Answer to Question #145655 in Microeconomics for Caroline Mwatela

Question

Given the demand function Qd = 400 - Q2

Compute the price elasticity of demand when P= 10, and comment on the elasticity of the good.

Answer 1

$\bold {Answer}$

$\eta_d =$ $-0.667$

It is Inelastic since $\left| -0.667 \right | < 1$

$\bold {Solution}$

We are given $Q_d = 400 - P^2$

When $P = 10,$ $Q_d = 400 - (10)^2$

$= 400-100$

$= 300$

$\eta_d = \dfrac {dQ}{dP} × \dfrac {P_0}{Q_0}$

$\dfrac {dQ}{dP} = \dfrac {d}{dP} (400-P^2)$

$= -2P$

When $P = 10,$ $\dfrac {dQ}{dP} = -2(10)$

$= -20$

Therefore, $\eta_d = -20 × \dfrac {10}{300}$

$=- \dfrac {200}{300}$

$= -0.666666667$

$= \bold {-0.667}$

$\therefore \space$ the elasticity of demand is $\bold {-0.667}$ and it is $\bold {inelastic}.$