Question

Suppose a monopolist faces the following demand curve:

P = 440 – 7Q.

The long run marginal cost of production is constant and equal to $20, and there are no fixed costs.

A) What is the monopolist’s profit maximizing level of output?

B) What price will the profit maximizing monopolist produce?

C) How much profit will the monopolist make if she maximizes her profit?

D) What would be the value of consumer surplus if the market were perfectly competitive?

E) What is the value of the deadweight loss when the market is a monopoly?

Answer 1

(A)

The demand curve of monopolist is as follows -

P = 440 - 7Q

Calculate Total revenue -

TR = P * Q = (440 - 7Q) * Q = 440Q - 7Q²

Calculate Marginal Revenue -

MR = dTR/dQ = 440 – 14Q

MC = $20

A monopolist's profit-maximizing level of output is that level of output at which marginal cost equals marginal revenue.

Equating marginal cost and marginal revenue in order to determine profit maximizing level of output -

MR = MC

440 - 14Q = 20

14Q = 420

Q = 30

The monopolist's profit-maximizng level of output (Q) is 30 units.

(B)

Demand curve of monopolist is as follows -

P = 440 - 7Q

The profit-maximizing level of output (Q) for monopolist is 30 units. Putting this value of Q in demand curve to ascertain the profit-maximizing price.

P = 440 – 7*30 = 440 – 210 = 230

The profit-maximizing monopolist will produce at a price of $230 per unit.

(C)

Total revenue of monpolist is as follows -

TR = P * Q = (440 - 7Q) * Q = 440Q - 7Q²

Putting value of Q in above equation to ascertain total revenue,

TR = (440*30) - 7*(30)² = 13,200 – 6,300 = 6,900

Calculate Total Cost -

Total cost = MC * Q = $20 * 30 = $600

Calculate profit of monopolist -

Profit = Total revenue - Total cost = $6900 - $600 = $6300

The monpolist will make a profit of $6300 if she maximizes her profit.

(D)

In a perfectly competitve market, firm produce that level of output at which price equals marginal cost to maximize profit.

Equating price and marginal cost to determine profit-maximzing level of output for the firm if the market were perfectly competitive,

P = MC

440 – 7Q = 20

7Q = 420

Q = 60

The profit-maximizing output (Q) for firm, if the market is perfectly competitive is 60 units.

Profit-maximizng price = $20 (equal to marginal cost)

Calculate consumer surplus -

Step 1 - Determining price when quantity demanded is zero -

P = 440 - 7Q = 440 - 7*0 = 440

Step 2 - Ascertaing consumer surplus -

CS = 1/2 * (Price when quantity demanded is zero - Profit maximizing price) * Profit-maximizing quantity

CS = 1/2 * ($440 - $20) * $60

CS = $12,600

The value of consumer surplus would be $12,600, if the market were perfectly competitive.