Question

uppose the annual demand function for the Honda Accord is Qd = 430 – 10 PA + 10 PC – 10 PGwhere PA and PC are the prices of the Accord and the Toyota Camry respectively (in thousands), and PGis the price of gasoline (per gallon). What is the elasticity of demand of the Accord with respect to the price of Camry when both cars sell for $20,000 and fuel costs $3 per gallon? What is the elasticity with respect to the price of gasoline?

Answer 1

Answer:

Qd = 400 units

elasticity of demand of the Accord with respect to the price of Camry = 0.5

elasticity with respect to the price of gasoline = -0.075

Explanation:

Solution:

The annual demand function for the Honda Accord is:

Qd = 430 – 10 PA + 10 PC – 10 PG

Where,

PA = Price of Honda Accord

PC = Price of Honda Camry

PG = Price of Gasoline per gallon.

Selling Price of both cars = $20,000

Fuel Cost = $3 per gallon.

a) Elasticity of Demand of the Accord with respect to the price of Camry.

First, we need to calculate the number of units demanded.

Qd = 430 – 10 PA + 10 PC – 10 PG

Qd = 430 – 10 (20) + 10 (20) – 10 (3.00)

Qd = 430 - 200 + 200 - 30

Qd = 430 - 30

Qd = 400 units

Cross-price elasticity of the Accord with respect to the price of the Camry will be:

Cross Price = (dQd/dPC) x (PC)/(Qd)

dQd/dPC = 10

PC = 20

Qd = 400

So,

Cross Price = 10* 20/400

Cross Price  = 0.5

b) Elasticity with respect to the price of gasoline?

Elasticity =  (dQd/dPG)*(PG/Qd)

dQd/dPG = -10

PG = 20

Qd = 400

Elasticity  = (-10)*(3/400)

Elasticity  =  -0.075