Question

A consumer buys a certain quantity of a good at a price of Rs.10 per unit. When price falls to Rs.8 per unit, she buys 40 per cent quantity. Calculate price elasticity of demand.

Answer 1

Hint: To find price elasticity of demand, we will use the formula ${{\text{E}}_{d}}=\dfrac{\%\Delta \text{ in Qd}}{\%\Delta \text{ in P}}$ , where $\%\Delta \text{ in Qd}$ is the percentage change in the quantity and $\%\Delta \text{ in P}$ is the percentage change in the price. We are given with $\%\Delta \text{ in Qd}$ which is 40%. We have to find $\%\Delta \text{ in P}$ using the formula $\%\Delta \text{ in P}=\dfrac{\Delta P}{P}\times 100$ . We can find $\Delta P$ by subtracting the initial price from the new price.

Complete step by step answer:
We have to find the price elasticity of demand. We know that Price Elasticity of Demand (PED) is the percentage change in the quantity demanded of a good or service by the percentage change in the price.
$\Rightarrow {{\text{E}}_{d}}=\dfrac{\%\Delta \text{ in Qd}}{\%\Delta \text{ in P}}$
where $\%\Delta \text{ in Qd}$ is the percentage change in the quantity and $%\Delta \text{ in P}$ is the percentage change in the price.
We are given that $\%\Delta \text{ in Qd}=40\%$ . We have to find $\%\Delta \text{ in P}$ . We can write the percentage change in the price as follows.
$\Rightarrow \%\Delta \text{ in P}=\dfrac{\Delta P}{P}\times 100...\left( i \right)$
We are given that the initial price of the goods is Rs.10.
$\Rightarrow P=\text{Rs }10$
We are also given with the new price of the good as
\[\Rightarrow {{P}_{1}}=\text{Rs }8\]
We can find the change in the price, that is $\Delta P$ , by subtracting the initial price from the new price.
$\Rightarrow \Delta P={{P}_{1}}-P=8-10=\left( - \right)\text{Rs }2$
Let us substitute these values in the formula (i).
$\begin{align}
  & \Rightarrow\%\Delta \text{ in P}=\dfrac{-2}{10}\times 100 \\
 & \Rightarrow \%\Delta \text{ in P}=\left( - \right)20\% \\
\end{align}$
Now, we have to substitute the values in the formula for PED.
$\begin{align}
  & \Rightarrow {{\text{E}}_{d}}=\dfrac{40\%}{-20\%} \\
 & \Rightarrow {{\text{E}}_{d}}=-2 \\
\end{align}$
Hence, the price elasticity of demand is -2.

Note: Students must be thorough with all the formulas related to PED. We have found the PED to be -2 which is a negative value. PED will always be negative meaning that there exists an inverse relationship between the price and demand. A value of PED, which is lesser than 1 is considered as relatively inelastic demand, while a value more than 1 suggests relatively elastic demand. Here, we obtained PED less than 1. Hence, the demand is inelastic.