Question

2) Product price (p) and demand (D) are typically related linearly. Company A has performed extensive market research to develop a better relationship. They determined that the selling price of a product, p, is related to the demand for their product, D, in accordance with the following improved relationship

P= 92.5 – 0.09 (D^1.1) (in dollars)

Demand is given in units per year. In addition, there is a fixed cost of $40,000 per year and a variable cost of $40 per unit. Determine the demand level that maximizes total revenue and (b) maximum profit for this product.

Answer 1

(a) Total Revenue(TR) = Price *Quantity = PD = (92.5 – 0.09 (D^1.1))D

Let first Maximize TR

Max: (92.5 – 0.09 (D^1.1))D

FOC:

dTR/dD = 0 => 92.5 - 2.1*0.09D^1.1 = 92.5 -0.189D^1.1 = 0

=> D = 278.72 ----------------Revenue Maximizing quantity

(b) Total Cost = Fixed cost + Variable cost = 40,000 + 40Q

MC = dTC/dD = 40

In order to maximize profit a firm produces that quantity at which MR = MC

MR = dTR/dD = 92.5 - 2.1*0.09D^1.1

MC = 40

=> 92.5 - 2.1*0.09D^1.1 = 40

=> D = 166.55

Hence Profit maximizing Quantity = 166.55 units