CHAPTER 10: MARKET POWER — MONOPOLY AND MONOPSONY

IPMX Managerial Economics — Complete Solution Manual

CHAPTER OVERVIEW

Topic: How firms with market power set prices and output to maximize profit, and how monopsony buyers exploit buyer-side market power.

Core Logic Chain:

• Monopolist faces downward-sloping demand → MR < P → produces less than competitive market.
• Profit maximum: MR = MC. Price set from demand curve at that quantity.
• Market power measured by Lerner Index: (P − MC)/P = −1/Ed.
• Deadweight loss from monopoly = forgone surplus from units not produced.
• Monopsony: buyer sets quantity where MFC = Marginal Value; pays less than competitive wage.

PART I: QUESTIONS FOR REVIEW — FULLY SOLVED

Question 1

A monopolist is producing where MC exceeds MR. How should it adjust output?

Answer: The monopolist should reduce output.

Logic: If MC > MR, the cost of the last unit exceeds the revenue it generates. Cutting output saves more cost than it sacrifices in revenue → profit increases. The monopolist should reduce output until MR = MC.

Question 2

The percentage markup (P − MC)/P — how does it depend on elasticity? Why is it a measure of monopoly power?

Concept: Lerner Index.

Formula derivation: For a profit-maximizing monopolist: MR = MC. Since MR = P(1 + 1/Ed), setting MR = MC: $P(1+\frac{1}{E_d})=MC$ $\frac{P-MC}{P}=-\frac{1}{E_d}=\frac{1}{|E_d|}$

Interpretation:

• Higher |Ed| (more elastic demand) → lower markup → closer to competition.
• Lower |Ed| (less elastic demand) → higher markup → more monopoly power.
• The markup directly measures how far price exceeds MC — the definition of market power.
• In perfect competition: |Ed| → ∞ → markup = 0 (P = MC).

The Lerner Index = (P−MC)/P = 1/|Ed|. It measures monopoly power: larger markup = more market power.

Question 3

Why is there no market supply curve under monopoly?

Under perfect competition, the supply curve is derived from each firm's MC curve — price is given and the firm supplies accordingly.

Under monopoly, there is only one firm, and it does not simply respond to price. Instead, it chooses its own price-quantity combination based on MR = MC. For a given MC, the monopolist might choose different quantities (and different prices) depending on the shape of the demand curve. The "supply" depends on demand — this dependency means no unique relationship between price and quantity supplied exists independent of demand.

There is no supply curve under monopoly because the monopolist's output depends on both cost (MC) and demand (MR), not on price alone.

Question 4

Why might a firm have monopoly power even if it is not the only producer?

A firm has monopoly power if it faces a downward-sloping demand curve — which it does whenever:

• Its product is differentiated from rivals (brand loyalty, patents, unique quality).
• There are high switching costs for consumers.
• Its geographic location gives it local advantages.
• It controls a key input or distribution channel.

Example: A hospital in a small town faces some monopoly power even if there are other hospitals in distant cities — because consumers have limited mobility.

Question 5

Types of barriers to entry that give rise to monopoly power (with examples).

Question 6

Factors that determine how much monopoly power a firm has.

Three core factors:

1. Elasticity of market demand: More inelastic demand → higher markup (Lerner Index = 1/|Ed|).
2. Number and proximity of close substitutes: More substitutes → more elastic demand → less power.
3. Elasticity and number of competing firms: In oligopoly, each firm's demand is more elastic if rivals can quickly expand output.

The firm's monopoly power is greater when:

• The industry demand is inelastic.
• Barriers to entry are high (limiting substitutes from new entrants).
• Differentiation is strong.

Question 7

Why is there a social cost to monopoly? If gains could be redistributed, would the social cost disappear?

Social cost: Monopoly produces Q_m < Q_c (competitive quantity). The units between Q_m and Q_c have value (to consumers) exceeding their production cost — but they go unproduced. This is deadweight loss — it cannot be recovered through redistribution.

Why redistribution doesn't eliminate social cost:

• DWL is a loss of total surplus — not a transfer.
• Redistributing monopoly profit transfers wealth from consumers to producers (or vice versa), but the foregone transactions (those Q between Q_m and Q_c) represent real value destroyed.
• Even after redistribution, society is poorer by the DWL triangle.

Social cost = DWL (area of triangle between demand, MC, from Q_m to Q_c). Redistribution of monopoly profits cannot recover this loss — it disappears as real economic value.

Question 8

Why does monopolist's output increase if government forces a lower price? What price maximizes output?

Why output increases: With a price ceiling below the monopoly price, the effective MR = ceiling price for quantities up to the demand at that price. This is higher than the monopolist's unconstrained MR at the monopoly output. So MR > MC at Q_m → the firm expands output.

Price that maximizes output: Set ceiling at P = MC. At this price:

• The firm produces where MC = P (as if competitive).
• No incentive to restrict output further.
• Output equals competitive equilibrium quantity.

Question 9

How should a monopsonist decide how much to buy? More or less than a competitive buyer?

Decision rule: Monopsonist buys where Marginal Factor Cost (MFC) = Marginal Value (demand curve).

