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