Question

. For each of the following demand functions, determine if the good is normal or inferior. If it is normal, is it a necessary, or luxury good? x1 = 1000 + p2 √ m − p1 √ m

Answer 1

x₁ =1000 + p₂ $\sqrt{}$ m - p₁  $\sqrt{}$  m

x₁ =1000+  $\sqrt{}$  m (p₂- p₁)

Take the first order differentiation of x₁ w.r.t m , we get:

= 1/2 (p₂- p₁) m^-1/2

Income elasticity of demand = 1/2 (p₂- p₁) m^-1/2 (m/x₁) > 0.

Because income elasticity is greater than 0 or positive .This implies that the good is a normal good.

The income elasticity is less than 1 , therefore ,it is a necessity good.

If the income elasticity is more than 1 ,then it would be a luxury good.