MFC > supply price (because to hire one more unit, the monopsonist must raise wages for ALL units). So MFC > AVC of inputs → monopsonist sets MFC = demand, buying fewer units than competitive market.

Result: Monopsonist buys LESS than competitive buyers at a lower price — both quantity and price are below competitive levels.

Question 10

What is monopsony power? Why might a firm have it even if not the only buyer?

Monopsony power: The ability to pay below the competitive wage/price for inputs by exploiting an upward-sloping supply curve.

A firm has monopsony power whenever it faces an upward-sloping supply of inputs — which occurs if:

• It is a large buyer relative to the local labor market.
• Workers have limited geographic mobility.
• There are few alternative employers in the area.
• Specialized skills are required by only a few employers.

Question 11

Sources and determinants of monopsony power.

Sources:

• Concentrated buying power (single large employer, employer collusion).
• Specialized inputs with few alternative buyers.
• Geographic isolation (one factory town).
• Long-term contracts or switching costs for suppliers.

Determinants (parallel to seller-side):

1. Elasticity of supply of inputs: more inelastic supply → more monopsony power.
2. Number of competing buyers: more buyers → more elastic supply to any one buyer.
3. Ability of sellers to organize (unions reduce monopsony power).

Question 12

Why is there a social cost to monopsony? If gains redistributed, does social cost disappear?

Monopsony causes input quantity to fall below competitive level → some input suppliers who would supply at the competitive wage cannot find buyers. These foregone transactions represent DWL.

Redistribution doesn't help: DWL is real lost value (like the monopoly case). The low-paying monopsonist gains surplus, but the loss to uncovered suppliers exceeds this gain. DWL cannot be recovered by redistribution.

Question 13 & 14

Antitrust Laws — Coverage and Enforcement

Key laws: Sherman Act (1890): prohibits monopolization and restraint of trade. Clayton Act (1914): prohibits anticompetitive mergers, tying arrangements. FTC Act (1914): created Federal Trade Commission.

Enforcement: DOJ Antitrust Division (criminal cases, major mergers), FTC (civil cases, consumer protection). State AGs also enforce. Private lawsuits available (treble damages).

Examples: U.S. v. Microsoft (bundling IE with Windows), AT&T breakup (1982), Google antitrust investigation (ongoing).

PART II: EXERCISES — FULLY SOLVED

Exercise 1: Demand Increase — Does Price Always Rise?

Part 1: Will demand increase always raise monopoly price?

Concept Being Used: Monopolist sets MR = MC. Price depends on both demand and MR curve shift.

Answer: Not necessarily.

When demand increases, the MR curve shifts right (more demand at each quantity). However:

• If the demand becomes more elastic at the new equilibrium, MR increases faster than demand → price might not rise (or could even fall).
• For example, a parallel rightward shift of a linear demand curve raises both P and Q. But a demand increase that also makes demand more elastic could yield lower P with higher Q.

Key insight: Price = MR / (1 + 1/Ed) = MC / (1 + 1/Ed). If Ed increases in magnitude (more elastic), P/MC ratio falls even as MC stays constant.

Part 2: Will supply increase always lower monopsony price?

Similarly, not necessarily. If supply becomes more inelastic at higher quantities, MFC could shift in ways that don't uniformly lower the price paid.

Answer: An increase in demand does NOT always raise monopoly price; it depends on how elasticity changes. Similarly, more supply does not always lower the monopsony price.

Exercise 2: Caterpillar Tractor — What to Know Before Pricing

To advise on how a 5% price increase affects sales, Caterpillar needs:

1. Price elasticity of demand for its products: Ed = %(ΔQ)/%(ΔP). A 5% price increase reduces quantity by 5% × |Ed|.
2. Cross-price elasticities with competitors (John Deere, Komatsu): if demand is elastic due to substitutes, a 5% price rise could cause significant market share loss.
3. Market demand vs. firm demand: Even if market demand is inelastic (farm equipment is essential), Caterpillar's individual demand could be more elastic due to competition.
4. Buyer heterogeneity: Different segments (large farms vs. small) may have different elasticities.

Why these matter: The Lerner Index (P−MC)/P = 1/|Ed| tells Caterpillar its optimal pricing. Without knowing Ed, it cannot determine whether a price increase raises or lowers profits. If |Ed| > 1, a price increase reduces revenue.

Exercise 3: Constant Elasticity Demand — Does MC Increase of 25% Raise Price 25%?

Given: Ed = −2 (constant), MC = $20, profit-maximizing price.

Concept Being Used: With constant elasticity demand, the monopoly pricing rule gives a stable markup.

Lerner Index: (P − MC)/P = 1/|Ed| = 1/2 → P = 2 × MC.

Step-by-step: At MC = $20: P = 2 × 20 = $40. If MC rises 25% to $25: P = 2 × 25 = $50.

Price increase: (50 − 40)/40 = 25%. Yes, price rises by exactly 25%.

Why: With constant elasticity, P is always proportional to MC (P = MC / (1 + 1/Ed) = MC × Ed/(Ed+1) = MC × (−2)/(−1) = 2MC). A fixed percentage change in MC translates to the same percentage change in P.

