A consumer spends Rs 100 on a good priced at Rs 4 per unit. When its price falls by 25 percent, the consumer spends Rs 75 on the good. Calculate the price elasticity of demand by the Percentage method.

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#### Solution

Given:

Actual Total Expenditure (TE_{0}) Rs 100

Change in Total Expenditure (TE_{1}) Rs 75

Actual Price (P_{0}) Rs 4

Percentage change in price - -25

Percentage change in price = `(P_1 - P_0)/P_0 xx 100`

`= -25 = (P_1 - 4)/4 xx 100`

`(-100)/100 = P_1 - 4`

`P_1 = 3`

Therefore,

Price (P) |
Total Expenditure (TE) = Price (P) × Quantity (Q | Quantity (Q) = `"TE"/P` |

P_{0} = Rs = 4 |
TE_{0} = Rs 100 |
Q_{0} = 2 |

P_{1} = Rs 3 |
TE_{1} = Rs 75 |
Q_{1}= 25 |

`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 = (-) ((25 - 25)/25 xx 100)/-25`

`Ed = (-) (-20)/25`

∴ Ed = 0

Thus, the price elasticity of demand is 0.

Concept: Elasticity of Demand

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