Question

A consumer spends Rs. 400 on a good priced at Rs. 4 per unit. When the price rises by 25 percent, the consumer continues to spend Rs. 400. Calculate the price elasticity of demand by percentage method.

Answer 1

Given:

Initial Total Expenditure $\left(T{E}_0\right)=Rs.400$

Final Total Expenditure $\left(T{E}_1\right)=Rs.400$

Initial Price $\left(P_0\right)=Rs.4$

Percentage change in price $=+25$

Percentage change in price $=\frac{P_1-P_0}{P_0}\times 100$

$25=\frac{P_1-4}{4}\times 100$

$\frac{100}{100}=P_1-4$

$P_1=5$

Price $\left(P\right)$	Total Expenditure $\left(TE\right)=$ Price $\left(P\right)$ $\times$ Quantity $\left(Q\right)$	Quantity $\left(Q\right)=\frac{TE}{P}$
$P_0=Rs.4$	$T{E}_0=Rs.400$	$Q_0=100$
$P_1=Rs.1$	$T{E}_1=Rs.400$	$Q_1=80$

Now,

$E_d=(-)\frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$

$E_d=(-)\frac{\frac{Q_1-Q_0}{Q_0}\times 100}{25}$

$E_d=(-)\frac{\frac{80-100}{100}\times 100}{25}$

$E_d=(-)\frac{-20}{25}$

$E_d=0.8$

$\therefore E_d=0.8$

Thus, the price eleasicity of demand is $0.8$.