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Question
A consumer spends Rs 100 on a good priced at Rs 4 per unit. When price rises by 50 percent, the consumer continues to spend Rs 100 on the good. Calculate the price elasticity of demand by percentage method
Solution
Given:
Actual Total Expenditure (TE0) Rs 100
Change in Total Expenditure (TE1) Rs 100
Actual Price (P0) Rs 4
Percentage change in price = -50
Percentage change in pri = `(P_1 - P_0)/P_0 xx 100`
`-50 = (P_1 - 4)/4 xx 100`
`(-200)/100 = P_1 - 4`
`P_1 = 2`
Therefore,
| Price (P) | Total Expenditure (TE) = Price (P) × Quantity (Q) | Quantity (Q) = `"TE"/P` |
| P0 = Rs 4 | TE0 = Rs 100 | Q0 = 25 |
| P1 = Rs 2 | TE1 = Rs 100 | Q1= 50 |
Ed = (-) `"Percentage change in quantity demanded"/"Percentage change in price"`
Ed = (-) `("Change in demand"/"Actual demand" xx 100)/(-50)`
Ed = (-) `((Q_1 - Q_2)/Q_0 xx 100)/(-50)`
Ed = (-) `((50 - 25)/25 xx 100)/(-50)`
`Ed = (-) 100/(-5)`
∴ Ed = 2
Thus, the price elasticity of demand is 2.
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