(25 total points) Suppose a monopolist faces the following demand curve: P = 88

Question

(25 total points) Suppose a monopolist faces the following demand curve: P = 88 – 3Q. The long run marginal cost of production is constant and equal to $4, 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?

Explanation / Answer

(A)

The demand curve of monopolist is as follows -

P = 88 - 3Q

Calculate Total revenue -

TR = P * Q = (88 - 3Q) * Q = 88Q - 3Q2

Calculate Marginal Revenue -

MR = dTR/dQ = d(88Q - 3Q2)/dQ = 88 - 6Q

MC = $4

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

88 - 6Q = 4

Q = 14

The monopolist's profit-maximizng level of output (Q) is 14 units.

(B)

Demand curve of monopolist is as follows -

P = 88 - 3Q

The profit-maximizing level of output (Q) for monopolist is 14 units. Putting this value of Q in demand curve to ascertain the profit-maximizing price.

P = 88 - 3Q = 88 - 3*14 = 88 - 42 = $46

The profit-maximizing monopolist will produce at a price of $46 per unit.

(C)

Total revenue of monpolist is as follows -

TR = P * Q = (88 - 3Q) * Q = 88Q - 3Q2

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

TR = (88*14) - 3*(14)2 = $1,232 - $588 = $644

Calculate Total Cost -

Total cost = MC * Q = $4 * 14 = $56

Calculate profit of monopolist -

Profit = Total revenue - Total cost = $644 - $56 = $588

The monpolist will make a profit of $588 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

88 - 3Q = 4

Q = 28

The profit-maximizing output (Q) for firm, if the market is perfectly competitive is 28 units.

Profit-maximizng price = $4 (equal to marginal cost)

Calculate consumer surplus -

Step 1 - Determining price when quantity demanded is zero -

P = 88 - 3Q = 88 - 3*0 = 88

Step 2 - Ascertaing consumer surplus -

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

CS = 1/2 * ($88 - $4) * $28

CS = $1,176

The value of consumer surplus would be $1,176, if the market were perfectly competitive.

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