Question

Suppose that a change in the price of bread from R10 to R12.50 leads to a change in the quantity demanded of bread from 65 units to 90 units. Use the arc elasticity method to calculate and interpret the price elasticity of demand for bread

Answer 1

$$Solution$$

The arc price elasticity of demand measures the responsiveness of quantity demanded to a price. Arc elasticity measures elasticity at the midpoint between two selected points on the demand curve by using a midpoint between the two points.

This can be obtained as shown below;

$Arc Ed = [(Qd2 – Qd1) / midpoint Qd] ÷ [(P2 – P1) / midpoint P]$

$Midpoint\ Qd = \frac{Qd_1 + Qd_2} {2} =\frac{90+65}{2}=77.5\\ Midpoint\ Price = \frac{P_1 + P_2} {2} =\frac{12.50+10}{2}=11.25\\ \%\ change\ in\ qty\ demanded =\frac{90-65}{77.5}=0.3226\\ \%\ change\ in\ price = \frac{12.50-10}{2}=1.25\\ Arc\ E_d =\frac{0.3226}{1.25}=0.25808$

We can conclude that the price elasticity of bread, when the price increases from 12.5 to 10, is 0.26.