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

Answer 1

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.