Microeconomics Exam 2 Study Guide: Perfect Competition, Monopoly, and Pricing Strategies

Perfect Competition

Competitive Firms and Markets

Perfect competition describes a market structure where many firms sell identical products, and no single firm can influence the market price. Firms are price takers and must accept the equilibrium price determined by market supply and demand.

• Profit Maximization: Firms maximize profit by producing the quantity where price equals marginal cost ($P = MC$).

• Shutdown Rule: In the short run, a firm should shut down if price is less than average variable cost ($P < AVC$).

• Long-Run Equilibrium: Entry and exit of firms drive economic profit to zero, so $P = minimum ext{ }ATC$.

Mathematical Skills:

• Solving for profit-maximizing quantity

• Calculating economic profit: $\pi = TR - TC = Pq - C(q)$

• Determining shutdown point

• Finding long-run equilibrium number of firms

Example Problem: Given $P = 150$, $C = (1/3)q^2 + 6q + 1,500$, $MC = q + 6$ 1. Set $P = MC$: $150 = q + 6$ ⇒ $q = 144$ 2. Calculate profit: $\pi = 150(144) - [(1/3)(144^2) + 6(144) + 1,500]$ 3. Check shutdown: $AVC = (1/3)q^2 + 6q$ at $q = 12$; since $P > AVC$, produce.

Long-Run Competitive Equilibrium

In the long run, firms enter or exit the market until economic profit is zero and all firms produce at minimum average total cost.

• Each firm maximizes profit: $P = MC$

• Zero economic profit: $P = minimum ext{ }ATC$

• Number of firms adjusts until entry/exit profit is zero

Example Problem: Given $C = 25 + q^2$, $ATC = 25/q + q$, Market demand: $Q = 480 - p$ 1. Find minimum $ATC$: $MC = 2q$, $ATC = 25/q + q$ 2. Set $MC = ATC$: $2q = 25/q + q$ ⇒ $q = 5$ 3. At $q = 5$, $P = MC = 10$ (long-run equilibrium price) 4. Market quantity: $Q = 480 - 10 = 470$ 5. Number of firms: $470/5 = 94$ firms

Applying the Competitive Model

Market Interventions and Welfare

Government interventions such as taxes and price controls affect market outcomes and welfare.

• Effects of Taxes: Taxes shift supply curves, reduce equilibrium quantity, and create deadweight loss.

• Consumer and Producer Surplus: Surplus measures the benefit to buyers and sellers; taxes and controls reduce surplus.

• Deadweight Loss (DWL): DWL is the loss of total surplus due to market inefficiency, such as taxes or monopoly pricing.

• Price Controls: Ceilings (maximum price) and floors (minimum price) can cause shortages or surpluses.

Mathematical Skills:

• Calculating welfare measures: Consumer Surplus (CS), Producer Surplus (PS), Deadweight Loss (DWL)

• Tax incidence analysis

• Determining effects of price controls

Monopoly

Monopoly Pricing and Profit Maximization

A monopoly is a market with a single seller who has significant control over price. Monopolists maximize profit by producing where marginal revenue equals marginal cost ($MR = MC$).

• Deriving Marginal Revenue: If $P = a - bQ$, then $MR = a - 2bQ$

• Finding Monopoly Price and Quantity: Set $MR = MC$ and solve for $Q$; substitute $Q$ into demand to find $P$

• Calculating Monopoly Profit: $\pi = TR - TC$ or $\pi = (P - ATC)Q$

• Lerner Index: Measures market power: $L = \frac{P - MC}{P}$

Example Problem: Given $P = 100 - 2Q$, $MC = 20$ 1. $MR = 100 - 4Q$ (twice as steep as demand) 2. Set $MR = MC$: $100 - 4Q = 20$ ⇒ $Q = 20$ 3. Price: $P = 100 - 2(20) = 60$ 4. If $ATC = 30$, then $\pi = (60 - 30)(20) = 600$

Deadweight Loss from Monopoly

Monopoly pricing leads to a reduction in total surplus compared to perfect competition, resulting in deadweight loss.

• Find competitive $Q$: Set $P = MC$ using demand curve

• Find monopoly $Q$: Set $MR = MC$

• Calculate price difference at competitive quantity

• Use triangle formula for DWL

Key Insight: DWL represents trades that do not occur under monopoly but would under competition.

Natural Monopoly and Regulation

Natural monopolies occur when average cost declines over the relevant range of output, making it most efficient for a single firm to serve the market.

• Marginal Cost Pricing ($P = MC$): Efficient quantity, but firm may suffer losses ($P < ATC$)

• Average Cost Pricing ($P = ATC$): Zero economic profit, but some deadweight loss

• Unregulated Monopoly: Largest profit, most deadweight loss, lowest quantity

Example: Electricity, water service

Price Discrimination

Types of Price Discrimination

Price discrimination occurs when a firm charges different prices to different consumers for the same product, not based on cost differences.

