Question

Assume that the quarterly demand for an SUV produced by an automobile company is Qd = 150,000 – 1.5P, where Qd is quantity demanded and P is price per vehicle.

A. Using the concept of elasticity of demand, what price should be charged to maximize revenue from sales of this SUV? Clearly show your steps and manual (hand and calculator) calculations.

B. Derive the equation for total revenue for this product. Clearly show you steps.

C Using (b) above, determine the unit price that maximizes total revenue from sales. Clearly show your steps and manual calculations.

Answer 1

Qd = 150,000 - 1.5P

(A) Revenue is maximized when demand is unitar elastic, which is at mid-point of the demand curve.

When Qd = 0, P = 150,000 / 1.5 = 100,000 (Vertical intercept of demand curve)

Therefore, revenue-maximizing price = Vertical intercept of demand curve / 2 = 100,000 / 2 = 50,000

(B) When P = 50,000,

Qd = 150,000 - (50,000 x 1.5) = 150,000 - 75,000 = 75,000

Total revenue = P x Qd = 50,000 x 75,000 = 3,750,000,000 = 3,750 million

(C)

Qd = 150,000 - 1.5P

1.5P = 150,000 - Qd

P = (150,000 - Qd) / 1.5

Total revenue (TR) = P x Qd = (150,000Qd - Qd²) / 2

TR is maximized when dTR/dQd = 0

(150,000 - 2Qd) / 2 = 0

150,000 - 2Qd = 0

2Qd = 150,000

Qd = 75,000

P = (150,000 - 75,000) / 1.5 = 75,000 / 1.5 = 50,000