# What is Demand Function? Types, Example, Graph, Formula

## What is Demand Function?

Demand function represents the relationship between the quantity demanded for a commodity (dependent variable) and the price of the commodity (independent variable).

## Demand Function Formula

Mathematically, a function is a symbolic representation of the relationship between dependent and independent variables.

Let us assume that the quantity demanded of a commodity X is Dx, which depends only on its price Px, while other factors are constant. It can be mathematically represented as:

Dx = f (Px)

However, the quantitative relationship between Dx and Px is expressed as:

Dx = a – bPx

Where a (intercept) and b (relationship between Dx and Px) are constants.

## Types of Demand Function

### Linear demand function

In the linear demand function, the slope of the demand curve remains constant throughout its length. A linear demand equation is mathematically expressed as:

Dx = a – bPx

In this equation, a denotes the total demand at zero price.

b = slope or the relationship between Dx and Px

b can also be denoted by change in Dx for change in Px

If the values of a and b are known, the demand for a commodity at any given price can be computed using the equation given above.

For example, let us assume a = 50, b = 2.5, and Px= 10:

Demand function is:

Dx = 50 – 2.5 (Px)

Therefore, Dx = 50 – 2.5 (10)
or Dx= 25 units

The demand schedule for the above function is given in Table

When the demand schedule is plotted on a graph, it produces a linear demand curve, which is shown in Figure below.

### Non linear demand function

In the non linear or curvilinear demand function, the slope of the demand curve (ΔP/ΔQ) changes along the demand curve. Instead of a demand line, non-linear demand function yields a demand curve.

A non-linear demand equation is mathematically expressed as:

Dx = a (Px)-b

Or of a rectangular hyperbola of the form

Dx = (a/Px + c) b

where a, b, c> 0

Exponent –b of price in the non-linear demand function refers to the coefficient of the price elasticity of demand.

Figure, represents a non-linear demand function:

Reference
1. D N Dwivedi, Managerial Economics, 8th ed, Vikas Publishing House

2. Petersen, Lewis & Jain, Managerial Economics, 4e, Pearson Education India

3. Brigham, & Pappas, (1972). Managerial economics, 13ed. Hinsdale, Ill.: Dryden Press.

4. Dean, J. (1951). Managerial economics (1st ed.). New York: Prentice-Hall.