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.

Answer 1

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.