Pricing Example

Given a demand function for a product of d=1000 - 0.5p, a fixed cost of 10,000 and a variable cost of 50 per unit, find the price that will maximize the profit. At that price, what is the demand? What is the profit?

Solution:

D=1000-0.5P

Revenue = P(1000-0.5P) = -0.5P² + 1000P

FC = 10000

VC = 50 (1000-0.5P) = 50,000 - 25P

TC = -25P + 60,000

Profit = -0.5P² + 1000P - [-25P + 60,000]

= -0.5P² + 1025P - 60,000

Slope of profit line = -P + 1025

At maxima, slope = 0 = -P + 1025

Hence, P= $1025.

At that price, D = 1000 - 0.5(1025) = 487.5 units

Profit = -0.5P² + 1025P - 60,000

= -0.5 (1025 *1025) + 1025 (1025) - 60,000

= $465,312.50