Question

If the quantity demanded for Apple is given by :
Qd= 300-2,55PA+7,62PB+0,75Y
If PA=90cents,PB=50cents and QD=860
Calculate and interpret the income elasticity of demand for apples.

Answer 1

Solution:

First derive Income value (Y):

Qd = 300 – 2.55PA + 7.62PB + 0.75Y

860 = 300 – 2.55(90) + 7.62(50) + 0.75Y

860 = 300 – 229.5 + 381 + 0.75Y

860 = 451.5 + 0.75Y

860 – 451.5 = 0.75Y

408.5 = 0.75Y

Y = 544.67

 

Income elasticity of demand for apples (YED) = $\frac{\triangle Q}{\triangle Y}\times \frac{ Y}{Q}$

$\frac{\triangle Q}{\triangle Y} = 0.75$

= $0.75\times \frac{ 544.67}{860} = 0.48$

 

Income elasticity of demand for apples (YED) = 0.48

The income elasticity of demand for apples is positive and between zero and 1. This means that YED of apples is income inelastic and a normal good and since the value is between zero and one, this means it is also a necessity.