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).

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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 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.

Types of Demand Function

2 types of demand function are:

Linear demand function
Non linear 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:

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 OF COMMODITY X	PRICE LEVELS OF COMMODITY 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:

What is Demand Function?