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Question
A consumer spends Rs 1000 on a good priced at Rs 8 per unit. When price rises by 25 percent, the consumer continues to spend Rs 1000 on the good. Calculate the price elasticity of demand by percentage method.
Solution
Actual Total Expenditure (TE0 ) = Rs 1000
Change in Total Expenditure (TE1 ) = Rs 1000
Actual Price (P0) Rs 8
Percentage change in price 25%
Percentage change in price = `(P_1 - P_0)/P_0 xx 100`
`25 = (P_1 - 8)/8 xx 100`
`200/100 = P_1 - 8`
`P_1 = 10`
Therefore,
| Price (P) | Total Expenditure (TE) = Price (P) × Quantity (Q) | Quantity (Q) = `"TE"/P` |
| P0 = Rs 8 | TE0 = Rs 1000 | Q0 = 125 |
| P1 = Rs 10 | TE1 = Rs 1000 | Q1 = 100 |
`Ed = (-) "Percentage change in quantity demanded"/"Percentage change in price"`
`Ed = (-) ("Changeindemand"/"Actualdemand"xx100)/25`
Ed = (-) `((Q_1 - Q_0)/Q_0 xx 100)/25`
`Ed = (-) ((100 - 125)/125 xx 100)/25`
`Ed = (-) (-20)/25`
∴ Ed = 0.8
Thus, the price elasticity of demand is 0.8.
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