#### Question

A consumer spends Rs 1,000 on a good priced at Rs10 per unit. When its price falls by 20 percent, the consumer spends Rs800 on the good. Calculate the price elasticity of demand by the Percentage method

#### Solution

Given:

Actual Total Expenditure (TE_{0}) Rs 1000

Change in Total Expenditure (TE_{1}) Rs 800

Actual Price (P_{0}) Rs 10

Percentage change in price = -20

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

`-20 = (P_1 - 10)/10 xx 100`

`(-200)/100 = P_1 - 10`

`P_1 = 8`

Therefore,

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

P_{0} = Rs 10 |
TE_{0} = Rs 1000 |
Q_{0} = 100 |

P_{1} = Rs 8 |
TE_{1} = Rs 80 |
Q_{1} = 100 |

Ed = (-) `"Percentage change in quantity demaded"/"Percentage change in price"`

Ed = (-) `("Changeindemand"/"Actualdemand" xx 100)/(-20)`

Ed = (-) `((Q_1 - Q_2)/100 xx 100)/(-20)`

Ed = (-) `((100 - 100)/100 xx 100)/(-20)`

∴ Ed = 0

Thus, the price elasticity of demand is 0.

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Solution A consumer spends Rs 1,000 on a good priced at Rs10 per unit. When its price falls by 20 percent, the consumer spends Rs800 on the good. Calculate the price elasticity of demand by the Percentage method Concept: Elasticity of Demand.