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. - Economics

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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.

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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) \[\text{Total Expenditure }\left( TE \right) = Price\left( P \right) \times Quantity\left( Q \right)\]
 
\[\text{ Quantity }\left( Q \right) = \frac{TE}{P}\]
P0 = Rs 5 TE0 = Rs 200  Q0 = 40
P1= Rs 4 TE1 = Rs 200 Q1 = 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.

Concept: Elasticity of Demand
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