Question

Solve the following problems on Cross elasticity of demand and classify the nature of relationship between the two goods. 6)A consumer had purchased 2 kg. of Society tea powder (Good X) when the price of Wagh bakri tea powder (Good Y) was Rs.400/- per kg. Later on the price of Wagh bakri tea rises to Rs. 430/- per kg. As a result the consumers demand for Society tea powder rises to Rs.4 kg. 7) A consumer had purchased 12 numbers of ball pen (Good X) when the price of Classmate brand Note book (Good Y) was Rs.100 /- each. Later on the price of Classmate brand note book rises to Rs.130/- each, as a result the consumers demand for ball pen falls to 6 units.

Answer 1

(6)

Cross elasticity of demand=$\frac{\%change in quantity}{\%change in price}$

$\%$ change in quantity=${\frac{Q_{2}-Q_{1}}{(Q_2+Q_{1})\div2}\times 100\%}={\frac{{4}-{2}}{(4+{2})\div2}\times 100\%}=66.66\%$

$\%$ change in price=${\frac{P_{2}-P_{1}}{(P_2+P_{1})\div2}\times 100\%}={\frac{{430}-{400}}{(430+{400})\div2}\times 100\%}=7.23\%$

Cross price elasticity=$\frac{66.66\%}{7.23\%}=+9.22$

The cross price elasticity of demand is positive therefore the good are substitute goods.

(7)

Cross elasticity of demand=$\frac{\%change in quantity}{\%change in price}$

$\%$ change in quantity=${\frac{Q_{2}-Q_{1}}{(Q_2+Q_{1})\div2}\times 100\%}={\frac{{6}-{12}}{(12+{8})\div2}\times 100\%}=-66.66\%$

$\%$ change in price=${\frac{P_{2}-P_{1}}{(P_2+P_{1})\div2}\times 100\%}={\frac{{130}-{100}}{(130+{100})\div2}\times 100\%}=26.08\%$

Cross price elasticity of demand=$\frac{-66.66\%}{26.08\%}=-2.56$

The cross price elasticity of demand is negative therefore the good are complementary goods.