📖 微观经济学综合练习

Economics

I. Lesson Focus

II. The Problem

A firm producing a consumer good faces a downward-sloping demand curve. It must decide on output level, pricing strategy, whether to enter a monopolistically competitive market, and how to respond to a per-unit tax imposed by the government. CFA Level I exams frequently combine questions on price elasticity, marginal analysis, cost curves, profit-maximization rules across market structures, and tax incidence. Candidates who cannot seamlessly link these concepts often lose marks on both calculation and scenario-based questions. This lesson systematically reviews and integrates all key microeconomic tools through comprehensive practice, enabling candidates to solve integrated problems quickly and accurately.

III. Rapid Review of Core Microeconomic Concepts

Microeconomics studies how individual economic agents (consumers and firms) allocate scarce resources. CFA Level I emphasizes the following building blocks:

1. Demand and Supply Analysis: Demand and supply functions, market equilibrium, consumer surplus, and producer surplus.
2. Elasticity: Price elasticity, income elasticity, and cross elasticity. The basic formula is: $$ E_d = \frac{\%\Delta Q_d}{\%\Delta P} $$ Candidates must master both point and arc elasticity calculations and the relationship between elasticity and total revenue (|E_d| > 1 implies that a price decrease increases total revenue).
3. Consumer Theory: Diminishing marginal utility, indifference curves, and budget constraint lines.
4. Production and Cost: Total cost (TC), fixed cost (FC), variable cost (VC), average cost (AC), and marginal cost (MC). Short-run versus long-run cost curves differ markedly; the long-run average cost curve (LRAC) is U-shaped, reflecting economies and diseconomies of scale.
5. Market Structures:
6. Perfect competition: P = MR = MC; long-run economic profit equals zero.
7. Monopoly: MR = MC, P > MR; positive economic profit possible.
8. Monopolistic competition: Short-run behavior resembles monopoly; long-run entry and exit drive economic profit to zero, yet P > MC.
9. Oligopoly: Game theory, Nash equilibrium, and prisoner’s dilemma.

IV. Unified Profit-Maximization Decision Framework

Regardless of market structure, a firm maximizes profit where: $$ \text{Marginal Revenue (MR)} = \text{Marginal Cost (MC)} $$ In perfect competition, MR = P, so the rule simplifies to P = MC.
In imperfectly competitive markets, MR < P because the firm faces a downward-sloping demand curve; the firm must derive the MR curve first and set it equal to MC.

Economic profit = TR – TC = (P – AC) × Q.
Note that economic profit includes opportunity cost, whereas accounting profit does not.

V. Effects of Taxes and Subsidies

A per-unit tax shifts the supply curve upward by the amount of the tax, resulting in: - A higher equilibrium price, but the increase is less than the tax (depending on supply and demand elasticities). - Consumer burden share = E_s / (E_s + |E_d|) - Producer burden share = |E_d| / (E_s + |E_d|)

Tax incidence falls more heavily on the side of the market with the smaller elasticity.

Worked Cases

Case 1: Elasticity and Total Revenue

A product has demand Q_d = 120 – 2P. Current price P = 40, quantity = 40. (1) Calculate the point price elasticity. (2) If price falls to 35, how does total revenue change?

Solution: (1) E_d = (dQ/dP) × (P/Q) = (–2) × (40/40) = –2, so |E_d| = 2 > 1. (2) Original TR = 40 × 40 = 1,600. New P = 35, new Q = 120 – 70 = 50, new TR = 35 × 50 = 1,750. Total revenue rises by 150, consistent with the rule that when |E_d| > 1, a price cut increases revenue.

Case 2: Profit Maximization under Different Market Structures

Firm A is a perfect competitor. Market price P = 25, MC = 0.5Q + 5, AC = 0.25Q + 10 + 100/Q. Find the profit-maximizing output and economic profit.

Solution: MR = P = 25 = MC → 25 = 0.5Q + 5 → 0.5Q = 20 → Q = 40.
AC = 0.25(40) + 10 + 100/40 = 10 + 10 + 2.5 = 22.5.
Economic profit = (25 – 22.5) × 40 = 2.5 × 40 = 100 (positive short-run economic profit).

