Question

Suppose the demand for commodity X is estimated as follows:
X=68-1.6Px + 0.6Py + 0.08M

Where:
X=quantity of commodity X
Px=N20 is the price of X
Py= N40 is the price of Y
M=N1000 is the income of the consumer

Calculate:
1. The price elasticity of X
2. The cross-price elasticity of demand for X with respect to the change in the price of Y
3. The income elasticity of demand X .
Also interpret your result is in 1,2, and 3

Answer 1

$X=68-1.6PX + 0.6Py + 0.08M$

Given

Pc=20,PY=40 ,m=1000

$X=68-1.6(20) + 0.6(40) + 0.08(1000)\\=140\space units$

1) price elasticity of X

$=\frac{dX}{dPX}×\frac{PX}{X}\\=-1.6×\frac{20}{140}\\=-0.23$

$0.23<1, inelastic$

2)

The cross-price elasticity of demand for X with respect to the change in the price of Y

$=\frac{dX}{dPy}×\frac{Py}{X}\\=0.6×\frac{40}{140}\\=0.17$

$0.17>0,substitutes$

3)

The income elasticity of demand X

$=\frac{dX}{dPyM}×\frac{M}{X}\\=0.08×\frac{1000}{140}\\=0.57$

$0.57>0, normal \space good$