Question

The following table provides the demand for three goods (A, B, and C) at two prices for good A.

Price of GOOD A	Quantity Sold of A	Quantity Sold of B	Quantity Sold of C
$30	1400	400	500
$40	700	210	825

a) Calculate the midpoint cross-elasticity of demand between good A and B. Are these goods substitutes or complements?

b) Calculate the midpoint cross elasticity of demand between good A and C. Are these goods substitutes or complements?

Answer 1

a) Average price = 35
Percentage change in price = (40 - 30)/35 x 100 = 28.57%

Average quantity of B = (400 + 210)/2 = 305
Percentage change in quantity = (210-400)/305 x 100 = -62.30%

Cross price elasticity = -62.30/28.57 = - 2.18

The goods are complements as increase in the price of good A leads to fall in the quantity demanded of good B.

b) Average price = 35
Percentage change in price = (40 - 30)/35 x 100 = 28.57%

Average quantity of B = (500 + 825)/2 = 662.5
Percentage change in quantity = (825-500)/662.5 x 100 = 49.06

Cross price elasticity = 49.06/28.57 = 1.72

The goods are substitutes. This is because the rise in the price for good A leads to increase in the quantity demanded of good. C.