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.
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.
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