Question

Price X Y

20 40 50

30 40 40

40 60 50

50 55 60

60 60 40

70 70 60

1. Find the cross elasticity of commodity X and Y when price changed from

i. 20 to 30

ii. 40 to 50 

iii. 60 to 70

2. Interpret your answers in I, ii and iii above 

Answer 1

Cross Price Elasticity

$E_{xy}=\frac{\% change\ in\ Quantity\ of\ X}{\% change\ in\ price\ of\ Y}$

20 to 30

$E_{xy}=\frac{(0/40}{10/30}=0$

40 to 50

$E_{xy}=\frac{(-5/55)}{(10/50)}=-0.45$

60 to 70

$E_{xy}=\frac{(10/70)}{(10/70)}=1$

Interpretation

20 to 30

With a zero cross price elasticity, it can be interpreted as good X and Y are neither substitutes nor complements.

40 to 50

With a negative cross price elasticity of demand, the quantity of good X demanded reduces with the increase in price of good Y.

60 to 70

With a cross price elasticity equal to one, it symbolizes a unitary elasticity where, a unit change in price of good Y results to a unit change in demand for X.