Consider the demand curve $\mathrm { Q } ^ { \mathrm { d } } = 500 \mathrm { P } - 2$. If the price is 1 , the elasticity of demand is
A) $- 0.50$
B) $- 2$
C) 500
D) $- 500$

Question

Quizplus · Accepted Answer

The formula for elasticity of demand is

\begin{align*}
E_{d} &= \frac{	ext{percentage change in quantity demanded}}{	ext{percentage change in price}} \
&= \frac{\frac{\Delta Q/Q}{\Delta P/P}}{	ext{absolute value of } \frac{\Delta P}{P}}
\end{align*}

Plugging in the values when the price is 1, we get:

\begin{align*}
E_{d} &= \frac{\frac{\Delta Q/Q}{\Delta P/P}}{	ext{absolute value of } \frac{\Delta P}{P}} \
&= \frac{\frac{500}{1}\cdot \frac{-1}{500}}{	ext{absolute value of } \frac{-1}{1}} \
&= 2
\end{align*}

We take the absolute value of the percentage change in price because elasticity of demand is always positive by definition. Therefore, the best answer is (B).

Consider the Demand Curve Qd=500P−2\mathrm { Q } ^ { \mathrm { d } } = 500 \mathrm { P } - 2Qd=500P−2

Consider the Demand Curve $\mathrm { Q } ^ { \mathrm { d } } = 500 \mathrm { P } - 2$