Lesson 10: Monopoly

Warm-Up

One company holds the patent on a life-changing drug. No substitutes, no rivals, twenty years of legal protection. Unlike our wheat farmer, this firm doesn't take a price — it chooses one, by choosing how much to produce. But even a monopolist can't have everything: to sell more, it must charge less — on every unit. That single fact drives the entire monopoly model, and the graph it produces is the second-most-tested drawing in AP Micro after Lesson 9's.

Core Concept

What makes a monopoly

A monopoly is a single seller of a product with no close substitutes, protected by barriers to entry:

Barriers mean profits can persist in the long run — no entry machine to erode them (the single deepest difference from perfect competition).

Why MR < P for a price maker

The monopolist faces the market demand curve — downward-sloping. To sell one more unit it must cut the price on all units (single-price monopoly). Marginal revenue is therefore the new unit's price minus the revenue lost on every earlier unit:

MR < P for every unit after the first. For a linear demand curve, MR has the same intercept and twice the slope — it bisects the horizontal distance to demand and hits zero at demand's midpoint (where demand is unit elastic and TR peaks). A monopolist never knowingly operates on the inelastic half of demand: there, selling more lowers TR while raising TC.

The monopoly two-step

1. Quantity: produce where MR = MC → Qm.
2. Price: go up from Qm to the demand curve → Pm. (The demand curve tells you the most buyers will pay for Qm units.)

Profit = (Pm − ATC at Qm) × Qm — same rectangle logic as Lesson 9.

[GRAPH: Monopoly. X-axis "Quantity", Y-axis "Price/Cost". Downward demand D; MR below it with twice the slope, hitting the Q-axis at half of D's intercept. Upward MC; U-shaped ATC. MR = MC at Qm = 40; dashed line up to D gives Pm = $14; ATC at Qm = $9; profit rectangle (14 − 9) × 40 shaded. Efficient point where MC crosses D at Qc = 60, Pc = $10, labeled "allocatively efficient point". DWL triangle between D and MC from Qm to Qc shaded.]

The #1 graphing error in all of AP Micro: reading the price off the MR curve. Price ALWAYS comes from the demand curve above Qm.

Monopoly vs. perfect competition

Against a competitive industry with the same costs (Pc, Qc where MC crosses D):

The monopoly restricts output below the efficient level: units between Qm and Qc are worth more to buyers (height of D) than they cost to make (height of MC), but they're never produced. That lost surplus is the deadweight loss of monopoly.

Note what monopoly does not automatically mean: guaranteed profit. A monopolist with weak demand can run losses (ATC above demand everywhere) — draw ATC above the price and the same rules apply, including shutdown logic in the short run.

Worked Examples

Example 1 (easy): The two-step on a table

Demand: P = $20 at Q=1, $18 at 2, $16 at 3, $14 at 4, $12 at 5. MC constant at $8. Find Qm, Pm.

Solution: TR: 20, 36, 48, 56, 60 → MR: 20, 16, 12, 8, 4. MR ≥ MC through Q = 4 (MR = 8 = MC). Qm = 4, price from demand = $14.

Interpretation: Price is $14 (demand at Q=4), not $8 (that's MR/MC). The two-step in table form.

Example 2 (medium): Profit and DWL

From Example 1, ATC at Q = 4 is $10. If this market were competitive, output would be where P = MC: Q = 5? (P at 5 is $12 > 8; extend: at Q = 6, P = $10; at Q = 7, P = $8.) Take Qc = 7. Compute monopoly profit and describe the DWL.

Solution: Profit = (14 − 10) × 4 = $16. DWL = surplus lost on units 5–7, where willingness to pay ($12, $10, $8) ≥ MC ($8): lost surplus = (12−8) + (10−8) + (8−8) = $6.

Interpretation: DWL is not the monopolist's profit — profit is a transfer from consumers; DWL is value that no one gets.

Example 3 (AP-style): Graph reading

A single-price monopolist's graph shows: MR = MC at Q = 30; demand height at Q = 30 is $25; MC at Q = 30 is $13; ATC at Q = 30 is $18; MC crosses demand at Q = 45 where P = $19. Find (i) price, (ii) profit, (iii) the allocatively efficient output, (iv) DWL area description.

Solution: - (i) $25 (up to demand at Qm = 30) - (ii) (25 − 18) × 30 = $210 - (iii) Q = 45, where P (demand) = MC - (iv) The triangle between demand and MC from Q = 30 to Q = 45 — approximately ½ × 15 × (25 − 13) = $90 if the curves are straight.

Interpretation: Four questions, four different curves read at the right places. Slow is smooth; smooth is fast.

Example 4 (AP-style): Elastic-range logic

A monopolist is producing where demand is inelastic. Explain why this cannot be profit-maximizing.

Solution: In the inelastic range, MR < 0: cutting output raises TR (price effect dominates) — and producing less also lowers TC. Higher revenue + lower cost = higher profit, so the firm should keep cutting output until it's back in the elastic range where MR > 0.

Interpretation: "MR = MC with MC ≥ 0 implies MR ≥ 0 implies the elastic portion of demand" — a favorite conceptual MC question.

Common Mistakes

1. Reading price from MR or MC. Quantity from MR = MC; price from demand. Every year, thousands of students donate this point to College Board.
2. Labeling monopoly profit as DWL (or vice versa). Profit = rectangle (transfer). DWL = triangle between D and MC over the missing units (pure loss).
3. Assuming monopolies always profit. Barriers protect profits if demand is strong; a monopoly can lose money (ATC everywhere above D).
4. Drawing MR with the same slope as demand. Linear demand → MR twice as steep, same vertical intercept, zero at demand's midpoint.
5. Saying monopoly output is "where MC crosses demand." That's the efficient benchmark (Qc), precisely what monopoly fails to produce.

Practice Problems

10. (FRQ-style) Zenith Pharma holds the patent on Clarivex and is a single-price monopolist. (a) Draw a correctly labeled graph showing demand, MR, MC, and ATC for a monopolist earning positive economic profit. Label the profit-maximizing quantity Qm and price Pm, and shade the profit rectangle. (b) On your graph, label the allocatively efficient quantity Qe and shade the deadweight loss. (c) Explain why Zenith produces less than the allocatively efficient quantity. (d) The patent expires and identical generics flood in, making the market perfectly competitive. State what happens to price, output, and consumer surplus.