbeDouglas production function
		6.7 Isoquants and the constrained production optimization with two inputs
		6.8 Production Edgeworth box, contract curve, and the possibility frontier construction
		6.9 Short-run, long-run costs and the envelope average total costs derivation
		6.10 Perfect competitive markets: short-run, long-run supply curves and market equilibrium
		6.11 Monopolistic market equilibrium: the Chamberlin model
		6.12 Markets with high-entry barriers: monopoly and the Cournot duopoly model
		6.13 Game theory. Zero-sum games and minimax criterion: matrix and graphical resolutions
	7. Linear programming
		7.1 Standard formulation of a linear program and resolution methods
		7.2 Applications to the static production planning and capital budgeting
	8. Nonlinear optimization applied to the portfolio theory
		8.1 Portfolio modeling and the efficient frontier construction
		8.2 Investor’s utility and the optimal portfolio choice
P A R T III:
 Dynamic optimization
	9. Calculus of variations
		9.1 The fundamental problem of the Calculus of Variations
		9.2 Discrete approximate Calculus of Variations: Lagrange multipliers and contour lines solutions
		9.3 Set up of the Excel worksheet for Calculus of Variations problems: the Solver solution
		9.4 General cases developed in Excel with
		9.5 Dynamic optimization for a monopolist
		9.6 Unemployment and inflation
		9.7 The EisnereStrotz model
		9.8 The optimal consumption Ramsey model
		9.9 Inventory dynamic optimization
		9.10 Optimal capital structure and the
		9.10 Optimal capital structure and the firm cost of capital	#493,0,-343		9.11 Contour lines solution for Calculus of Variations using the VBA code
		9.12 Calculus of Variations with functionals involving two independent functions
		9.13 Calculus of Variations constrained problems
		9.14 Checking the Second-Order Conditions in Excel
	10. Theory of optimal control
		10.1 The optimal control problem and the Pontryagin’s maximum principle
		10.2 Nonlinear Hamiltonian and linear Hamiltonian (bang-bang control)
		10.3 Setup of the Excel worksheet for optimal control problems
		10.4 Bang-bang control problems
		10.5 Consumption model
		10.6 Investment model
		10.7 Inventory optimization
		10.8 Two state variables control problems
		10.9 Current-value Hamiltonian
		10.10 Constraints on the state variable: a linear case with an inventory application with VBA
		10.11 Steepest descent numerical approach for optimal control problems using VBA
		10.12 Checking the sufficient conditions in Excel
	11. Discrete dynamic programming
		11.1 Bellman’s principle, discrete shortest path problems, and the Excel MINIFS function
		11.2 Discrete dynamic systems: tabular method, Excel data table, and Solver
		11.3 Cargo loading allocation problems: tabular method and the Excel Solver
		11.4 Multistage allocation problems using the Excel Solver
		11.5 Equality constrained optimization problems using the recursive Bellman’s approach
		11.6 Dynamic economic problems solved with Discrete Dynamic Programming
		11.7 Discrete Dynamic Programming, Optimal Control theory, and Calculus of Variations: a synthesis
P A R T IV:  Special topics
	12. Dynamic production planning and inventory modeling
		12.1 Multiperiod production models with linear programming
		12.2 WagnereWhitin algorithm for inventory dynamic modeling
		12.3 Eliezer Naddor stochastic single-period inventory models
	13. Data analysis for business and economics
		13.1 A simple way to organize a spreadsheet using the VBA code and bookmarks
		13.2 Pivot tables, Pivot charts, and dynamic dashboards for managerial data analysis
		13.3 Basic descriptive statistics
		13.4 Some numerical calculus applied to continuous densities
		13.5 Univariate, multivariate regression analysis and the ANOVA tables
	14. Essential Monte Carlo analysis
		14.1 The Monte Carlo method and the generation of random numbers
		14.2 The Monte Carlo method for business decisions
		14.3 Numerical integration
Index