A consumer spends Rs 200 on a good priced at Rs 5 per unit. When the price falls by 20 percent, he continues to spend Rs 200. Find the price elasticity of demand by percentage method.
Solution
\[\text{ Initial Total Expenditure }\left( T E_0 \right) = Rs 200\]
\[\text{ Final Total Expenditure }\left( T E_1 \right) = Rs 200\]
\[\text{ Initial Price }\left( P_0 \right) = Rs 5\]
\[\text{ Percentage change in price }=  20\]
\[\text{ Percentage change in price }= \frac{P_1  P_0}{P_0} \times 100\]
\[  20 = \frac{P_1  5}{5} \times 100\]
\[\frac{ 100}{100} = P_1  5\]
\[ P_1 = 4\]
Price (P)  \[\text{Total Expenditure }\left( TE \right) = Price\left( P \right) \times Quantity\left( Q \right)\]

\[\text{ Quantity }\left( Q \right) = \frac{TE}{P}\]

P_{0} = Rs 5  TE_{0} = Rs 200  Q_{0} = 40 
P_{1}= Rs 4  TE_{1}_{ }= Rs 200  Q_{1}_{ }= 50 
\[E_d = \left(  \right)\frac{\text{ Percentage change in quantity demanded }}{\text{ Percentage change in price }}\]
\[ E_d = \left(  \right)\frac{\frac{Q_1  Q_0}{Q_0} \times 100}{ 20}\]
\[ E_d = \left(  \right)\frac{\frac{50  40}{40} \times 100}{ 20}\]
\[ E_d = \left(  \right)\frac{25}{ 20}\]
\[ E_d = 1 . 25\]
\[ \therefore E_d = 1 . 25 \]
Thus, the price elasticity of demand is 1.25.