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.

Graphical Representation of the Demand Curve

demand curve

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.

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