# Demand Function Concept with Examples

## Introduction:

• The demand for a good/commodity is indicated by the desire to purchase the good and his/her willingness to pay for it at a particular price at a particular time. Price is one of the major factors that influence Demand. However, there are several factors that affect the demand apart from Price of the good.

## Demand Function:

• The demand function shows an algebraic relationship between Demand and the factors that influence demand. It is a functional expression between Demand & its determinants. Here Demand is taken as a dependent variable & the determinants/factors are taken as independent variables
• Price of the good is the primary factor that affects demand and therefore is one of the determinants of the demand function. The relationship between demand & price of the good keeping all other factors constant (ceteris paribus) is reflected in the Law of Demand which shows an inverse relationship between the demand of a good & its price. (Px)

#### The demand function can also be studied under two separate modes:

• Individual Demand deals with the demand of an individual consumer of a particular good in study. One could map out a schedule for the quantity demanded by the consumer at various prices. It helps in studying the behaviour of an individual consumer/firm.
• Market Demand deals with aggregate demand for a good in the market. It is the sum of all individual demands of a particular good at a particular price.

### A linear Demand function takes the form:

Q = a – b P
• Where Q denotes Quantity Demanded, P denotes Price.
• a is the intercept & b is the slope of the demand curve. If Price of a good rise by 1 unit, the quantity demanded would fall by ‘b’ units.
• Since there is an inverse relationship between quantity demanded & its price, the function is negatively sloped i.e. the demand curve slopes downwards.

## Numerical Questions for Practice

#### 1.

The linear demand function of a good X is given by Q = 100 – 6P.
a. Determine quantity demanded when Price is 5 ₹
b. Determine the Price at which Qty demanded will be 40 units.

#### Solution:

(a) Q = 100 – 6(5) = 100 – 30 = 70
(b) 40 = 100 – 6P, hence, P = 10 ₹

#### 2.

The demand function for a soft drink (x) is given by Qx = 500 – 3P + 0.2 I + 0.3 P{where, P stands for Price of Soft-drink(x), I stands for consumer’s income, and Py stands for Price of another good (y)}.
a. What can be deduced about the relation between x & y?
b. If consumer income is fixed at ₹ 1000 and the price of Y is fixed at ₹ 100, then give the demand function.

#### Solution:

(a) Since the sign of the coefficient of Py is positive, it shows that there is a positive relationship between Price of Y and Demand of X i.e. if Price of Y rises, Quantity Demanded of X rises. This shows X & Y are substitutes. (Say, Y could be a natural fruit juice).
(b) Substituting the values gives, Qx = 500 – 3P + 0.2(1000) + 0.3(100) = 500 – 3P + 200 + 30
Hence, Qx = 730 – 3P is the demand function.

#### 3.

The individual demand curve of firm A is given by QA = 90 – 0.4 P and individual demand curve for Firm B is given by QB = 100 – 0.2P.
a. Calculate combined demand function if the market has only two firms A & B
b. Deduce the market demand at the price of 20 ₹

#### Solution:

(a) Combined Demand = QA + QB = 90 + 100 – (0.4 + 0.2) P = 190 – 0.6 P
(b) At P = 20, Demand would be = 190 – 0.6(20) = 190 -12 = 178 units. 