Answer to Question #130982 in Microeconomics for yasir

Question

Mr. Alex 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 Alex?

Answer 1

ANSWERS

Point elasticity of demand $= -2$

Arch elasticity of demand $= -1.4$

SOLUTIONS

Price elasticity of demand (PED) is a measure of the responaiveness of quantity demanded to changes in own price of a good. Point elasticity measures elasticity at a specific point, that is, between two points along a demand curve, however arc elasticity of demand measures elasticity of demand at the mid point between two points along a demand curve.

From the given data, the following is deduced:

$P_{0} = Rs \space 100, \space P_{1} = Rs \space 75 \\ Thus, \space ∆P = P_{1} - P_{0}$

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

$= -Rs \space 25$

Also,

$Q_{0} = 10 \space kg, \space Q_{1} = 15 \space kg \\ Thus, \space ∆Q = Q_{1} - Q_{0}$

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

$= 5 \space kg$

Where ∆ represent change.

Calculating Point elasticity of demand

$PED = \dfrac {percentage \space change \space in \space quantity \space demanded}{percentage \space change \space in \space own\space price}$

$= \dfrac {\%∆Q}{\%∆P}$

$\%∆Q = \dfrac {∆Q}{Q_{0}}×100$

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

$= 50 \%$

$\%∆P = \dfrac {∆P}{P_{0}}×100$

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

$= -25\%$

$\therefore \space PED = \dfrac {50\%}{-25\%}$

$= -2$

Calculating Arch elasticity of demand

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

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

$= 12.5 \space kg$

$$\therefore \space \%∆Q = \dfrac {5 \space kg}{12.5 \space kg}×100$$

$= 40\%$

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

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

$= Rs \space 87.50$

$Thus, \space \%∆P = \dfrac {-Rs \space 25} {Rs \space 87.50}× 100$

$= - 28.571429\%$

$\therefore \space PED = \dfrac {40\%}{-28.571429\%}$

$= -1.3999998$

$= -1.40$