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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. - Economics

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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.

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Solution

Given:
\[\text{ Initial Total Expenditure }\left( T E_0 \right) = Rs 400\]
\[\text{ Final Total Expenditure }\left( T E_1 \right) = Rs 400\]
\[\text{ Initial Price }\left( P_0 \right) = Rs 4\]
\[\text{ Percentage change in price }= + 25\]
\[\text{ Percentage change in price }= \frac{P_1 - P_0}{P_0} \times 100\]
\[25 = \frac{P_1 - 4}{4} \times 100\]
\[\frac{100}{100} = P_1 - 4\]
\[ P_1 = 5\]

Price (P) \[\text{Total Expenditure }\left( TE \right) =\text{ Price }\left( P \right) \times \text{ Quantity }\left( Q \right)\]
 
\[\text{ Quantity }\left( Q \right) = \frac{TE}{P}\]+
P0 = Rs 4 TE0 = Rs 400  Q0 = 100
P1= Rs 5 TE1 = Rs 400 Q1 = 80

Now,
\[E_d = \left( - \right)\frac{\text{ Percentage change in quantity demanded }}{\text{ Percentage change in price }}\]
\[ E_d = \left( - \right)\frac{\frac{Q_1 - Q_0}{Q_0} \times 100}{25}\]
\[ E_d = \left( - \right)\frac{\frac{80 - 100}{100} \times 100}{25}\]
\[ E_d = \left( - \right)\frac{- 20}{25}\]
\[ E_d = 0 . 8\]
\[ \therefore E_d = 0 . 8 \]

Thus, the price elasticity of demand is 0.8.
Concept: Elasticity of Demand
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