Demystifying Mathematics and
Mathematical Economics. Mathematical versus Non-mathematical Economics. Mathematical
Economics versus Econometrics. Ingredients of a Mathematical Model: Variables
and Economic Variables. Ingredients of a Mathematical Model: Constants and
Parameters. A Few Aspects of Logic: Propositions, Implications and Necessary
and Sufficient Conditions. The Real-Number System. Use of Sets in economics:
Set Notation. Use of Sets in economics: Operations of Sets. Use of Sets in
economics: Laws of Operations of Sets. Cartesian Coordinates. What are
Functions? Domain and Range in a Function. Difference between Function and
Relations. Economic Example of Schultz Demand Function. Economic Example of
Cost Function of Cleaning Impurities from a Lake. Economic Example of Function:
Laffer Curve. Types of Functions: Constant Functions. Types of Functions:
Polynomial Function: Linear Functions. Interpreting Linear Economic
Functions. Applications of Linear
Functions: Population and Consumption Functions. Types of Functions: Polynomial
Function: Quadratic Functions. Quadratic Cost function and Profit Function of a
Monopoly. Quadratic Function and Production Possibilities Frontier. Types of
Functions: Polynomial Function: Cubic Functions. Cubic Cost functions. Rational
Functions. Other Types: Rectangular Hyperbolic Function. Other Types:
Non-algebraic Exponential Functions. Population Growth using General
Exponential Functions. Other Types: Non-algebraic Natural Exponential Functions.
Population Growth using Natural Exponential Functions. Other Types:
Non-algebraic Logarithmic Functions. Other Types: Non-algebraic Natural
Logarithmic Functions. Rate of Growth of GNP using Logarithmic Functions.
Inverse Functions. Functions with Two or More Independent Variables. Surfaces
and Distance in Graphs of two or more independent variables. Equations and
Identities. Types of equations in Economics: Definitional Equations. Fiscal
Surplus and Fiscal Deficit Using Equations. Types of equations in Economics:
Behavioral Equations. Types of equations in Economics: Conditional Equation. Structural
and Reduced Form Equations. Constructing a Partial Linear Market Equilibrium. Solving
using Elimination of Variable Method. Shifts in Demand in Market Equilibrium. Shifts
in Supply in Market Equilibrium. Effect of Tax on Producer on Partial Market
Equilibrium. Effect of Tax on Consumer on Partial Market
Equilibrium. Partial Market Equilibrium-A Nonlinear Model. General Market
Equilibrium: General form of Two Good Case. General Market Equilibrium:
Numerical solution of Two Good Case. General Market Equilibrium: n-Good Case. National
Income Equilibrium. National Income Equilibrium with Induced and Autonomous Tax.
National Income Equilibrium with Proportion of Government Expenditure. Matrices
and Vectors. Array and Summation forms of Matrices. Matrices Operations. Using
Product of Matrices to Calculate Total Cost. Using Product of Matrices to
Calculate Total Revenue and Profit. Question of Matrix Division. Commutative,
Associative, and Distributive Laws. Vector Operations. Transpose of a Matrix. Cofactors
of a Matrix. Adjoint of a Matrix. Determinant of a Matrix. Sarrus''''s rule for
3x3 order Determinant of a Matrix. Inverse of a Matrix. Condition(s) for
Non-singularity. Expression of National Income using Matrix Form. Minor and
Cofactors. Market Model Analysis Using Matrix Inversion Method. National Income
Analysis Using Matrix Inversion Method. Equilibrium Prices using Matrix
Inversion Method. Solving Market Model using Cramer''''s Rule. Equilibrium Prices
using Cramer''''s Rule. National Income Determination using Cramer''''s Rule. Input-Coefficient
Matrix. Economic Meaning of Hawkins-Simon Condition. Input-Output Analysis in
case of Open Economy. Input-Output Analysis in case of Closed Economy. The Need
and Nature of Comparative Statics. Concept of Limit and continuity. Rate of
Change, Slope & Derivative. Differentiation Rules for Single variable
functions: Constant Function Rule and Power Function Rule. Sum-Difference Rule
of Differentiation. Sum-Difference Rule: Numerical Analysis of Cost Function. Understanding
graphs of Function and its derivatives. Product Rule of Differentiation. Relationship
between Average Revenue and Marginal Revenue using Product Rule. Quotient Rule
of Differentiation. Marginal Propensity to Consume via Differentiation with and
without Tax. Relationship Between Marginal-Cost and Average-Cost Functions
using Quotient Rule. Variable and Fixed Cost components in total cost function.
