Question

A car manufacturer producers two (2) core products: SUVs (product X) and sports cars (Product Y). Sports cars are selling at $20,000 per units, and SUVs have a selling price of $40,000 per unit. Due to changing consumer preferences, the price of sports cars increases by 50%; as a result, the demand for SUVs falls from 10,000 units to 5,000.

Using the "arc method," the cross price elasticity of demand for SUVs is:

Answer 1

Ans. Using the arc method:

1) % change in sports cars ( increases ) = change in price/ average price x 100 =  50%

2) % change in demand (falls) for SUVs = change in demand/average demand x 100

= ( 5000 - 10,000)/(10,000 + 5,000)/2 x 100

= ( - 5,000)/7,500 x 100

= ( - 66.67 % )

then,

The cross-price elasticity of demand for SUVs = % change in demand for SUVs/% change in the price of sports cars

= ( - 66.67 % )/50%

= - 1.33

Hence, the cross - price elasticity of demand for SUVs is ( -1.33 ).

Note: Negative sign denoted that Sports cars and SUVs are complementary goods because complementary goods have a negative relationship between the price of one good and the demand for other good.