Final Answer: Yes, price also rises by 25%. With constant elasticity demand, price is proportional to MC, so equal percentage changes in MC lead to equal percentage changes in P.

Exercise 4: Monopolist with Linear Demand and Cost

Given: P = 120 − 0.02Q (in cents per unit), C = 60Q + 25,000.

Part (a): Profit-maximizing production, price, profit

Step 1: Revenue and MR $TR=P\times Q=(120-0.02Q)Q=120Q-0.02Q^2$ $MR=\frac{d(TR)}{dQ}=120-0.04Q$

Step 2: Marginal cost $MC=\frac{dC}{dQ}=60$

Step 3: Set MR = MC $120-0.04Q=60\Rightarrow 0.04Q=60\Rightarrow Q^{*}=1,500$

Step 4: Price $P^{*}=120-0.02(1500)=120-30=90\text{ cents}$

Step 5: Profit $\pi =TR-TC=90(1500)-[60(1500)+25000]$ $=135,000-90,000-25,000=20,000\text{ cents}=\$200$

Part (b): Tax of 14 cents per unit → MC rises to 74 cents

Step 1: New MR = MC $120-0.04Q=74\Rightarrow 0.04Q=46\Rightarrow Q^{*}=1,150$

Step 2: New price $P^{*}=120-0.02(1150)=120-23=97\text{ cents}$

Step 3: New profit $\pi =97(1150)-[74(1150)+25000]=111,550-85,100-25,000=1,450\text{ cents}=\$14.50$

Interpretation: A tax of 14 cents raises price by only 7 cents (97 − 90 = 7). With linear demand, tax is shared: monopolist passes on approximately half the tax to consumers.

Final Answers:

• (a) Q* = 1,500 units, P* = 90 cents, Profit = $200
• (b) With tax: Q* = 1,150, P* = 97 cents, Profit = $14.50

Exercise 5: Monopolist from Demand Table (MC = $10)

Given: Demand table; P = 18 − 0.5Q (derived from table: P ranges from 18 at Q=0 to 0 at Q=36).

Part (a): Marginal revenue

Derive MR from demand (P = 18 − 0.5Q): $TR=(18-0.5Q)Q=18Q-0.5Q^2$ $MR=18-Q$

Part (b): Profit-maximizing output and price

Set MR = MC: 18 − Q = 10 → Q* = 8, P* = $14.

Profit (assuming only variable costs, TC = 10Q): $\pi =(P-MC)\times Q=(14-10)\times 8=\$32$

Part ©: Competitive equilibrium

P = MC = $10: Q_c = 2(18−10) = 16 (or from demand: Q = 2(18−P) = 16). P_c = $10, Q_c = 16.

Part (d): Social gain from competitive pricing

Deadweight loss from monopoly = area of triangle between monopoly and competitive points: $DWL=\frac{1}{2}(P_m-MC)(Q_c-Q_m)=\frac{1}{2}(14-10)(16-8)=\frac{1}{2}(4)(8)=\$16$

Gainers: Consumers gain the DWL ($16) plus the producer surplus transferred (rectangle from $10 to $14 over 8 units = $32).

Losers: Monopolist loses the rectangle ($32 in producer surplus transferred to consumers). But gains of consumers exceed losses of monopolist by $16 (the DWL recovered).

Net social gain = $16 (the DWL recovered by competitive pricing).

Final Answers:

• (a) MR = 18 − Q
• (b) Q* = 8, P* = $14, Profit = $32
• © Competitive: Q = 16, P = $10
• (d) Social gain = $16 (DWL eliminated). Consumers gain, monopolist loses.

Exercise 6: Monopoly vs. Competition — One Firm Industry

Given: C = 100 + 2q², MC = 4q, P = 90 − 2Q, MR = 90 − 4Q.

Part (a): Monopoly equilibrium

Set MR = MC: $90 - 4Q = 4Q \Rightarrow 90 = 8Q \Rightarrow Q_m = 11.25$ $P_m=90-2(11.25)=90-22.5=\$67.50$

Profit: $\pi =TR-TC=67.50(11.25)-[100+2(11.25{)}^2]$ $=759.375-100-253.125=\$406.25$

Part (b): Competitive equilibrium (P = MC)

$90-2Q=4Q\Rightarrow 6Q=90\Rightarrow Q_c=15,P_c=60$

Profit: ${\pi }_c=60(15)-[100+2(225)]=900-100-450=\$350$

Part ©: Graph description and profit comparison

The graph has:

• Demand curve D: P = 90 − 2Q (downward sloping).
• MR curve: P = 90 − 4Q (twice the slope, intersects x-axis at Q=22.5).
• MC = AC (above FC): MC = 4Q (upward sloping through origin).
• AC = 100/Q + 2Q (U-shaped).

Two ways to see profit difference:

1. Rectangle method: Monopoly profit = area of rectangle (P_m − AC_m) × Q_m. Competitive profit = (P_c − AC_c) × Q_c. Difference = $406.25 − $350 = $56.25.
2. DWL area: DWL = area of triangle (monopoly creates) = (1/2)(P_m − MC_m)(Q_c − Q_m). At Q_m = 11.25: MC_m = 4(11.25) = $45. P_m = $67.50. Q_c = 15. DWL = (1/2)(67.50 − 45)(15 − 11.25) = (1/2)(22.50)(3.75) = $42.19. But this is not equal to the profit difference — because this is a one-firm analysis comparing profit levels, not total surplus.

