Mathematical Economics

  1. Comparative Static Analysis
    1. The Nature of Comparative Statics
      1. Definition and Purpose
        1. Distinction from Static and Dynamic Analysis
          1. Methodology of Comparative Statics
          2. Differentiation of Functions of One Variable
            1. The Derivative as a Rate of Change
              1. The Derivative as a Slope
                1. Basic Differentiation Rules
                  1. Power Rule
                    1. Sum and Difference Rule
                      1. Product Rule
                        1. Quotient Rule
                          1. Chain Rule
                          2. Derivatives of Common Functions
                            1. Polynomial Functions
                              1. Exponential Functions
                                1. Logarithmic Functions
                                  1. Trigonometric Functions
                                  2. Higher-Order Derivatives
                                    1. Second Derivatives
                                      1. nth Derivatives
                                    2. Partial Differentiation
                                      1. Functions of Several Variables
                                        1. Partial Derivatives
                                          1. Definition and Notation
                                            1. Geometric Interpretation
                                            2. Techniques of Partial Differentiation
                                              1. Cross Partial Derivatives
                                                1. Young's Theorem
                                                  1. Homogeneous Functions
                                                    1. Definition and Properties
                                                      1. Euler's Theorem
                                                      2. Homothetic Functions
                                                      3. Total Differentials and Total Derivatives
                                                        1. The Total Differential
                                                          1. Definition and Calculation
                                                            1. Approximation Properties
                                                            2. The Total Derivative
                                                              1. Chain Rule for Several Variables
                                                              2. Applications in Economics
                                                                1. Elasticity Analysis
                                                                  1. Marginal Analysis
                                                                2. The Implicit Function Theorem
                                                                  1. Implicit Functions
                                                                    1. Derivatives of Implicit Functions
                                                                      1. Conditions for Existence
                                                                        1. Applications in Comparative Statics
                                                                          1. Economic Examples
                                                                          2. Applications to Economic Models
                                                                            1. Comparative Statics of Market Models
                                                                              1. Effect of Parameter Changes on Equilibrium
                                                                                1. Demand and Supply Shifts
                                                                                2. Comparative Statics of National-Income Models
                                                                                  1. Multiplier Analysis
                                                                                    1. Fiscal Policy Effects
                                                                                    2. Comparative Statics in Consumer Theory
                                                                                      1. Income and Substitution Effects
                                                                                        1. Slutsky Equation
                                                                                        2. Comparative Statics in Producer Theory
                                                                                          1. Input Demand Response
                                                                                            1. Output Supply Response

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                                                                                        3. Linear Models and Matrix Algebra

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                                                                                        5. Optimization Problems