The document discusses functions and their applications in economics. It defines a function as a formula or rule relating a dependent variable to an independent variable. Some key function types discussed include: 1) Constant functions where the dependent variable is equal to a fixed constant value, regardless of the independent variable. 2) Linear functions where the dependent variable is equal to a constant plus the independent variable multiplied by another constant, forming a straight line graph. 3) Examples of demand, supply, total revenue, total cost, and profit functions are given, which are important in economics for showing how quantities vary with each other.

1. Janardan Bhagat Shikshan Prasarak Sanstha’s
Changu Kana Thakur
Arts, Commerce & Science College, New Panvel
Re-Accredited ‘A+’ Grade by NAAC
‘College with Potential for Excellence’ Status Awarded by University Grants Commission
‘Best College Award’ by University of Mumbai
Basic Course
Mathematics and Statistics Techniques
By
Dr. S.I. Unhale
Associate Professor,
Department of Mathematics

2. Syllabus
Sr. No. Modules / Units
2 Functions and Their Applications
Functions: Constant function, linear function, Demand, Supply, Total Revenue
function, Total cost and Profit function and their applications. Quadratic functions
and equations.
Arithmetic and Geometric Progression

3. Topic: Functions and their Applications
Introduction: In Economics, we deals with quantities
such as amount of goods demanded in the market or
supplied by a firm, their cost of production, their prices,
total income(Revenue) due to their sale etc. Such
quantities change their values. Hence, they are called
variables.

4. These variables are inter-related i.e. the value of one
depends on some other variable or variables. For example,
suppose the cost of production of a particular good depends
on quantity of good produced. Here, if ‘C’ is the cost of
production and ‘x’ is the quantity of good produced. Then
the value of ‘C’ depends on the value of ‘x’.
Here ‘C’ is called dependent variable and ‘x’ is called
independent variable and ‘C’ is function of ‘x’.

5. In general, if the values of a variable ‘y’ depends on the values of the
variable ‘x’ then ‘y’ is the dependent variable and ‘x’ is the
independent variable. Also ‘y’ is said to be function of ‘x’.
Definition: Function: Function is nothing but some formula or rule
between dependent and independent variable.
Functions are usually denoted by f, g, h, F, G etc.
We write this as y = f(x).
e.g.: 1) y= 2x +5 or f(x) = 2x + 5.
2) y = 𝑥2+ 2 x +5 are the functions.

6. Types of Functions
1) Constant function: The function of the type
y = C or f(x) = C , C is constant, is called a constant
function.
e.g.: 1) y = 5 or f(x) = 5
2) y = 10 or f(x) = 10
are constant functions.

7. Types of Functions Contd…..
2) Linear function: The function given as
y = a + b x or f(x) = a + b x , where a and b are
constants and b ≠ 0, is called a linear function.
Graph of this function is a straight line.
e.g.: 1) y = 6 + 3 x or f(x) = 6 + 3 x
2) y = 10 + 5 x or f(x) = 10 + 5 x
are linear functions.

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