Question

Calculate the income elasticities for the following demand functions.

a) x(p,m) = m/2p*

b) x(p,m) = 10/p*

Answer 1

Demand is given by $x =\frac{ m}{(2p)}$

Price elasticity is given by

$Ep=\frac{ \frac{dx}{x}}{ \frac{dp}{p}} =\frac{ dx}{dp} \times \frac{p}{x}$

$\frac{dx}{dp} = \frac{-m}{2} \times \frac{ 1}{p\\^2}$

Plugging in,

$Ep=\frac{ -m}{2} \times \frac{ 1}{p^2} \times \frac{2p^2}{m} = -1$

Income elasticity is given by

$Em =\frac{\frac{dx}{x}}{ \frac{dm}{m}} = \frac{dx}{dm} \times \frac{m}{x}$

$\frac{dx}{dm} =\frac{ 1}{2p}$

Plugging in,

$Em= \frac{1}{(2p)} \times 2p = 1$