Final Answers:

• (a) Monopoly: Q = 11.25, P = $67.50, Profit = $406.25
• (b) Competition: Q = 15, P = $60, Profit = $350
• © Monopoly earns $56.25 more profit. The DWL from monopoly = $42.19.

Exercise 7: Monopolist with Known Elasticity

Given: Q = 800, P = $40, Ed = −2.

Part (a): Marginal cost

Lerner Index: (P − MC)/P = 1/|Ed| = 1/2 $40 - MC = 20 \Rightarrow MC = $20$

Part (b): Percentage markup

$(P-MC)/P=(40-20)/40=50\%$

Part ©: Profit

AC = $15, FC = $2,000, Q = 800. TC = AC × Q = 15 × 800 = $12,000. TR = 40 × 800 = $32,000. $\pi =TR-TC=32,000-12,000=\$20,000$

Final Answers:

• (a) MC = $20
• (b) Markup = 50%
• © Profit = $20,000

Exercise 8: Monopolist with Two Factories

Given: C₁ = 10Q₁², C₂ = 20Q₂²; P = 700 − 5Q, Q = Q₁ + Q₂.

Concept Being Used: Multi-plant profit maximization: equalize MC across plants and set equal to MR.

Step 1: Individual plant MC curves $M{C}_1=20Q_1,M{C}_2=40Q_2$

Step 2: Derive total MC (minimize cost for any Q)

Set MC₁ = MC₂: 20Q₁ = 40Q₂ → Q₁ = 2Q₂. Total Q = Q₁ + Q₂ = 2Q₂ + Q₂ = 3Q₂ → Q₂ = Q/3, Q₁ = 2Q/3. $M{C}_{total}=20Q_1=20\times \frac{2Q}{3}=\frac{40Q}{3}$

Step 3: Derive MR $TR=(700-5Q)Q=700Q-5Q^2\Rightarrow MR=700-10Q$

Part (b): Set MR = MC_total $700-10Q=\frac{40Q}{3}$ $700=10Q+\frac{40Q}{3}=\frac{30Q+40Q}{3}=\frac{70Q}{3}$ $Q=\frac{700\times 3}{70}=30$

$Q_1=\frac{2\times 30}{3}=20,Q_2=\frac{30}{3}=10$ $P=700-5(30)=\$550$

Verify: MC₁ = 20(20) = 400; MC₂ = 40(10) = 400; MR = 700 − 300 = 400. ✓ All equal.

Profit: $\pi =550(30)-[10(400)+20(100)]=16500-4000-2000=\$10,500$

Part ©: Labor costs rise in Factory 1 only

With higher MC₁, at same Q₁ = 20, MC₁ increases. To re-equalize:

• Factory 1 output (Q₁): Decreases (higher cost → produce less).
• Factory 2 output (Q₂): Increases (to compensate, keeping MC₁ = MC₂).
• Total output (Q): Decreases (MR = new MC_total at higher cost → lower intersection with MR curve).
• Price ℗: Increases (less total output → higher price on demand curve).

Final Answers:

• (b) Q₁ = 20, Q₂ = 10, Q = 30, P = $550, Profit = $10,500
• © Q₁ falls, Q₂ rises, total Q falls, price rises.

Exercise 9: Drug Company with Two Plants

Given: MC₁ = 20 + 2Q₁, MC₂ = 10 + 5Q₂, P = 20 − 3(Q₁+Q₂).

Concept Being Used: Multi-plant profit max; check corner solution if MR < min MC of a plant at zero.

Step 1: Check Plant 1 viability

At Q₁ = 0: MC₁ = 20. MR = 20 − 6Q. At Q = 0: MR = 20. As Q increases, MR falls. Setting MR = MC₁ would require: 20 − 6Q = 20 + 2Q₁ → negative Q₁. Plant 1 should not produce.

Step 2: Only Plant 2 produces

MR = MC₂: 20 − 6Q₂ = 10 + 5Q₂ (with Q₁ = 0, Q = Q₂) $10=11Q_2\Rightarrow Q_2=\frac{10}{11}\approx 0.91\text{ units}$

Step 3: Price $P=20-3\left(\frac{10}{11}\right)=20-\frac{30}{11}=\frac{220-30}{11}=\frac{190}{11}\approx \$17.27$

Verify: MR = 20 − 6(10/11) = 20 − 60/11 = 160/11 ≈ $14.55. MC₂ = 10 + 5(10/11) = 10 + 50/11 = 160/11. ✓ MC₁ at Q₁=0 = $20 > MR = $14.55 → correct not to use Plant 1. ✓

Final Answer: Produce only in Plant 2: Q₁ = 0, Q₂ = 10/11 ≈ 0.91 units, P = 190/11 ≈ $17.27/unit.

Exercise 10: Alcoa Aluminum Antitrust Case

Background: Alcoa controlled 90% of primary aluminum. Secondary (recycled) aluminum = 30% of total supply. Alcoa argued this limits its monopoly power.

