Demand Function

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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.

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: Law of Demand


Types of Demand Function

2 types of demand function are:

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  1. Linear demand function
  2. 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:

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

Quantity Demanded of
Commodity X

5
10
15
20

Price Levels of
Commodity X

18
16
14
12

Demand Curve in Linear Demand Function
Demand Curve in Linear Demand Function

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

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:

Non linear Demand Function
Non linear Demand Function

Read: What is Demand?

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.

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