Question

Suppose the demand of the good is P = 10 - Q. A monopolist's total cost is TC = 2 + 4Q. What's the optimal price and quantity of the monopolist?

calculate the monopolist's profit (or loss)

also calculate the deadweight loss from monopoly

Answer 1

Answer - Suppose the demand of the good is P = 10 - Q. A monopolist's total cost is TC = 2 + 4Q.

Total revenue (TR) of the monopolist = P*Q = (10 – Q)*Q

Marginal revenue (MR) = d(TR)/dQ = 10 – 2Q

Marginal cost (MC) = d(TC)/dQ = 4

The condition for profit maximization for a monopolist is MR = MC.

Thus, equating MR = MC, we get,

10 – 2Q = 4;

Or, 2Q = 6;

Or, Q = 3.

Therefore, optimal quantity of the monopolist = 3 units.

The optimal price to be charged by the monopolist is determined from the demand curve faced by the monopolist.

Thus, optimal price = 10 – 3 = $7.

The monopolist’s profit = TR – TC = 7*3 – (2+4*3) = 21 – 14 = $7.

The deadweight loss is the burden due to distortion from perfect competition.

In perfect competition, the condition for profit maximization is P = MC.

Thus, equating P = MC, 10 – Q = 4;

Or, Q = 6 units.

The equilibrium price in perfect competition = 10 – 6 = $4.

When MR = MC, price = $4

The deadweight loss of the monopolist

= ½ * (Monopolist price – Perfect competition price) * (Perfect competition quantity - Monopolist quantity) + ½ * (price obtained by setting MR equal to MC - Perfect competition price) * (Perfect competition quantity - Monopolist quantity)

= ½* (7 - 4) * (6 – 3) + ½ * (4 – 4) * (6 – 3)

= ½* 3 * 3 + 0

= $4.50