Functions can model relationships between variables in business and economics. A function y=f(x) indicates that the dependent variable y depends on the independent variable x. For a business, total cost C can be a function of quantity produced Q, written as C=f(Q). Similarly, revenue R can be a function of Q, as R=f(Q). Profit π can then be derived as π=R-C. As an example, if a business has total cost function C=150+7Q and revenue function R=20Q, then the profit function is π=20Q-150-7Q. For multivariate functions with multiple independent variables, total cost C could depend on quantities

1. North South University School of Business and Economics
Application of Functions in Business and Economics
Functions:
Functions can be applied in situations when a particular variable (e.g. cost, demand) depends upon certain
other variable(s) (e.g. quantity of output produced, price).
The symbol of a function, 𝒚 = 𝒇 (𝒙) indicates that ‘𝒚’ depends upon ‘𝒙’ , here ‘𝒚’ is the dependent
variable and ‘𝒙’ is the independent variable (note: this function has only one independent variable and
hence are called univariate functions).
Application in business:
If a business firm produces only one product and Q is the amount of that product or output and C is the total
cost of production, then we can apply the above concept of function, i.e., C = f (Q) which implies the
total cost (C) of the business firm depends upon the amount of output produced (Q). Similarly if the
revenue (R) of the business firm depends only upon the output (Q) then we may write: R = f (Q).
Given, the above information we may derive the profit (𝝅) function using Profit = Revenue – Cost
𝝅 = 𝑹 − 𝑪
E.g. A particular business has the following total cost function: 𝐶 = 150 + 7𝑄
If the business produces 100 units, then Q = 100, and 𝐶 = 150 + 7(100) = 220
So, we may conclude (interpret) that the total cost of producing 100 units is $ 220.
E.g. If the revenue function of the same business is: 𝑅 = 20𝑄
then the profit function of the business can be derived: 𝝅 = 𝑹 − 𝑪 = 20𝑄 − 150 − 7𝑄
Now, if the business produces and sells 500 units, then, 𝜋 = 20(500) − 150 − 7(500) = 6350
So, we may conclude (interpret) from the last line that if the business produces and sells 500 units then it will
make a profit of $ 6350.
So far we have looked at univariate functions, i.e., functions containing only one independent variable.
Now let us look at the concept of multivariate functions (contains more than one independent variable).
Multivariate Functions:
If a business firm produces two products (A and B) and the amount of these two products are QA and QB
respectively, then the total cost of production (C) depends upon the amount of product A and B.
Hence, we can write: C = f (QA , QB) note: there are two independent variables here
E.g. 𝐶 = 𝑓(𝑄 𝐴, 𝑄 𝐵) = 3𝑄 𝐴
2
+ 𝑄 𝐵
2
Here, if the business produces 2 units of product A and 3 units of product B,
Then, 𝐶 = 𝑓(2, 3) = 3(2)2
+ 32
= 21
So we may conclude (interpret) that the total cost of producing 2 units of product A and 3 units of product B
is $ 21.
E.g. In a factory the amount of product or output (Q) produced depends upon the number of labor or
workers (L) and the number of machines or capital (K).
Hence, we may write: 𝑄 = 𝑓(𝐿, 𝐾) note: this function is called a production function
Let’s assume, 𝑄 = 10𝐿0.5
𝐾0.5
If the business employs 16 workers and 4 machines, then, 𝑄 = 10(16)0.5(4)0.5
= 80 𝑢𝑛𝑖𝑡𝑠
So, we may conclude (interpret) that if the business employs 16 workers and 4 machines then it can produce
80 units of product or output.