Question

Assume that good A and good B are related goods and QB=1691-400PB+6PA-6Y. Suppose that PB=0.1 Birr, PA=0.3 Birr and Y (income) =10 Birr. Then compute.
- Price elasticity of demand for good B.
Income elasticity of demand for good B and
- explain nature of the good.
- Cross price elasticity of demand and state the nature of the goods whether they are substitute, complementary or unrelated.

Answer 1

Solution:

First derive the value of QB:

QB = 1691 – 400(0.1) + 6(0.3) – 6(10) = 1691 – 40 + 1.8 – 60 = 1691 + 1.8 – 40 – 60 = 1592.8

QB = 1592.8

a.). Price elasticity of demand for good B:

PEd = $\frac{\triangle Q}{\triangle PB }\times \frac{PB}{Q }$

$PEd = -400\times \frac{0.1}{1592.8 } = -0.025$

The demand for good B is price inelastic, that is demand is not sensitive to price changes.

b.). Income elasticity of demand for good B:

Income elasticity of demand (YEd) = $\frac{\triangle Q}{\triangle I }\times \frac{I}{Q }$

$-6\times \frac{10}{1592.8 } = -0.038$

The demand is income inelastic. Therefore, the good is inferior since it has a negative income elasticity of demand, which means that demand falls as income increases.

c.). Cross price elasticity of demand and state the nature of the goods:

Cross price elasticity of demand of good B with respect to good A:

Cross price elasticity of demand = $\frac{\triangle Q}{\triangle PA }\times \frac{PA}{Q }$

$6\times \frac{0.3}{1592.8 } = 0.0012$

The goods are substitutes since the value is greater than zero.