Consider a profit-maximizing monopoly pricing under the following conditions. The profit-maximizing quantity is 40 units, the profit-maximizing price is $160, and the marginal cost of the 40th unit is $120. If the good were produced in a perfectly competitive market, the equilibrium quantity would be 50, and the equilibrium price would be $150. The demand curve and marginal cost curves are linear. What is the value of the deadweight loss created by the monopolist?
A)$40
B)$100
C)$200
D)$400

Question

Quizplus · Accepted Answer

To find the deadweight loss, we need to first find the consumer surplus and producer surplus under the monopoly pricing and the perfectly competitive pricing.

Under monopoly pricing: 
- Price = $160 
- Quantity = 40 
- Total revenue = (price x quantity) = $6,400 
- Total cost = (marginal cost x quantity) = ($120 x 40) = $4,800 
- Profit = (total revenue - total cost) = $1,600

Consumer surplus: 
- Area below the demand curve and above the price, up to quantity = 40 
- Consumer surplus = 0.5 x (160-0) x 40 = $3,200

Producer surplus: 
- Area above the marginal cost curve and below the price, up to quantity = 40 
- Producer surplus = 0.5 x (160-120) x 40 = $800

Under perfectly competitive pricing: 
- Price = $150 
- Quantity = 50 
- Total revenue = (price x quantity) = $7,500 
- Total cost = (marginal cost x quantity) = ($120 x 50) = $6,000 
- Profit = (total revenue - total cost) = $1,500

Consumer surplus: 
- Area below the demand curve and above the price, up to quantity = 50 
- Consumer surplus = 0.5 x (150-0) x 50 = $3,750

Producer surplus: 
- Area above the marginal cost curve and below the price, up to quantity = 50 
- Producer surplus = 0.5 x (150-120) x 50 = $1,500

Deadweight loss = (consumer surplus under perfect competition - consumer surplus under monopoly) + (producer surplus under perfect competition - producer surplus under monopoly) - (monopoly profit)

Deadweight loss = ($3,750 - $3,200) + ($1,500 - $800) - $1,600 = $550 + $700 - $1,600 = $(-350)

Note that the negative value indicates that there is no deadweight loss, but rather a gain in overall surplus from the monopoly pricing. However, this answer choice is not provided, so the closest option is C) $200.

Consider a Profit-Maximizing Monopoly Pricing Under the Following Conditions