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Introductory mathematical economics

Danao, Rolando Altarejos

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  • Notes
    Includes index.
    • Content
    • Preface:A word about logical implications -- Elements of linear algebra : Matrices and vectors -- Matrix operations -- Vector spaces -- Properties of matrix operations -- The transpose of a matrix -- Determinants -- The inverse of a square matrix -- Linear independence and nonsingularity -- Matrix inversion -- Simultaneous linear equations -- Eigenvalues and eigenvectors -- Quadric forms problems -- Input-output analysis : The input-output model -- The hawkins-simon condition -- The brauer-solow condition -- Approximation of the inverse of the leontief matrix -- Interpretation of the inverse of the leontief matrix -- Demand for primary inputs -- Direct and indirect effects -- Duality and prices -- Concluding remarks problems -- Linear programming : Formulating the linear programming problem (LP) -- Forms of the LP -- Assumptions on the standard form of the LP -- Graphical solution of the LP -- A computational from of the LP -- Basic solutions -- Feasibility, optimality, and unboundedness -- Pivoting -- The simplex algorithm -- Economic interpretation of the simplex algorithm -- Termination of the simplex algorithm and degeneracy -- The two-phase simplex method -- Duality in linear programming -- Interpretation of duality -- Income distribution in a leontief economy problems -- Topics in the theory of functions : Topological concept in R" -- Functions or mappings -- Special types of functions of one variable -- Functions defined from other functions -- Limits -- Continuity -- Differentiation : The derivative as a rate of change -- The derivative as a slope of a curve -- Differentiability and smoothness of a curve -- The significance of the sign of the derivative -- Differentiability and continuity in R -- Differentiation rules : Sum, difference, product, and quotient rules -- The chain rule -- The inverse function rule -- Derivative of the logarithmic function -- Derivative of the exponential function -- Derivative of the power function -- Implicit differentiation -- Logarithmic differentiation -- L'hospital's rule : An application of L'hospital's rule -- Marginal and average functions, elasticity, and rates of growth -- Partial derivatives : Geometric interpretation of the partial derivative -- Marginal functions -- Partial elasticity -- Differentiability and continuity in R" -- Total differentials and total derivatives : Directional derivatives -- Tangent vectors and gradients -- Implicit function theorem : The case f(x,y) = 0, x,y Є R -- The case f(x,y) = 0, x Є Rn, y Є R -- The simultaneous equation case -- Matrix derivatives -- Taylor's theorem : Taylor's theorem for a function of one variable -- Taylor's theorem for a function of several variables -- Homogeneous functions -- Homothetic functions problems -- Nonlinear programming : Introduction -- Global and local optima -- First-order necessary condition for local optima -- Second-order sufficient condition for local optima -- Second-order necessary condition for local optima -- Optima of concave and convex functions -- Optima of quasiconcave and quasiconvex functions -- Constrained optimization -- Optimization with one equality constraint : The two-variable case -- Solution by direct substitution -- Graphical solution -- The lagrange multiplier method -- Optimization with one equality constraint: the n-variable case --Optimization with several equality constraints -- Interpretation of the lagrange multiplier -- Optimization with inequality constraints -- The kukn-tucker conditions -- The kunk-tucker conditions under explicit nonnegativity constraints -- Interpretation of the kuhn-tucker-lagrange multipliers -- Sufficient conditions for optimality problems -- Consumer choice : Preferences:the behavioral axioms -- The utility function -- Utility Maximization -- The marshallian demand functions and the indirect utility function -- Expenditure minimization -- The hicksian demand functions and the indirect expenditure function -- The relationship between utility maximization and expenditure function problems -- Producer choice : Production:the technological axioms -- The production function -- Profit maximization -- Input demand, output supply, and indirect profit functions -- Cost minimization -- The conditional input demand functions and the indirect cost functions -- Cost curves, marginal cost, and average cost -- Cost curves of homogeneous production functions -- The relationship between profit maximization and cost minimization problems.
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