Question

Price elasticity of demand of a good is -1 calculate percentage of change in price that will raise the demand from 20 units to 30 units

Answer 1

Price elasticity of demand (PED) is a measure of the sensitivity or responsiveness of quantity demanded to a change in own price of the good. PED is always negative.

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

$PED = \dfrac {\% \space ∆ \space in \space Qnty \space dd} {\% \space ∆ \space in \space own \space price}$

Let p% represent a percentage change in price.

$\% \space ∆ \space in \space Qnty \space dd = \dfrac {(Q_1 - Q_0)} {Q_0} × 100$

$From \space the \space given \space data \space : \\ Q_0 = 20 \space units \space and \space Q_1 = 30 \space units$

$\% \space ∆ \space in \space Qnty \space dd = \dfrac {(30 - 20)} {20} × 100$

$= 10 × 5$

$= 50 \%$

PED = -1, hence |PED| = 1

$Therefore, \\ PED = \dfrac {p \%} {50 \%}$

$=> 1 = \dfrac {p \%} {50 \%}$

$Cross \space multiplication \space gives: \\ p \% = 50 \% × 1$

$=> p \% = 50 \%$

Hence, the percentage change in price is 50%. Specifically, Price decreased by 50%

According to the law of demand, own price of a commodity and quantity demanded are inversely related, ceteris paribus.

Therefore, in this case, price fell by 50% since quantity demanded increased by 50%