Question

A consumer buys 10 units of a commodity at a price of Rs. 10 per unit. He incurs an expenditure of Rs. 200 on buying 20 units. Calculate price elasticity of demand by percentage method. Comment on the shape of the demand curve based on this information.

Answer 1

$\begin{array}{ccc}\text{Price (P)}& \text{Quantity demanded}& \text{Total expenditure}\\ \left(P\right)& \left(\text{units}\right(Q\left)\right)\left(Rs\right)& \left(Rs\right)(P\times Q)\\ 10& 10& 100\\ 10& 20& 200\end{array}$

Total Expenditure = Price $\left(P_1\right)\times \text{Quantity}\left(Q_1\right)$

$200=Price\left(P_1\right)\times 20$

$200÷20=Price\left(P_1\right)$

Price $P_1=Rs.10$ per unit.

$\Delta P=10-10=0,\Delta Q=20-10=10$

Percentage Change in Quantity Demanded

$=\frac{\Delta Q}{Q}\times 100=\frac{10}{10}\times 100=100\%$

Percentage Change in Price

$=\frac{\Delta P}{P}\times 100=\frac{10}{10}\times 100=0\%$

$E_d=\frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}$

or $E_d=\infty =\frac{100}{0}=\infty$

Elasticity of demand is perfectly elastic. Therefore, demand curve is a straight line parallel to X-axis.