📖 垄断市场

Economics

I. Lesson Focus

This lesson examines the monopoly market structure, its profit-maximization decision, pricing behavior, and efficiency implications compared with perfect competition. Candidates must be able to derive marginal revenue from a demand curve, solve for the monopoly quantity and price, calculate deadweight loss, and evaluate regulatory responses to natural monopoly.

II. The Problem

A technology company holds an exclusive patent on critical software and operates as the sole supplier. How should it set output and price to maximize profit? Compared with a perfectly competitive market, does monopoly create a net loss in social welfare? CFA exams frequently require candidates to calculate a monopolist’s marginal revenue, profit-maximizing output and price, and to quantify the reduction in consumer surplus, the gain in producer surplus, and the resulting deadweight loss. These calculations and efficiency comparisons form the core of this lesson.

III. Definition and Characteristics of Monopoly

A monopoly exists when a single firm is the only seller in an industry. Its defining features are: - Single seller - No close substitutes for the product - Very high barriers to entry (patents, control of key resources, government franchises, or natural monopoly conditions) - The firm is a price maker rather than a price taker

Unlike a perfectly competitive firm, a monopolist faces the entire market’s downward-sloping demand curve. Consequently, its marginal revenue (MR) curve lies below the demand (D) curve and MR is always less than price (P).

IV. Profit-Maximization Decision for a Monopolist

The monopolist maximizes profit at the output where marginal revenue equals marginal cost: MR = MC. Because MR < P, the monopolist sets the price corresponding to that output on the demand curve, resulting in P > MC.

Key Relationships: - Total revenue TR = P × Q - Average revenue AR = TR / Q = P - Marginal revenue MR = ΔTR / ΔQ - For a linear demand curve P = a – bQ, the MR curve is MR = a – 2bQ (twice the slope of demand)

Because of high barriers to entry, a monopolist can earn positive economic profit in both the short run and the long run.

V. Efficiency Comparison: Monopoly versus Perfect Competition

Monopoly creates allocative inefficiency through: 1. Lower output than under perfect competition (Qm < Qc) 2. Higher price than under perfect competition (Pm > Pc) 3. Positive deadweight loss (DWL) 4. Transfer of consumer surplus to producer surplus, with a net reduction in total surplus

Consumer surplus (CS) is the area below the demand curve and above the price.
Producer surplus (PS) is the area above the marginal-cost curve and below the price.
Deadweight loss is the triangular area between the demand curve and MC curve from Qm to Qc that represents foregone mutually beneficial transactions.

VI. Natural Monopoly and Government Regulation

A natural monopoly occurs when economies of scale are so large that average cost declines over the entire relevant range of demand, making it most efficient for a single firm to supply the market (e.g., electricity transmission, water distribution).

Regulatory approaches include: - Marginal-cost pricing (P = MC): eliminates DWL but produces losses, requiring government subsidies - Average-cost pricing (P = AC, also called fair-return pricing): allows the firm to break even but leaves some DWL - Price-cap regulation

Worked Cases

Case 1: Linear Demand and Monopoly Pricing

A monopolist faces the demand P = 100 – 2Q and constant MC = 20.

Calculate: (1) profit-maximizing output and price, (2) economic profit, (3) deadweight loss relative to perfect competition.

Solution: MR = 100 – 4Q
Set MR = MC: 100 – 4Q = 20 → 4Q = 80 → Qm = 20
Pm = 100 – 2(20) = 60

TR = 60 × 20 = 1,200; TC = 20 × 20 = 400; Profit = 800

Under perfect competition: P = MC → 100 – 2Q = 20 → Qc = 40, Pc = 20
DWL = ½ × (60 – 20) × (40 – 20) = ½ × 40 × 20 = 400

Case 2: Consumer Surplus, Producer Surplus, and DWL

Using the data from Case 1.

Monopoly: CS = ½ × (100 – 60) × 20 = 400
PS = (60 – 20) × 20 = 800
Total surplus = 1,200; DWL = 400

Perfect Competition: CS = ½ × (100 – 20) × 40 = 1,600
PS = 0 (constant MC)
Total surplus = 1,600

Case 3: Regulation of a Natural Monopoly

A natural monopolist has TC = 500 + 10Q and faces demand P = 50 – 0.5Q.

(1) Find unregulated monopoly output and price.
(2) Find output and price under average-cost pricing.

Solution: MC = 10
MR = 50 – Q
Set MR = MC: 50 – Q = 10 → Qm = 40, Pm = 50 – 0.5(40) = 30

For AC pricing set P = AC: 50 – 0.5Q = 500/Q + 10
Solving the quadratic yields Q ≈ 25, P ≈ 37.5 (firm breaks even).

Traps

Key Formulas

• Profit-maximization condition: $MR = MC$
• Linear demand $P = a - bQ$ implies $MR = a - 2bQ$
• Lerner Index: $\frac{P - MC}{P} = -\frac{1}{E_d}$
• Deadweight loss: $DWL = \frac{1}{2} \times (P_m - MC) \times (Q_c - Q_m)$
• Natural monopoly: long-run average cost (LRAC) declines throughout the relevant output range

Practice Questions

Q1. A monopolist maximizes profit at the output level where:
A. P = MC
B. P = MR
C. MR = MC
D. MR = AC

Q2. Relative to a perfectly competitive market, a monopoly typically produces:
A. Higher output and lower price
B. Lower output and higher price
C. The same consumer surplus
D. Zero deadweight loss

Q3. A monopolist faces demand P = 80 – 4Q and MC = 8. The profit-maximizing output is:
A. 9
B. 12
C. 18
D. 20

Q4. A natural monopoly is most likely to occur in which industry?
A. Smartphone manufacturing
B. Electricity distribution network
C. Clothing retail
D. Restaurant services

Q5. If a regulator forces a natural monopolist to set price equal to marginal cost, the firm will:
A. Earn positive economic profit
B. Incur losses and require a government subsidy
C. Produce less than the unregulated monopoly output
D. Increase deadweight loss

Q6. A monopolist’s marginal revenue curve lies:
A. Coincident with the demand curve
B. Above the demand curve
C. Below the demand curve
D. Identical to the average-cost curve

Q7. The Lerner Index measures:
A. Price elasticity of demand
B. The extent to which price exceeds marginal cost
C. Height of entry barriers
D. Degree of economies of scale

Q8. Which of the following is least likely to be a barrier to entry into a monopoly?
A. Patent protection
B. Government franchise
C. Economies of scale
D. Large number of buyers

Answers

Takeaways

• A monopolist faces the market demand curve; its MR curve lies below demand and has twice the slope for linear demand.
• Profit is maximized where MR = MC, but the price charged exceeds MC.
• Monopoly reduces total surplus by creating deadweight loss and transferring consumer surplus to the producer.
• Natural monopoly arises from continuously declining average cost; regulators often use average-cost pricing to balance efficiency and firm viability.
• The Lerner Index quantifies monopoly power as the proportional markup of price over marginal cost.
• High barriers to entry enable monopolists to sustain positive economic profit in the long run.