Question

The price of good A went from $2 to $2.50 and the quantity of good B went from 50 units to 40 units. If you use arc elasticity, cross-price elasticity is _____ and goods A and B are _____.

a. -1; substitutes.

b. +1; complements.

c. +1; substitutes.

d. -1; complements.

Answer 1

When the price of good A is Pa = $2, the quantity of good B sold, Qb = 50 units

When the price of good A is Pa' = $2.50, the quantity of good B sold, Qb' = 40 units

Percentage change in the price of good A(using mid-point method) = (Pa' - Pa)/[(Pa + Pa')/2] * 100 = ($2.50 - $2)/[($2 + $2.50)/2 * 100 = $0.5/$2.25 * 100 = +22.22%

Percentage change in the quantity of good B sold = (Qb' - Qb)/[(Qb + Qb')/2] * 100 = (40 - 50)/[(50 + 40)/2] * 100 = -10/45 * 100 = -22.22%

The cross-price elasticity of the given goods = (% change in the quantity demanded of good B)/(% change in the price of good A) = (22.22)/(-22.22) = -1

As the cross-price elasticity of the given goods is negative, goods A and B are complementary goods.

Ans: d. -1; complements