Question

A consumer spends Rs.400 on a good priced at Rs.8 per unit. When its price falls by 25 per cent, the consumer spends Rs.500 on the good. Calculate the price elasticity of demand by the percentage method.

Answer 1

Hint: Here the price elasticity of demand (PED) is an economic measure of the change in the quantity demanded of a product related to its change in price. Price of elasticity basically measures the responsiveness of demand after the change in price. In general, people desire less things if those things become more expensive. The demand is price elastic if the price change leads to a bigger % change in demand, then the PED will be therefore greater than 1.

Complete step-by-step solution:
Given that the initial price per unit = Rs.8
Expenditure by the consumer when Rs.8 per unit = Rs.400
When the price falls by 25% of the initial price of Rs.8 is given by:
\[ \Rightarrow 8 \times \dfrac{{25}}{{100}} = 2\]
$\therefore $The fall in price is Rs.2 , as it is the 25% of Rs.8
Now the new price per unit is given by:
$ \Rightarrow $Rs.8 – Rs.2 = Rs.6
$\therefore $The new price per unit is Rs.6
Expenditure by the consumer when Rs.6 per unit = Rs.500

Price (in Rs.)	Expenditure (in Rs.)	Quantity demand (No. of units purchased)
$8$	$400$	\[\dfrac{{400}}{8} = 50\]
$6$	$500$	$\dfrac{{500}}{6} = 83.33$

Now calculating the % change in demand quantity :
$ \Rightarrow \dfrac{{50 - 83.33}}{{50}} \times 100 = - 66.66\% $
$\therefore $The % change in demand quantity is -66.66%.
Now the price elasticity of demand is given by the negative of the ratio of % change in demand to the ratio of % change in price.
$ \Rightarrow $- (% change in demand)/(% change in price)
$\therefore $Price elasticity of demand $ = - \dfrac{{( - 66.66\% )}}{{25\% }}$
$ \Rightarrow - \dfrac{{( - 66.66\% )}}{{25\% }} = 2.6667$
$ \simeq 2.67$

The price elasticity of demand is 2.67

Note: Note that given to find out the price elastic demand, therefore the price elastic demand is always greater than 1. But the price inelastic demand is less than 1.