• First-Degree (Perfect) Price Discrimination: Charge each customer their maximum willingness to pay (WTP); captures all consumer surplus; no DWL.

• Second-Degree (Quantity/Volume Discounts): Different prices based on quantity purchased; customers self-select into pricing tiers.

• Third-Degree (Group Pricing): Different prices for different consumer groups based on observable characteristics; MR must be equal across markets.

• Two-Part Pricing: Fixed fee plus usage fee; optimal strategy is $P = MC$ for usage and fixed fee to capture consumer surplus.

• Bundling: Selling products together; increases profit when reservation prices are negatively correlated.

Example Problem: Two customer types: Type I: WTP = $8$for 1 unit, $10$ total for 2 units Type II: WTP = $10$for 1 unit, $15$ total for 2 units Uniform pricing: Best single price = $8$⇒ Revenue = $16$ (both buy 1 unit) Volume discount: Package 1 unit for $8$(Type I selects) ⇒ Revenue $8$ Package 2 units for $15$(Type II selects) ⇒ Revenue $15$ Total: $23$vs. $16$ under uniform pricing

Critical Conceptual Understanding

Calculus is used to derive marginal revenue and marginal cost, which are essential for profit maximization.

• Marginal Revenue: $MR = \frac{dTR}{dQ}$

• Marginal Cost: $MC = \frac{dTC}{dQ}$

• Profit Maximization: Set $MR = MC$

• Elasticity: $\varepsilon = \frac{dQ}{dP} \frac{P}{Q}$

Comparing Market Structures

Perfect Competition vs. Monopoly

Market structures differ in terms of number of firms, market power, efficiency, and surplus distribution.

Feature	Perfect Competition	Monopoly
Number of firms	Many	One
Market power	None (price taker)	Significant
Demand curve	Horizontal (perfectly elastic)	Downward sloping
P vs. MC	$P = MC$	$P > MC$
Economic profit (LR)	Zero	Positive possible
Efficiency	Allocatively efficient	Deadweight loss
Consumer surplus	Higher	Lower
Producer surplus	Lower	Higher

Short-Run vs. Long-Run in Perfect Competition

Short Run

• Number of firms fixed

• Firms can earn positive or negative economic profit

• Supply curve: horizontal sum of MC curves above AVC

• Some firms may shut down if $P < AVC$

Long Run

• Number of firms adjusts through entry/exit

• Zero economic profit ($P = minimum ATC$)

• Supply curve: horizontal at minimum efficient scale

• All firms produce at minimum efficient scale

Entry/Exit Process:

• If $\pi > 0$: entry increases supply, price falls, profit moves toward zero

• If $\pi < 0$: exit decreases supply, price rises, profit moves toward zero

Problem-Solving Strategies

For Perfect Competition Questions

1. Start with the firm's decision rule: $P = MC$ (if producing)

2. Check shutdown condition: Compare $P$ to minimum $AVC$

3. Calculate profit: $\pi = (P - ATC)q = TR - TC$

4. Long-run analysis: Find minimum $ATC$ (set $MC = ATC$)

5. Verify reasonableness: In short run, $\pi$ can be positive, negative, or zero; in long run, $\pi = 0$ at equilibrium

For Monopoly Questions

1. Set $MR = MC$: Solve for profit-maximizing quantity $Q^*$

2. Find price from demand: Substitute $Q^*$ into $P = a - bQ$

3. Calculate profit: $\pi = TR - TC$ or $\pi = (P - ATC)Q$

4. Compare to competition: Note $Q_{monopoly} < Q_{competitive}$, $P_{monopoly} > P_{competitive}$

5. Calculate DWL: Triangle between demand and MC from $Q^*$ to $Q_c$

For Price Discrimination Questions

1. Identify the type: perfect PD, group PD, two-part, second-degree

2. For perfect price discrimination: Set $P = MC$ (last unit), $CS = 0$ (all captured by firm), $DWL = 0$

3. For second-degree: Identify customer types and their WTP by quantity, design packages so each type self-selects

Key Formulas

• Profit: $\pi = TR - TC$

• Marginal Revenue: $MR = \frac{dTR}{dQ}$

• Marginal Cost: $MC = \frac{dTC}{dQ}$

• Lerner Index: $L = \frac{P - MC}{P}$

• Elasticity: $\varepsilon = \frac{dQ}{dP} \frac{P}{Q}$

Additional info:

• Examples and problem types are based on typical intermediate microeconomics exam questions.

• Graphical analysis is essential for comparing market structures and understanding welfare effects.

• Students should be comfortable with calculus-based optimization and interpreting supply/demand graphs.