**Demand Function **is the relationship between the quantity demanded and the** **price of the commodity.

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

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## 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).

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

**D _{x} = f (P_{x})**

However, the quantitative relationship between D_{x} and P_{x} is expressed as:

**D _{x} = a – bP_{x}**

Where, a (intercept) and b (relationship between D_{x} and P_{x}) are constants.

Also Read: Law of Demand

## Types of Demand Function

2 **types of demand function** are:

### 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:

**D _{x} = a – bP_{x}**

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

b = slope or the relationship between D_{x} and P_{x}

b can also be denoted by change in D_{x} for change in P_{x}

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 P_{x}= 10:

Demand function is:

D_{x} = 50 – 2.5 (P_{x})

Therefore, D_{x} = 50 – 2.5 (10)

or D_{x}= 25 units

The demand schedule for the above function is given in Table

Quantity Demanded ofCommodity X | Price Levels ofCommodity X |
---|---|

5 | 18 |

10 | 16 |

15 | 14 |

20 | 12 |

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:

D_{x} = a (P_{x})^{-b}

Or of a rectangular hyperbola of the form

D_{x} = (a/P_{x} + 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:

Also Read: What is Demand?

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