Part (a): Argument in favor of Alcoa's position

• The relevant market is total aluminum supply (primary + secondary), not just primary.
• Secondary aluminum is a close substitute for primary — consumers can use either.
• If Alcoa raised prices, secondary producers would supply more, limiting Alcoa's price power.
• The effective market share = primary/(primary + secondary) < 90%.
• High cross-price elasticity between primary and secondary = competitive discipline on Alcoa.

Part (b): Argument against Alcoa's position

• Alcoa itself controlled the supply of secondary aluminum (it had sold most of the scrap in circulation originally). This "vertically integrated" recycling is not truly competitive supply.
• The recycling sector depends on Alcoa's past production — Alcoa could reduce future scrap availability by limiting current production.
• Secondary aluminum may have quality differences for certain uses, limiting substitutability.
• The relevant question is long-run market control, where Alcoa's integrated control over the full aluminum cycle gives sustained monopoly power.

Part ©: Judge Hand's ruling

Judge Learned Hand ruled against Alcoa — finding it guilty of monopolization. He held that Alcoa had deliberately maintained its monopoly through continuous investment and expansion to forestall competitors, even if the methods used were individually legal. This established the concept that achieving monopoly through superior efficiency is legal, but deliberately using a position of dominance to exclude competition is not.

Exercise 11: Monopolist with Price Ceiling — Lerner Index

Given: P = 11 − Q, AC = MC = $6.

Part (a): Monopoly equilibrium

MR = 11 − 2Q. Set MR = MC: 11 − 2Q = 6 → Q* = 2.5, P* = $8.50.

Profit = (P − MC) × Q = (8.50 − 6)(2.5) = $2.50 × 2.5 = $6.25

Lerner Index: (8.50 − 6)/8.50 = 2.50/8.50 ≈ 0.294

Consumer Surplus: CS = 0.5(11 − 8.50)(2.5) = 0.5 × 2.50 × 2.5 = $3.125

Part (b): Price ceiling at $7

At P = $7, demand: Q = 11 − 7 = 4. With ceiling, effective MR = $7 for Q ≤ 4. Since MC = $6 < $7, firm produces Q = 4 (ceiling binds as profit per unit = $1 > 0).

Profit = (7 − 6)(4) = $4.00

Lerner Index = (7 − 6)/7 = 1/7 ≈ 0.143 (reduced monopoly power)

CS = 0.5(11 − 7)(4) = 0.5 × 4 × 4 = $8.00 (increased significantly)

Part ©: Price ceiling that maximizes output

Output is maximized when P = MC (competitive level). Set ceiling = MC = $6.

At P = $6: Q = 11 − 6 = 5 units (maximum).

Profit = (6 − 6)(5) = $0 (zero profit — break-even regulated monopoly).

Lerner Index = 0 (no monopoly power).

Final Answers:

• (a) Q* = 2.5, P* = $8.50, Profit = $6.25, Lerner Index = 0.294
• (b) With $7 ceiling: Q = 4, Profit = $4, Lerner Index = 0.143
• © Ceiling of $6 maximizes output at Q = 5, Lerner Index = 0

Exercise 12: MMMT — Monopoly in Short and Long Run

Given: Q = 10,000/P², SRTC = 2,000 + 5Q, LRTC = 6Q.

Setup: From Q = 10,000/P² → P = 100/Q^(1/2). TR = PQ = 100Q^(1/2). MR = 50Q^(−1/2) = 50/√Q.

Part (a): Short-run profit maximization

$M{C}_{SR}=5$ Set MR = MC: 50/√Q = 5 → √Q = 10 → Q* = 100

$P^{*}=100/\sqrt{100}=\$10$

${\pi }_{SR}=10(100)-[2000+5(100)]=1000-2000-500=-\$1,500\text{ (loss!)}$

Should it shut down? VC = 5Q = $500. TR = $1,000 > VC = $500. → TR > VC → Do NOT shut down. Firm contributes $500 toward fixed costs.

Part (b): Long-run profit maximization

$M{C}_{LR}=6$ Set MR = MC: 50/√Q = 6 → √Q = 50/6 → Q = (50/6)² = 2500/36 ≈ 69.44 units

$P^{*}=100/\sqrt{2500/36}=100/(50/6)=\$12$

${\pi }_{LR}=12(2500/36)-6(2500/36)=(12-6)(2500/36)=6\times 69.44=\$416.67\text{ (profit!)}$

In LR, no fixed costs → TR = $833.33 > TC_LR = $416.67. Do NOT shut down. Firm earns positive profit.

Part ©: Can MC be lower in SR than LR?

Here MC_SR = $5 < MC_LR = $6. This is unusual but can occur.

Normally in competitive LR, firms optimize all inputs → LRMC ≤ SRMC (envelope theorem). But here the cost functions are given exogenously, and the relationship reversed. The SRTC = 2000 + 5Q implies constant variable cost ($5/unit). The LRTC = 6Q implies all costs are variable at a slightly higher rate. In the short run, the firm has already made investments that allow cheaper production, but these come with high fixed costs. In the long run, without those fixed-cost investments, the marginal unit is more expensive.

