Question

Suppose that there is a natural monopoly that faces a demand curve D(P) = 10000 - 2P with the total cost function C(Q) = 1000 + 100Q.

The profit maximizing quantity for the natural monopolist, in the presence of a marginal cost pricing rule is ______ units

The profit maximizing price that will be set by the monopolist that will be set in the presence of a marginal cost pricing rule is $_______

The average total cost per unit at the profit maximizing level of output in the presence of a marginal cost pricing rule is $______

The profit for the natural monopolist under the marginal cost pricing rule, given they set the profit maximizing price and level of output, is $______

Answer 1

The profit maximizing quantity for the natural monopolist, in the presence of a marginal cost pricing rule is 4,900 units

The profit maximizing price that will be set by the monopolist that will be set in the presence of a marginal cost pricing rule is $100.

The average total cost per unit at the profit maximizing level of output in the presence of a marginal cost pricing rule is $100.20.

The profit for the natural monopolist under the marginal cost pricing rule, given they set the profit maximizing price and level of output, is $-1,000.

Explanation:

The demand equation is:

Q = 10,000 - 2P

2P = 10,000 - Q

P = 5,000 - 0.5Q        [This is inverse demand function]

TC = 1,000 + 100Q

MC = 100

The marginal cost pricing rule is that,

P = MC

5,000 - 0.5Q = 100

0.5Q = 4,900

Q = 4,900 / 0.5 = $9,800

P = 5,000 - 0.5(9,800) = $100

TC = 1,000 + 100Q = 1,000 + 100(4,900) = 491,000

ATC = TC / Q = 491,000 / 4,900 = $100.20

TR = P * Q = $100 * 4,900 = $490,000

Profit = TR - TC = 490,000 - 491,000 = -$1,000               [This is a loss]