Question

Mr. Ali was buying 10 kg of sugar when the price of one kg was Rs 100. Now the price has come down to Rs 75 and he is buying 15 kg of sugar. Find the point elasticity and the arc elasticity of demand for sugar by Ali?

Answer 1

ANSWERS

Point elasticity of demand = $-2$

Arch elasticity of demand $-1.4$

SOLUTIONS

Price elasticity of demand is a measure of the sensitivity of quantity demanded to changes in own price of the good. Point elasticity measure elasticity between two different points along the demand curve whereas arc elasticity measure elasticity at the mid point between two points.

We are given that,

$P_{0} = Rs \space 100, \space P_{1} = Rs \space 75$

$Thus, \space ∆P = P_{1} - P_{0}$

$= Rs \space 75 - Rs \space 100$

$= -Rs \space 25$

Also,

$Q_{0} = 10 \space kg, \space Q_{1} = 15 \space kg$

$Hence, \space ∆Q = Q_{1} - Q_{0}$

$= 15 \space kg - 10 \space kg$

$= 5 \space kg$

Point elasticity of demand.

$\eta_{d} = \dfrac {\dfrac{∆Q}{Q_{0}}×100}{\dfrac {∆P}{P_{0}}×100}$

$= \dfrac {∆Q}{Q_{0}} × \dfrac {P_{0}}{∆P}$

$= \dfrac {5 \space kg}{10 \space kg} × \dfrac {Rs \space 100}{-Rs \space 25}$

$= 0.5 × (-4)$

$= -2$

Arc elasticity of demand

Average quantity, $\hat {Q} = \dfrac {10 \space kg + 15 \space kg}{2}$

$= \dfrac {25 \space kg}{2}$

$= 12.5 \space kg$

Average price, $\hat {P} = \dfrac {Rs \space 100 + Rs \space 75}{2}$

$= \dfrac {Rs \space 175}{2}$

$= Rs \space 87.50$

Elasticity,

$\eta_{d} = \dfrac {\dfrac{∆Q}{\hat{Q}}×100}{\dfrac {∆P}{\hat{P}}×100}$

$= \dfrac {∆Q}{\hat{Q}} × \dfrac {\hat{P}}{∆P}$

$= \dfrac {5 \space kg}{12.5 \space kg} × \dfrac {Rs \space 87.50}{-Rs \space 25}$

$= 0.4 × (-3.5)$

$= -1.4$