Question

^{Assume the quantity demanded for a particular commodity is given by the formula (Q)= 8000P^(-1.5). Compute the elasticity of demand}

Answer 1

Solution:

Elasticity of demand (Ed) =$\frac{\%\triangle Q}{\%\triangle P} = \frac{\triangle Q}{\triangle P}\times \frac{ P}{Q}$

This is a constant elasticity of demand:

E_d = $\frac{\triangle Q}{\triangle P}\times \frac{ P}{Q}$

$\frac{\triangle Q}{\triangle P} = -12,000P^{-2.5}$

$\frac{ P}{Q} = \frac{ P}{8,000P^{-1.5} }$

E_d = $-12,000P^{-2.5} \times \frac{ P}{8,000P^{-1.5} } = -1.5P^{-2.5} \times \frac{ P}{P^{-1.5} }$

= $= -1.5P^{-2.5} P P^{1.5} = -1.5P^{-2.5} P^{2.5} = -1.5$

Elasticity of demand (E_d) = -1.5