Question

Cutting Edge Pharmaceuticals Pty Ltd (a monopoly firm) has the following demand (average revenue) function:

AR = 100 – Q
The marginal cost of production is given as constant and equal to $10.

a) What is the equation for the MR function? In showing this equation for the MR function explain the relationship between average revenue and marginal revenue. Determine the profit-maximizing level of output of the firm

b) What is the equilibrium monopoly price set by the firm and what will be the monopoly profit earned?

c) Illustrate the market demand and marginal cost, the average cost of this firm as well as, profit-maximizing price quantity and profit level on a diagram

Answer 1

P (AR) = 100 - Q

(a)

Total revenue (TR) = P x Q = 100Q - Q²

MR = dTR/dQ = 100 - 2Q

If price elasticity of demand be E, then relationship between MR and AR (P) is:

MR = P x [1 - (1/E)]

Profit is maximized when MR = MC.

100 - 2Q = 10

2Q = 90

Q = 45

(b)

When Q = 45,

P = 100 - 45 = 55

Profit = Q x (P - MC) = 45 x (55 - 10) = 45 x 45 = 2025

(c)

From demand function, when Q = 0, P = 100 (vertical intercept) and when P = 0, Q = 100 (horizontal intercept).

From MR function, when Q = 0, MR = 100 (vertical intercept) and when MR = 0, Q = 100/2 = 50 (horizontal intercept).

Since MC is constant, AC = MC = 10.

In following graph, profit is maximized at point A where MR intersects MC with price P0 (= 55) and quantity Q0 (= 45). Profit equals area P0BAC.