#### Question

A consumer spends Rs 60 on a good priced at Rs 5 per unit. When price rises by 20 percent, the consumer continues to spend Rs 60 on the good. Calculate the price elasticity of demand by percentage method.

#### Solution

Given that

Actual Total Expenditure (TE_{0}) Rs 60

Final Total Expenditure (TE_{1}) Rs 60

Actual Price (P_{0}) Rs 5

Percentage change in price = -20%

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

`-20 = (P_1 - 5)/5 xx 100`

`- 100/100 = P_1 - 5`

`P_1 = 4`

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

P_{0} = Rs 5 |
TE_{0} = Rs 60 |
Q_{0} = 1 |

P_{1} = Rs 4 |
TE_{1} = Rs 60 |
Q_{1}= 15 |

Therefore,

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

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

Ed = `((Q_1 -Q_0)/Q_0 xx 100)/(-20)`

Ed = (-) `((15 - 12)/12 xx 100)/(-20)`

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

∴ Ed 1.25

Thus, the price elasticity of demand is 1.25