📖 微观经济学周测（10 题）

Economics

I. Lesson Focus

This lesson consolidates core microeconomic concepts tested at CFA Level I: demand and supply analysis, elasticity, cost structures, producer decision-making rules, market structures (perfect competition, monopoly, monopolistic competition, oligopoly), and the effects of government intervention. Candidates must master formulas, graphical interpretations, numerical applications, and common conceptual traps. The session reviews underlying theory while testing understanding through 8 targeted multiple-choice questions with detailed explanations.

II. The Problem

CFA Level I candidates frequently lose marks in microeconomics by confusing shutdown and breakeven points, misapplying elasticity rules to total revenue changes, incorrectly identifying marginal revenue in different market structures, and failing to calculate deadweight loss or economic profit under varying conditions. This weekly quiz reviews the complete microeconomic toolkit with real formulas, three fully worked numerical cases, and eight high-quality practice questions that mirror actual exam difficulty and style.

III. Core Microeconomic Framework Review

Microeconomics studies the decisions of individual consumers and firms and how they interact in markets. Key analytical tools include:

• Demand and Supply: The demand curve slopes downward; the supply curve slopes upward. Market equilibrium price and quantity occur at their intersection.
• Elasticity: Price elasticity of demand $E_d = \frac{\%\Delta Q_d}{\%\Delta P}$. Point elasticity is often calculated as $\frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$. Income elasticity and cross-price elasticity follow similar logic.
• Consumer Theory: Utility maximization occurs when $\frac{MU_x}{P_x} = \frac{MU_y}{P_y}$. Consumer surplus is the area below the demand curve and above the market price.
• Producer Theory: Total cost $TC = TVC + TFC$. Average total cost $ATC = TC/Q$. Marginal cost $MC = \Delta TC / \Delta Q$. The universal profit-maximization rule is $MR = MC$.

IV. Cost Structures and Firm Decisions

In the short run, firms face fixed and variable costs. Critical thresholds are: - Breakeven Point: $P = ATC$ (economic profit equals zero). - Shutdown Point: $P =$ minimum $AVC$. If price falls below this, the firm should cease production to minimize losses. - In the long run, all costs are variable. Firms operate at the minimum point of the long-run average cost ($LRAC$) curve under perfect competition.

Under perfect competition, $P = MR = MC = AR$ and long-run economic profit is zero due to free entry. In monopoly, $MR < P$, positive economic profit can persist, but society suffers deadweight loss.

V. Market Structure Comparison

Worked Cases

Case 1: Price Elasticity and Total Revenue

A product has demand $Q_d = 200 - 4P$. Price rises from $20 to $25. Calculate price elasticity and determine the effect on total revenue.

Solution:
At $P_1 = 20$, $Q_1 = 120$.
At $P_2 = 25$, $Q_2 = 100$.
$\% \Delta Q = (100-120)/120 \times 100\% = -16.67\%$.
$\% \Delta P = (25-20)/20 \times 100\% = 25\%$.
$E_d = -16.67/25 = -0.667$ (inelastic).
Initial $TR_1 = 20 \times 120 = 2,400$. New $TR_2 = 25 \times 100 = 2,500$.
Total revenue rises. When demand is inelastic, a price increase raises total revenue.

Case 2: Short-run Decision in Perfect Competition

A perfectly competitive firm has $TC = 50 + 6Q + 0.5Q^2$ and faces market price $P = 20$. Find the profit-maximizing output, whether the firm should produce, and economic profit.

Solution:
$MC = 6 + Q$. Set $MC = P$: $6 + Q = 20 \Rightarrow Q = 14$.
$ATC = 50/14 + 6 + 0.5 \times 14 \approx 16.57$.
$AVC = 6 + 0.5 \times 14 = 13$.
Since $P = 20 > ATC = 16.57$, the firm earns positive economic profit $\pi \approx (20-16.57) \times 14 \approx 48$.
Because $P > AVC$, the firm should continue producing in the short run.

Case 3: Monopoly Pricing and Deadweight Loss

A monopolist faces demand $P = 100 - 2Q$ and $TC = 20 + 4Q$. Find the profit-maximizing price and quantity. Compare with the perfectly competitive outcome ($P = MC$) and calculate deadweight loss.

Solution:
$TR = 100Q - 2Q^2$, so $MR = 100 - 4Q$.
Set $MR = MC$: $100 - 4Q = 4 \Rightarrow Q = 24$, $P = 100 - 48 = 52$.
Competitive equilibrium: $P = MC = 4$, $Q = 48$.
Deadweight loss is the triangular area: $0.5 \times (48-24) \times (52-4) = 0.5 \times 24 \times 48 = 576$.

Traps

Key Formulas

• Price elasticity of demand: $E_d = \frac{\%\Delta Q_d}{\%\Delta P}$
• Marginal revenue (perfect competition): $MR = P$
• Profit-maximization rule (all structures): $MR = MC$
• Economic profit: $\pi = (P - ATC) \times Q$
• Consumer surplus: area below demand curve, above price
• Shutdown rule (short run): produce only if $P \geq \min AVC$
• Breakeven: $P = ATC$
• Linear demand $P = a - bQ$ implies $MR = a - 2bQ$

Practice Questions

Q1. If the price of a good rises by 10% and quantity demanded falls by 25%, the price elasticity of demand is closest to:
A. -0.4
B. -2.5
C. 0.4
D. 2.5

Q2. In a perfectly competitive market, a firm’s short-run supply curve is:
A. Its AVC curve
B. Its ATC curve
C. The portion of its MC curve above AVC
D. The portion of its MC curve above ATC

Q3. When demand is elastic, an increase in price will cause:
A. Total revenue to increase
B. Total revenue to decrease
C. Total revenue to remain unchanged
D. Insufficient information

Q4. A monopolist has marginal cost of 15 and faces demand elasticity of -2. The profit-maximizing price is closest to:
A. 20
B. 30
C. 22.5
D. 10

Q5. Which of the following is NOT a characteristic of perfect competition?
A. Firms are price takers
B. Products are homogeneous
C. Barriers to entry exist
D. Perfect information

Q6. If the cross-price elasticity between two goods is +1.5, the goods are:
A. Complements
B. Substitutes
C. Independent
D. Inferior goods

Q7. A firm has fixed costs of 200 and variable costs $VC = 4Q^2$. At a price of 24, the output level at the shutdown point is closest to:
A. 0
B. 10
C. 25
D. Cannot be determined

Q8. A per-unit tax imposed on a monopolist is most likely to result in:
A. Increased output
B. Increased consumer surplus
C. Increased deadweight loss
D. Higher price and lower output

Answers

Takeaways

• The universal profit-maximization condition is always $MR = MC$; only the relationship between MR and P differs across market structures.
• Perfect competition long-run equilibrium: $P = MR = MC = ATC = \min LRAC$, resulting in zero economic profit.
• Price elasticity determines the effect of price changes on total revenue: elastic demand favors “lower price, higher volume”; inelastic demand favors price increases.
• Short-run shutdown depends on AVC; long-run exit depends on ATC.
• Monopoly produces less than the socially optimal quantity, creating deadweight loss. Government intervention (taxes, price ceilings, antitrust) can mitigate but often creates additional distortions.
• Economies of scale correspond to the declining portion of the LRAC curve; diseconomies correspond to the rising portion.