Answer to Question #131076 in Microeconomics for tooba

Question

Q.4150 Two points on the demand curve for volleyballs are shown (P, Q) = (19, 55) and (P, Q) = (21, 45). Where P is price per volley ball in pounds and Q is Quantity demanded.

a) What is the elasticity of demand between these two points?

Answer _____________________________________________________________________


b) What is the point elasticity of demand at price 19 when price rises to 21?

Answer 1

a) Answer: $\eta_{d} = -2$

Solution

The question requires arc elasticity of demand. Arc elasticity of demand calculates elasticity at the midpoint of the two given points; elasticity will not be affected by the direction of movement between the two points.

$∆P = |21 - 19|$

$= 2$

$∆Q = |45 - 55|$

$= 10$

Average price: $\hat P = \dfrac {19 + 21}{2}$

$= \dfrac {40}{2}$

$= 20$

Average quantity: $\hat Q = \dfrac {55 + 45}{2}$

$= \dfrac {100}{2}$

$= 50$

$\%∆P = \dfrac {∆P}{\hat P}×100\%$

$= \dfrac {2}{20}×100\%$

$= 10\%$

$\%∆Q = \dfrac {∆Q}{\hat Q}×100\%$

$= \dfrac {10}{50}×100\%$

$= 20\%$

Elasticity: $\eta_{d} = \dfrac {\%∆Q}{\%∆P}$

$= - \dfrac {20\%}{10\%}$

$= -2$

b) Answer: $\eta_{d} = -1.73$

Solution

$∆P = 21 - 19$

$= 2$

$∆Q = 45 - 55$

$= -10$

$\%∆P = \dfrac {∆P}{P_{0}}×100\%$

$= \dfrac {2}{19}×100\%$

$= 10.5263157\%$

$\%∆Q = \dfrac {∆Q}{Q_{0}}×100\%$

$= \dfrac {-10}{55}×100\%$

$= -18.1818181\%$

Elasticity: $\eta_{d} = \dfrac {\%∆Q}{\%∆P}$

$= \dfrac {-18.1818181\%}{+10.5263157\%}$

$= -1.72727273$

$= -1.73$