Topics
Unit 1
Introduction to Micro and Macro Economics
Mathematical Logic
Mathematical Logic
Matrices
- Determinant of a Matrix
- Types of Matrices
- Algebra of Matrices
- Properties of Matrices
- Elementary Transformations
- Inverse of Matrix
- Application of Matrices
- Properties of Transpose of a Matrix
Differentiation
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Inverse Functions
- Derivatives of Logarithmic Functions
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Second Order Derivative
Applications of Derivatives
- Introduction of Derivatives
- Increasing and Decreasing Functions
- Maxima and Minima
- Application of Derivatives to Economics
Integration
Definite Integration
- Fundamental Theorem of Integral Calculus
- Properties of Definite Integrals
Applications of Definite Integration
- Standard Forms of Parabola and Their Shapes
- Standard Forms of Ellipse
- Area Under Simple Curves
Differential Equation and Applications
- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equation by Eliminating Arbitary Constant
- Differential Equations with Variables Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
- Application of Differential Equations
Matrices
Commission, Brokerage and Discount
- Commission and Brokerage Agent
- Discount
Insurance and Annuity
- Concept of Insurance
- Fire Insurance
- Accident Insurance
- Marine Insurance
- Annuity
Linear Regression
- Regression
- Types of Linear Regression
- Fitting Simple Linear Regression
- The Method of Least Squares
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Properties of Regression Coefficients
Time Series
- Introduction to Time Series
- Uses of Time Series Analysis
- Components of a Time Series
- Mathematical Models
- Measurement of Secular Trend
Index Numbers
- Index Numbers
- Types of Index Numbers
- Index Numbers - Terminology and Notation
- Construction of Index Numbers
- Simple Aggregate Method
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number
Linear Programming
- Introduction of Linear Programming
- Linear Programming Problem (L.P.P.)
- Mathematical Formulation of Linear Programming Problem
Assignment Problem and Sequencing
- Assignment Problem
- Hungarian Method of Solving Assignment Problem
- Special Cases of Assignment Problem
- Sequencing Problem
- Types of Sequencing Problem
- Finding an Optimal Sequence
Probability Distributions
- Mean of a Random Variable
- Types of Random Variables
- Random Variables and Its Probability Distributions
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Binomial Distribution
- Bernoulli Trial
- Mean of Binomial Distribution (P.M.F.)
- Variance of Binomial Distribution (P.M.F.)
- Poisson Distribution
- Expected Value and Variance of a Random Variable
Continuity
Differentiation
Applications of Derivative
Indefinite Integration
- Definition of an Integral
- Integral of Standard Functions
- Rules of Integration
- Methods of Integration
- Integration by Parts
Definite Integrals
Ratio, Proportion and Partnership
Commission, Brokerage and Discount
Insurance and Annuity
- Insurance and Annuity
Demography
- Concept of Demography
- Uses of Vital Statistics in Demography
- Measurements of Mortality
- Life Tables
Bivariate Data and Correlation
Regression Analysis Introduction
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Regression Coefficient of X on Y and Y on X
- Regression Propertise
Random Variable and Probability Distribution
Management Mathematics
- Inequations in Management Mathematics
- Linear Programming Problem in Management Mathematics
- Assignment Problem
- Sequencing in Management Mathematics
Notes
Introduction :
Index numbers are one of the most used statistical tools in economics. An index number is a device to measure changes in an economic variable (or group of variables) over a period of time. Index numbers were originally developed to measure changes in the price level. In the present context, it is also used to measure trends in a wide variety of areas that includes stock market prices, cost of living, industrial and agricultural production, changes in exports and imports etc. Index numbers are not directly measurable, but represent relative changes.
Definitions of Index Numbers :
1) Spiegel :
“An index number is a statistical measure designed to show changes in a variable or a group of related variables with reference to time, geographical location and other characteristics such as income, profession etc.”
2) Croxton and Cowden :
“Index Numbers are devices for measuring differences in the magnitude of a group of related variables.”
Features of Index Numbers :
1) Index numbers are statistical devices.
2) Index numbers are specialized averages which are capable of being expressed in percentages.
3) Index numbers measure the net change in one or more related variables over a period of time or between two different time periods or two different localities.
4) Index number which is computed from a single variable is called a ‘univariate index’,whereas an index which is constructed from a group of variables is called a ‘composite index’.
5) The year for which the index number is prepared is the current year.
6) The year with which the changes are measured is called the base year.
7) The base year’s index is assumed as 100 and accordingly the value of the current year is calculated.
8) Index numbers are also referred to as ‘barometers of economic activity’, since it is used to measure the trends and changes in the economy.
Related QuestionsVIEW ALL [58]
Using the following data, construct Fisher’s Ideal index and show how it satisfies Factor Reversal Test and Time Reversal Test?
| Commodity | Price in Rupees per unit | Number of units | ||
| Basic year | Current year | Base year | Current year | |
| A | 6 | 10 | 50 | 56 |
| B | 2 | 2 | 100 | 120 |
| C | 4 | 6 | 60 | 60 |
| D | 10 | 12 | 50 | 24 |
| E | 8 | 12 | 40 | 36 |
