Question

You are given the following demand table which shows the relationship between the price of a Honda Civic and the quantity demanded of Civics and Toyota Corollas:

Price of Civic Quantity of Civics Quantity of Corollas

$20,000 600 1000

$16,000 1200 800

a) What is the arc price elasticity of demand for Civics?

b) What is the cross-price elasticity of demand for Corollas with respect to Civics?

Answer 1

Price of Civic	Quantity of Civic	Quantity of Corollas
$20,000	600	1000
$16,000	1,200	800

Civic Q1 = 600 , Q2 = 1200 , P1 = $20,000, P2 = $16,000

Corolla C1 = 1000 , C2 = 800

Midpoint of Q = (Q1 + Q2) / 2 , Midpoint of P = (P1 + P2) / 2

A).  ARC price elasticity of Demand for Civic = Change in demand (Q 2 - Q 1) / Midpoint of Q / Change in Price (P 2-P 1)/ Midpoint of P

= 1200-600 / (1200+600) / 2 / 16,000 - 20,000 / (20,000 + 16,000) / 2 = 600 /900 / 4,000 /18,000 = (2/3) / (2/9) = 3

Hence, Arc elasticity of demand is 3, which is greater than 1, so our demand for civics is elastic here.

B). Cross price elasticity of Demand = % change in quantity demanded of Corolla / % change in the price of civic

= (800 - 1000) *100 / 1000 / (16000 - 20000) * 100 / 20000

= 200 / 1000 / 4000 / 20000 = 1

So, Cross price elasticity between the demand of Corolla and the price of civic is 1 i.e Unitary Elastic. It means the percentage change in quantity demand of corolla is equivalent to the percentage change in the price of civic.