If the firm were a monopolist facing demand P = 50 – 0.5Q, then MR = 50 – Q.
Set 50 – Q = 0.5Q + 5 → 45 = 1.5Q → Q = 30, P = 50 – 15 = 35. AC must be recalculated at the new output.

Case 3: Tax Incidence and Market Equilibrium

Market demand: Q_d = 200 – 10P; supply: Q_s = 20 + 5P. Government imposes a 4 per-unit tax. Find the proportions borne by consumers and producers and the new equilibrium price.

Solution: Pre-tax equilibrium: 200 – 10P = 20 + 5P → 180 = 15P → P = 12, Q = 80.
Post-tax supply becomes Q_s = 20 + 5(P – 4) = 5P.
200 – 10P = 5P → 200 = 15P → P = 13.33 (price paid by consumers). Producers receive 13.33 – 4 = 9.33.
Consumer share of tax = 1.33/4 = 33.25%; producer share = 2.67/4 = 66.75%.
Using elasticities: pre-tax E_d = 10 × (12/80) = 1.5, E_s = 5 × (12/80) = 0.75. Consumer burden = 0.75 / (0.75 + 1.5) = 0.333 or 33.3%, confirming the result.

Traps

Key Formulas

• Price elasticity: $E_d = \frac{\%\Delta Q_d}{\%\Delta P} = \frac{dQ}{dP} \times \frac{P}{Q}$
• Total revenue–elasticity link: |E_d| > 1 → price cut increases TR; |E_d| < 1 → price cut decreases TR; |E_d| = 1 → TR maximized
• Profit maximization: MR = MC
• Perfect competition (long run): P = MR = MC = AC (minimum)
• Economic profit: π = TR – TC = (P – AC) × Q
• Tax incidence: Consumer share = E_s / (E_s + |E_d|)
• Marginal cost: MC = dTC/dQ
• Average cost: AC = TC/Q = AFC + AVC

Practice Questions

Q1. A good has price elasticity of demand equal to –1.8. If price falls by 5%, total revenue will:
A. Decrease by 9%
B. Increase by 9%
C. Increase by 1%
D. Remain unchanged

Q2. In long-run equilibrium of a perfectly competitive market, which statement is correct?
A. P > MC
B. P = MR = MC = AC
C. Firms earn positive economic profit
D. The supply curve is horizontal

Q3. For a monopolist, the marginal-revenue curve lies:
A. On top of the demand curve
B. Above the demand curve
C. Below the demand curve with twice the slope
D. On top of the MC curve

Q4. If supply elasticity is 0.5 and demand elasticity is –2.0, and a per-unit tax of 10 is imposed, the share borne by consumers is approximately:
A. 20%
B. 80%
C. 50%
D. 71.4%

Q5. Which of the following would shift the long-run average cost curve upward?
A. Economies of scale
B. Technological improvement
C. An across-the-board increase in input prices
D. Learning effects

Q6. A firm has TC = 100 + 20Q + 0.5Q², so MC = 20 + Q. At a market price of 50, the profit-maximizing output is:
A. 20
B. 30
C. 40
D. 50

Q7. In long-run equilibrium of monopolistic competition, a firm will:
A. Produce at the minimum of its AC curve
B. Set P = MC
C. Set P > MC while earning zero economic profit
D. Exit the market

Q8. If cross-price elasticity equals +2.5, the two goods are:
A. Complements
B. Substitutes
C. Inferior goods
D. Giffen goods

Answers

Takeaways

• Profit maximization always occurs where MR = MC; the difference across structures lies in the relationship between MR and P.
• Elasticity is the bridge connecting price changes to total revenue and tax incidence; master both calculation and interpretation.
• Long-run economic profit is zero in perfect competition, monopoly (if entry occurs), and monopolistic competition, yet P > MC in the latter two.
• Tax incidence is jointly determined by supply and demand elasticities; the less elastic side bears more of the burden.
• Distinguish clearly between accounting profit and economic profit; the latter includes opportunity cost.
• Cost-curve relationships (MC intersects AC and AVC at their minima) remain a high-frequency testable point.