Question

1. Income elasticity of demand

Calculate the income elasticity of demand for the following demand functions and assess its magnitude (is the good normal, inferior, a luxury or a necessity?).

1. Q =50 -10p + 3Y, at p = 2 and Y = 20

2. Q = 5 - 20p + 4Y, at p = 1 and Y = 50

3. Q = 70 – 3p – 2Y, at p = 15 and Y = 5

4.   Q = 35 - 20p + 0.5Y, at p = 1.5 and Y = $1,000,000,000

Answer 1

Income elasticity of demand, E =

where dQ/dY can be found using demand function.

a) Q = 50 -10p + 3Y, at p = 2 and Y = 20
So, Q = 50 - 10(2) + 3(20) = 50 - 20 + 60 = 90
E = (3)*(20/90) = 0.67
As 0 < E < 1 so the good is normal good and it is a necessity.

b) Q = 5 - 20p + 4Y, at p = 1 and Y = 50
So, Q = 5 - 20(1) + 4(50) = 5 - 20 + 200 = 185
So, E = 4*(50/185) = 1.08
As E > 1 so the good is normal good and it is a luxury.

c) Q = 70 – 3p – 2Y, at p = 15 and Y = 5
So, Q = 70 – 3(15) – 2(5) = 70 - 45 - 10 = 15
So, E = (-2)*(5/15) = -0.67
As E < 0, so the good is inferior.

d) Q = 35 - 20p + 0.5Y, at p = 1.5 and Y = $1,000,000,000
So, Q = 35 - 20(1.5) + 0.5(1,000,000,000) = 35 - 30 + 500,000,000 = 500,000,005
So, E = (0.5)*(1,000,000,000/500,000,005) = 1
As E = 1, so the good is normal.