Final Answers:

• (a) SR: Q* = 100, P* = $10, Profit = −$1,500 (loss but don't shut down)
• (b) LR: Q* ≈ 69.44, P* = $12, Profit ≈ $416.67 (positive)
• © Yes — SR MC can be less than LR MC when fixed investments yield lower variable costs

Exercise 13: Two Plants in Competitive Market

Situation: Competitive market, P = $10. Connecticut (CT) labor costs rise → MC_CT increases. Should firm shift production to Massachusetts (MA)?

Concept Being Used: Profit maximization with multiple plants in competitive market: set MC at each plant = market price P.

Answer: NO shift to MA is needed.

Reasoning:

• Before the CT cost increase: Both plants optimized at MC_MA = MC_CT = P = $10.
• After CT labor rise: At old output level, MC_CT > $10 → CT overproducing. CT should reduce output until MC_CT = $10 again.
• MA was already producing optimally at MC_MA = $10. Adding more MA output would push MC_MA > $10 → unprofitable.
• The optimal response is: reduce CT output (not transfer it to MA).
• Total firm output may fall; the firm cannot substitute MA production for CT at P = $10 without losing money.

Final Answer: The firm should reduce CT output but NOT increase MA output. MA was already at the profit-maximizing level (MC_MA = P = $10). Adding more MA output exceeds the market price.

Exercise 14: Monopsony for Teaching Assistants

Given: Demand: W = 30,000 − 125n; Supply: W = 1,000 + 75n.

Part (a): Monopsonist equilibrium

Step 1: Total expenditure on n TAs = n × W_supply = n(1,000 + 75n) = 1,000n + 75n².

Step 2: Marginal Factor Cost (MFC) $MFC=\frac{d(TE)}{dn}=1,000+150n$

Step 3: Set MFC = Demand (value of TAs to university): $1,000+150n=30,000-125n$ $275n=29,000\Rightarrow n^{*}=105.45\approx 105\text{ TAs}$

Step 4: Wage paid (from supply curve at n = 105): $W^{*}=1,000+75(105.45)=1,000+7,909=\$8,909$

Step 5: Competitive equilibrium (for comparison): Supply = Demand: 1,000 + 75n = 30,000 − 125n → 200n = 29,000 → n = 145. W = 1,000 + 75(145) = $11,875.

Monopsony hires fewer TAs (105 vs. 145) at a lower wage ($8,909 vs. $11,875). ✓

Part (b): Infinite supply at W = $10,000 (perfectly elastic supply)

Demand at W = $10,000: 10,000 = 30,000 − 125n → n = 160 TAs.

With a flat supply at $10,000, MFC = $10,000 (buying additional TAs doesn't raise the wage). The university sets MFC = Demand → hires 160 TAs at $10,000 each.

Final Answers:

• (a) Monopsonist hires ~105 TAs at $8,909/year
• (b) At flat supply of $10,000: hires 160 TAs

Exercise 15: Dayna's Doorstops — Price Ceilings and Deadweight Loss

Given: C = 100 − 5Q + Q², MC = −5 + 2Q, P = 55 − 2Q.

Part (a): Monopoly profit and consumer surplus

MR = 55 − 4Q. Set MR = MC: $55-4Q=-5+2Q\Rightarrow 60=6Q\Rightarrow Q^{*}=10$ $P^{*}=55-20=\$35$ $TC=100-50+100=\$150$ $\pi =35(10)-150=350-150=\$200$ $CS=\frac{1}{2}(55-35)(10)=\frac{1}{2}(20)(10)=\$100$

Part (b): Competitive output (P = MC)

$55-2Q=-5+2Q\Rightarrow 60=4Q\Rightarrow Q_c=15,P_c=25$ $T{C}_c=100-75+225=\$250;{\pi }_c=25(15)-250=375-250=\$125$ $C{S}_c=\frac{1}{2}(55-25)(15)=\frac{1}{2}(30)(15)=\$225$

Part ©: Deadweight loss from monopoly

$DWL=\frac{1}{2}(P_m-M{C}_m)(Q_c-Q_m)$ At Q_m = 10: MC = −5 + 20 = $15. $DWL=\frac{1}{2}(35-15)(15-10)=\frac{1}{2}(20)(5)=\$50$

Verification: Total surplus under monopoly = π + CS = 200 + 100 = $300. Under competition = π + CS = 125 + 225 = $350. Difference = $50 = DWL. ✓

Part (d): Price ceiling at $27

Demand at P = $27: Q = (55−27)/2 = 14. At Q = 14: MC = −5 + 28 = $23 < $27 → firm produces Q = 14.

$\pi =27(14)-[100-70+196]=378-226=\$152$ $CS=\frac{1}{2}(55-27)(14)=\frac{1}{2}(28)(14)=\$196$

DWL: from Q=14 to Q_c=15: $DWL=\frac{1}{2}(27-23)(15-14)=\frac{1}{2}(4)(1)=\$2$

Part (e): Price ceiling at $23

At P=$23: MR=$23. Set MC=MR: −5+2Q=23 → Q=14. (Same output.) At Q=14, demand price = 55−28 = $27 > $23 = ceiling. Firm is constrained to charge $23.

