Maathematics In Economics

WELCOME

BUDDING MANAGERS

GANDHIJI’S TALISMAN

“Whenever you are in doubt or when the self becomes too much with yu, apply the following test –

Recall the face of the poorest and the weakest man whom you may have seen and ask yourself if the step you contemplate is going to be of any use to him. Will it restore him to a control over his own life and destiny?

Then you will find your doubts and your self melting away”

-MOHANDAS KARAMCHAND GANDHI

BASIC FUNCTIONS USED IN COMMERCE AND ECONOMICS

• 1. Cost Function

• 2. Demand Function

• 3. Revenue Function

• 4. Profit Function

• 5. Break-even Analysis

• 6. Average amd Marginal Functions

• 7. Average and Marginal Cost

• 8. Average and Marginal Revenues

BASIC FUNCTIONS USED IN COMMERCE AND ECONOMICS

• 8. Average and Marginal Revenues• 9. Maximisation of Total Revenues• 10.Maximisation of Total Profit• 11. Minimization of Average Cost• 12. Determination of Cost Function & Average

Cost Function• 13. Determination of Revenue Function and

Demand Function from Marginal Revenue Function.

CONSTANT AND VARIABLE

A quantity which does not change is called a constant

and

a quantity which changes is called a variable.

Variable & Constant

• A variable is something that can take on different values.

• Endogenous variables - originating from within.

• Exogenous variables - originating from without.

• A constant is a magnitude that does not change (opposite of a variable).(Givens) e.g. a in ax.

Integers

• Positive Integers – • Whole numbers 1, 2, 3, 4, 5…

• Negative Integers -1, -2, -3, -4, -5 ….

• Together with number (0) which is neither – nor + , make up set of all integers.

Fractions

That which is not completyely whole.

• The values which fall between the integers are called fractions.

• e.g. ⅓, ⅔, ½, ⅝, ⅞ …. and -⅝, -⅜, -⅔, -½ ….make up set of all fractions.

Rational numbers & Irrational numbers

Those numbers which can be expressed as a ratio. (ratio-nal)

Set of all integers and set of all fractions make up set of all ratio-nal numbers.

Irrational numbers are those which fall between rational numbers and integers.

REAL NUMBERS

• Thus Integers, Fractions, Irrational and rational numbers all put together form a set of “real numbers”.

Imaginary numbers

There are also imaginary numbers such as square-root of negative numbers.

Function

• Function (f) – is the action of associating one thing with another.

In y = f(x),the functional notation “f” means a rule by which the set ‘x’ is converted or transformed into set ‘y’.

• The function converts x into y. f : x → y

• In y = f(x),

• The domain of f = all permissible values x can take.

• all the y values into which x values are mapped is called the range of f.

• or set of all values which the ‘y’ variable will take is called the range of ‘f’.

Constant function

y= f(x) = 7 OR y = 7 or f(x) = 7.

• Regardless of value of x, value of y remains static or the same.

This is a constant function.

Polynomial function

• Polynomial means “multiterm”.

• Polynomial function of a single variable x has the general form (formula)

Y = a x2 + b x + c

Linear & Quadratic Equations

• An equation is called a linear equation, if only a single variable occurs in the equation.

Example: x + 2 = 3x – 9 (Linear equation)

When the degree of the variable is ‘2’i.e. x2

As in ax2 + bx + c = 0, it is a quadratic equation.

• Rates of change in the equilibrium values of the variables:

• Consider the rate of change of any variable ‘y’ in response to a change in another variable x, where the two variables are related to each other by the function

• Y = f(x)• Y represents the equilibrium value of an

endogenous variable • X will be some parameter.• Presently we restrict to the simple case where

there is only one parameter.

Equilibrium & Parameter

• Equilibrium = a state of balance.

• Parameter = limit of a variable quantity.

The Difference Quotient:

• The symbol ∆ (the Greek Capital delta for “difference”) is used to denote “change” in value.

EXPONENTIAL LAWS ORBASIC LAWS OF INDICES

• If ‘m’ and ‘n’ are positive integers and ‘a’ is a non-zero real number then,

• Ist Law : am. an = am+n

EXPONENTIAL LAWS ORBASIC LAWS OF INDICES

• If ‘m’ and ‘n’ are positive integers and ‘a’ is a non-zero real number then,

2nd Law: am = 1 if m > n = 1 if n > m an am-n an-m

EXPONENTIAL LAWS ORBASIC LAWS OF INDICES

• If ‘m’ and ‘n’ are positive integers and ‘a’ is a non-zero real number then,

• 3rd Law : (am)n = amn

EXPONENTIAL LAWS ORBASIC LAWS OF INDICES

• If ‘m’ and ‘n’ are positive integers and ‘a’ is a non-zero real number then,

• 4th Law : (ab)m = ambm where ‘b’ is a non-zero real number.

EXPONENTIAL LAWS ORBASIC LAWS OF INDICES

• If ‘m’ and ‘n’ are positive integers and ‘a’ is a non-zero real number then,

• 5th Law: a m = am

b bm