Question

Monopoly: Work It Out

Earlier we mentioned the special case of a monopoly where MC = 0. Let’s find the firm’s best choice when more goods can be produced at no extra cost. Since so much e-commerce is close to this model—where the fixed cost of inventing the product and satisfying government regulators is the only cost that matters—the MC = 0 case will be more important in the future than it was in the past. For each demand curve, calculate the profit-maximizing level of output and price as well as the monopolist's profit.

a. ?=200−?, fixed cost = 1,000.

Profit-maximizing output Q = ________

Profit-maximizing price P = $__________

Monopolist's profit: $__________

b. ?=4,000−?, fixed cost = 900,000 (Driving the point home from part a)

Profit maximizing output Q = _________

Profit-maximizing price P = $__________

Monopolist's profit: $___________

c. ?=120−12?, fixed cost = 1,000

Profit-maximizing quantity Q = __________

Profit-maximizing price P = $__________

Monopolist's profit: $__________

Answer 1

A monopolist maximizes profit by equating Marginal revenue (MR) with MC.

Profit = Q x (P - MC) - Fixed cost

(a)

P = 200 - Q

Total revenue (TR) = P x Q = 200Q - Q²

MR = dTR/dQ = 200 - 2Q

200 - 2Q = 0

2Q = 200

Q = 100

P = 200 - 100 = 100

Profit = 100 x (100 - 0) - 1,000 = 100 x 100 - 1,000 = 10,000 - 1,000 = 9,000

(b)

P = 4,000 - Q

TR = 4,000Q - Q²

MR = 4,000 - 2Q

4,000 - 2Q = 0

2Q = 4,000

Q = 2,000

P = 4,000 - 2,000 = 2,000

Profit = 2,000 x (2,000 - 0) - 900,000 = 2,000 x 2,000 - 900,000 = 4,000,000 - 900,000 = 3,100,000

(c)

P = 120 - 12Q

TR = 120Q - 12Q²

MR = 120 - 24Q

120 - 24Q = 0

24Q = 120

Q = 5

P = 120 - (12 x 5) = 120 - 60 = 60

Profit = 5 x (60 - 0) - 1,000 = 5 x 60 - 1,000 = 300 - 1,000 = -700 (loss)