Answer to Question #169094 in Microeconomics for Bart

Question

Suppose the monthly demand for soda by a consumer is given by Q = 40 - 10P. At a price of $2 and quantity of 20, what is the own-price elasticity of demand for soda?

Answer 1

$\bold {Answer}$

Own-price elasticity of demand, $\eta_P = \bold {-1}$

Elasticity is unitary.

$\bold {Solution}$

Own price elasticity of demand $(\eta_p)$ is a measure of the sensitivity of quantity demanded to changes in own price of a good.

$\eta_p = \dfrac {dQ}{dP} × \dfrac {P}{Q}$

$\dfrac {dQ}{dP} = \dfrac {d}{dP}(40-10P)$

$= -10$

$When \space P= \$2, \space Q = 20 \space units$

$Thus,$

$\eta_p = -10 × \dfrac {2}{20}$

$= \bold {-1}$

Hence, the own price elasticity of demand is unitary.