**Definition:** **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 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.

Read: What is Economics? Definition, Meaning, Assumption

## Two Types of Demand Function

There are mainly two types of demand functions, which are discussed below:

### 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

### 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

Dx = a/Px + c

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

Read: Demand Function in Economics | Two Type

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