Obtaining Marginal Cost function from Average Cost function. Marginal Cost
Analysis. Marginal Revenue Analysis. Marginal Product Analysis. Rules of
Differentiation: Functions with different variables: Chain Rule. Marginal
Revenue Product of Labor (MRPL) Analysis. Marginal Analysis of Fishery
Production Function. Inverse Function Rule. Partial Differentiation: The
Concept. Marginal Physical Product of Labor and Capital using Partial
Derivatives. Marginal Utility functions using Partial Derivatives. Output
Elasticity of Labor and Capital using Partial Derivatives. Money Market Analysis
using Partial Derivatives. Partial Market Model using Partial Differentiation. National-Income
Model using Partial Differentiation. Second and Higher Order Derivatives. Economic
Applications of Second Derivative: Profit Maximization Condition. Numerical
Example of Profit Maximization Condition using Second Derivative. Young''''s
Theorem. Demand for Money Function Analysis using Partial Derivatives. Income
Elasticity of Demand using Partial Derivatives. Cross Price Elasticity of
Demand using Partial Derivatives. Partial Derivatives: Application on Herring
Production Function. Partial Derivatives: Application on Three Input Production
Function. Envelope Theorem. Roy''''s Identity. Hotelling''''s Lemma. Shephard Lemma. Differentials
versus Derivatives. Point Elasticity using Differentials. Elasticity of
Rectangular Hyperbolic Demand Curve. Income and Price Elasticity of Demand
using Differentials. Income and Price Elasticity of Import Function using
Differentials. Income Elasticity of Consumption using Differentials. Output
Elasticity of Cost. Concept of Total Differentials. Savings Function and Total
Differentials. General Utility Function and Total Differentials. Specific
Utility Function and Total Differentials. Price and Rain Elasticity of Supply
using Total Differentials. Local Price Elasticity of Foreign Demand of Exports
using Total Differentials. Concept of Total Derivatives. Complementarity
between Coffee and Sugar Using total Derivative. General Production Function
with time-dependent Labor and Capital. Specific Production Function with
time-dependent Labor and Capital. Concept of Implicit Differentiation. Production
Function Analysis using Implicit Differentiation. Marginal Rate of Technical
Substitution using Implicit Differentiation. Marginal Utilities and Marginal
Rate of Substitution using Implicit Differentiation. Nerlove-Ringstad
Production Function using Implicit Differentiation. Marginal Products of Three
Input Logarithmic Production Function. Exponential Functions and Growth. Instantaneous
Rate of Growth. Numerical Examples of Instantaneous Rate of Growth. Continuous
vs. Discrete Growth. Discounting and Negative Growth. Applications of
Continuous Compounding. Applications of Instantaneous Growth. Logarithms:
Meaning and Types. Laws of Logarithms. Laws of Logarithms for Transformation of
CES Production Function. Rules of Differentiation of Exponential and
Logarithmic Functions. Optimal Timing: A Problem of Wine Storage. Optimal
Timing: A Problem of Timber Cutting. Optimal Timing: Land Purchase for
Speculation. Optimal Timing: Art Collection. Optimal Timing: Diamond Purchase. Finding
the Rate of Growth using Exponential and Logarithmic Functions. Growth of
Exports of a Country. Finding the Point Elasticity. Rates of Growth of
Population, Consumption, and Per Capita Consumption. Rate of Growth of Per
Capita Employment. Rate of Growth of Export Earnings of a Country. Rate of
Growth of Sales. Rate of Growth of Profit. Concept of Optimization. Calculus
Approach to Optimization: 1st Order Test. Average Cost Analysis. Calculus
Approach to Optimization: 2nd Order Test. Matrix Approach to Optimization: 2nd
Order Test – Hessian. Profit Maximization Analysis. Numerical Example of Profit
Maximization. Profit Maximization of Technically Related Goods. Profit
Maximization of Monopolistic Firm producing Related Goods. Profit Maximization
of Firm producing Substitute Goods. Price Discrimination and Elasticity of
Demand. Cubic Total Cost Analysis. Marginal and Average Revenue Analysis. Short
Run Production Function Analysis. Total Cost, Total Revenue and Profit
Maximization. Quadratic Profit Function Analysis. Optimization of Exponential
Revenue Function. Optimization of More than one Choice variable. Economic
Application on Multi-Product Firm. Economic Application on Multi-Plant Firm. Price
Discrimination by Monopoly. Price Discrimination by Monopsony. Input Decision
of a Firm. Profit Maximization of two-product firm. Comparative-Static Aspects
of Optimization. Rationale for Constrained Optimization. Finding Stationary
Values using Substitution/Elimination Method. Finding Stationary Values using
Method of Lagrange Multiplier. Interpretation of the Lagrange Multiplier. Second
Order Condition: The Bordered Hessian. Utility Maximization and Consumer Demand.
Two Period Model of Utility. Convexity and Concavity using Second Order
Derivative. Utility Maximization and Consumer Demand: First Order Condition. Utility
Maximization and Consumer Demand: Second Order Condition. Numerical Example of
Utility Maximization. Law of Equi-Marginal Utility using Lagrangian Multiplier.
Economic Application of Production Function Maximization. Economic Application
on Logarithmically Transformed Production Function. Homogeneous Functions. Homogeneous
Production Function, Average Products and Capital-Labor ratio. Homogeneous
Production Function, Marginal Products and Capital-Labor ratio. Homogeneous
Production Function and Euler''''s Theorem. Cobb-Douglas Production Function and
Returns to Scale. Homogeneity and Returns to Scale of Three input Production
Function. Least-Cost Combination in Cobb-Douglas Production Function. Expansion
Path using First Order Condition. Homothetic Functions. Homotheticity of
Cobb-Douglas Production Function. Introducing CES Production Function. Homogeneity
of CES Production Function. Marginal Products of CES Production Function. Share
of Labor and Capital in CES Production Function. CES Production Function and
Euler''''s Theorem. Numerical CES Production Function Calculation.