$\pi =23(14)-226=322-226=\$96$ $CS=\frac{1}{2}(55-23)(14)=\frac{1}{2}(32)(14)=\$224$ $DWL=\$2\text{ (same as part d — output still 14)}$

Part (f): Price ceiling at $12

MC = $12: −5+2Q=12 → Q=8.5. Demand at $12: Q=(55−12)/2=21.5 > 8.5 → firm produces 8.5.

$\pi =12(8.5)-[100-42.5+72.25]=102-129.75=-\$27.75\text{ (loss)}$

Check: TR = $102 > VC = −42.5 + 72.25 = $29.75. → Still operating (TR > VC).

$CS=\frac{1}{2}(55-12)(8.5)=\frac{1}{2}(43)(8.5)=\$182.75$

DWL = area from Q=8.5 to Q_c=15: At Q=8.5: demand = 55−17=$38, MC=$12. Gap = $26.$DWL = \frac{1}{2}(38 - 12)(15 - 8.5) = \frac{1}{2}(26)(6.5) = $84.50$

Key insight: Ceiling at $12 (below competitive price $25) cuts output below monopoly level (8.5 < 10), creating MORE DWL than monopoly!

Summary Table:

Exercise 16: Natural Monopoly — Lake Wobegon Electric (LWE)

Given: 10 households, each Q = 50 − P. TC = 500 + Q. Market demand: Q = 10(50 − P) = 500 − 10P → P = 50 − Q/10. MC = 1, FC = 500.

Part (a): No DWL (P = MC = $1)

$Q=500-10(1)=490\text{ units}$ $CS=\frac{1}{2}(50-1)(490)=\frac{1}{2}(49)(490)=\$12,005$ $\pi =1(490)-[500+490]=490-990=-\$500\text{ (loss)}$

Part (b): Lowest price where LWE breaks even (P = AC)

Set P = AC: 50 − Q/10 = 500/Q + 1 → 49 = Q/10 + 500/Q

Multiply by 10Q: 490Q = Q² + 5,000 → Q² − 490Q + 5,000 = 0

$Q=\frac{490\pm \sqrt{{490}^2-4(5000)}}{2}=\frac{490\pm \sqrt{220100}}{2}\approx \frac{490\pm 469.1}{2}$

Two solutions: Q ≈ 479.6 (high output) or Q ≈ 10.4 (low output). For regulated utility: take Q ≈ 479.6 (efficient solution), P = 50 − 47.96 ≈ $2.04.

$CS\approx \frac{1}{2}(50-2.04)(479.6)\approx \frac{1}{2}(47.96)(479.6)\approx \$11,496$ $\pi \approx 0\text{ (break-even by construction)}$

DWL ≈ 0.5(2.04−1)(490−479.6) = 0.5(1.04)(10.4) ≈ $5.41 (small but positive)

Part ©: Kristina's two-part tariff plan

At P = MC = $1: Each household demands Q_i = 50 − 1 = 49 units.

Consumer surplus per household at P=$1:$CS_i = \frac{1}{2}(50 - 1)(49) = \frac{1}{2}(49)^2 = $1,200.50$

LWE's deficit = $500 (from part a). Fixed fee per household = $500/10 = $50/household.

Each household's net benefit = CS_i − Fixed fee = $1,200.50 − $50 = $1,150.50 > 0. No household will refuse — paying $50 gives net benefit of $1,150.50 from electricity access.

Final Answers:

• (a) P = MC = $1: Q = 490, CS = $12,005, Profit = −$500
• (b) Break-even price ≈ $2.04, DWL ≈ $5.41
• © Fixed fee = $50/household (each still gets CS of $1,150.50 > $0)

Exercise 17: Town-Owned Monopoly — Does Profit Redistribution Justify Monopoly Price?

Claim: Because profits are redistributed to citizens, it makes economic sense to charge monopoly price.

Answer: FALSE.

Reasoning:

1. Monopoly pricing creates DWL — some consumers value the good above MC but below monopoly price → they don't buy it → these potential gains are permanently lost.
2. Redistributing profits transfers monopoly profit from "consumers as buyers" to "consumers as shareholders" — the same people. This is like taking money from your left pocket and putting it in your right pocket.
3. But the DWL represents real economic destruction: transactions that would have generated value for all parties don't happen. This loss is NOT recovered through redistribution.
4. Charging competitive price (P = MC) eliminates DWL and maximizes total welfare, after which profits (= 0 with true competition) need no redistribution.
5. A town-owned utility should be regulated at P = MC or AC, not monopoly price.

The CEO is wrong. Redistribution of monopoly profits does not eliminate the deadweight loss. The community is worse off under monopoly pricing even with redistribution.

Exercise 18: Monopolist with Non-Linear Demand

Given: Q = 144/P², AVC = Q^(1/2), FC = 5.

