Answer to Question #193810 in Microeconomics for ahsan

Question

Colgate sells its standard size toothpaste for Rs. 25. Its sales have been on an average 8000 units per month over the last year. Recently, its competitor Sparkle reduced the price of its same standard size toothpaste from Rs. 35 to Rs. 30. As a result Colgate sales declined by 1500 units per month.

i)                  Calculate the cross elasticity between the two products.

ii)                What does your estimate indicate about the relationship between the two?

Answer 1

Solution:

i.). The cross elasticity of demand measures how sensitive the demand of a product is over a change in a corresponding product price.

The formula for cross elasticity of demand for Colgate and Sparkle will be as follows:

Cross elasticity of demand (XED) =$=\frac{\%\;change\; in\; quantity\; of\; Colgate}{\%\; change\; in\; price\;of\;Sparkle}$

Percentage change in the quantity of Colgate = $=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \times 100$

= $\frac{6500 -8000}{(6500+8000)/2 } \times 100 = \frac{-1500}{7250} \times 100 = -20.69\%$

 

Percentage change in the price of Sparkle = $\frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 } \times 100$

= $\frac{30 -35}{(30+35)/2 } \times 100 = \frac{-5}{32.5} \times 100 = -15.38\%$

 

Cross elasticity of demand (XED) = $\frac{-20.69\%}{-15.38\%} = 1.35$

 

ii.). The cross elasticity of demand between Colgate and Sparkle is positive. This means that Colgate and Sparkle are substitute goods. That is, a decrease in the price of Sparkle products will result in consumers purchasing more of it and less of Colgate products.