Setup: From Q = 144/P²: P = 12/Q^(1/2). VC = AVC × Q = Q^(1/2) × Q = Q^(3/2). $MC=\frac{d(VC)}{dQ}=\frac{3}{2}{Q}^{1/2}$ $TR=PQ=\frac{12}{\sqrt{Q}}\times Q=12\sqrt{Q}$ $MR=\frac{d(TR)}{dQ}=\frac{6}{\sqrt{Q}}$

Part (a): Profit-maximizing price and quantity

Set MR = MC: $\frac{6}{\sqrt{Q}}=\frac{3}{2}\sqrt{Q}\Rightarrow 6=\frac{3}{2}Q\Rightarrow Q^{*}=4$ $P^{*}=12/\sqrt{4}=\$6$ $\pi =TR-TC=12(2)-[8+5]=24-13=\$11$

Part (b): Government imposes P ≤ $4

At ceiling P = $4: Demand Q = 144/16 = 9. With ceiling, MR = $4 for Q ≤ 9. Set MC = $4: (3/2)√Q = 4 → √Q = 8/3 → Q = 64/9 ≈ 7.11.

Check: Q = 64/9 ≤ 9 (demand at $4). ✓ Firm produces Q ≈ 7.11 units.

$\pi =4\left(\frac{64}{9}\right)-[{\left(\frac{64}{9}\right)}^{3/2}+5]=\frac{256}{9}-[\frac{512}{27}+5]$ $=28.44-18.96-5=\$4.48$

Part ©: Ceiling that maximizes output

Output is maximized when P_ceiling = MC along the demand curve (P = MC on demand): $\frac{12}{\sqrt{Q}}=\frac{3}{2}\sqrt{Q}\Rightarrow 12=\frac{3}{2}Q\Rightarrow Q=8$ $P=12/\sqrt{8}=\frac{12}{2\sqrt{2}}=3\sqrt{2}\approx \$4.24$

Set ceiling at P ≈ $4.24 → maximizes output at Q = 8 units.

Final Answers:

• (a) Q* = 4, P* = $6, Profit = $11
• (b) At P = $4 ceiling: Q ≈ 7.11, Profit ≈ $4.48
• © Output-maximizing ceiling = $4.24, output = 8 units

Exercise 19: Uber Surge Pricing

Given: Weekday: P = 50 − Q; Surge: P = 100 − Q; MC = 0 (then MC = 10).

Part (a): Profit-maximizing prices with MC = 0

Weekday: MR = 50 − 2Q = 0 → Q = 25, P = $25. Surge: MR = 100 − 2Q = 0 → Q = 50, P = $50.

Part (b): Profit-maximizing prices with MC = $10

Weekday: 50 − 2Q = 10 → Q = 20, P = $30. Surge: 100 − 2Q = 10 → Q = 45, P = $55.

Part ©: Graph and welfare analysis — Surge with MC = $10

At surge Q = 45, P = $55:$\pi = (P - MC) \times Q = (55 - 10)(45) = 45 \times 45 = $2,025$

Competitive Q (P = MC): 100 − Q = 10 → Q_c = 90. $DWL=\frac{1}{2}(55-10)(90-45)=\frac{1}{2}(45)(45)=\$1,012.50$

Consumer Surplus: $CS=\frac{1}{2}(100-55)(45)=\frac{1}{2}(45)(45)=\$1,012.50$

Note: π = CS = DWL all equal $1,012.50 (a symmetric result from linear demand with the specific numbers here).

Final Answers:

• (a) Weekday: P = $25; Surge: P = $50 (MC = 0)
• (b) Weekday: P = $30; Surge: P = $55 (MC = $10)
• © Profit = $2,025, CS = $1,012.50, DWL = $1,012.50

PART III: LEARNING ENHANCEMENTS

Key Formula Sheet — Chapter 10

| Formula | Description | |---|---| | MR = MC | Monopoly profit maximization | | MR = P(1 + 1/Ed) | MR and demand elasticity link | | Lerner Index = (P−MC)/P = 1/|Ed| | Measure of monopoly power | | P = MC/(1 + 1/Ed) | Monopoly pricing rule | | DWL = 0.5(P_m − MC)(Q_c − Q_m) | Deadweight loss from monopoly | | MFC = d(WL)/dL | Monopsony Marginal Factor Cost | | Monopsony rule: MFC = MVL | Monopsony hiring decision |

Important Equilibrium Conditions

Common IPMX Exam Traps

1. "Monopoly supply curve exists" — Wrong. No unique supply curve under monopoly.
2. "A tax on monopolist is fully passed to consumers" — Wrong. With linear demand, only ~half is passed on.
3. "Monopoly DWL is recovered by redistributing profit" — Wrong. DWL is real destroyed value.
4. "Lower price ceiling always increases welfare" — Wrong. Ceiling below competitive price reduces output and increases DWL (worse than monopoly).
5. "Monopsony buys more than competitive market" — Wrong. Buys less, at lower price.
6. "Lerner Index = profit margin" — Not the same. Lerner Index = (P−MC)/P, not accounting profit margin.

Comparison: Monopoly vs. Perfect Competition

| Feature | Perfect Competition | Monopoly | |---|---|---| | Price | P = MC | P > MC | | Output | Socially optimal | Below optimal | | Profit (LR) | Zero | Positive | | Consumer surplus | Maximum | Reduced | | DWL | Zero | Positive | | Lerner Index | 0 | 1/|Ed| > 0 | | Supply curve | Exists | Does not exist |

End of Chapter 10 Solution Manual