ECON10004 · Introductory Microeconomics
Monopoly and Game Theory
A monopoly is a single seller of a product with no close substitute, so unlike the price-taking competitive firm it chooses a point on the downward-sloping market demand curve rather than taking the price as given. Because selling one more unit forces the price down on every unit, marginal revenue lies below price (MR < P), and the firm produces where MR = MC, then reads the price up to demand — opening a markup over marginal cost. The welfare half of the topic compares that outcome to the efficient P = MC benchmark, isolating the transfer to the firm and the deadweight loss destroyed on the units never made, and asks how a regulator should respond. Game theory then handles oligopoly, where each firm's best move depends on its rivals': payoff matrices, dominant strategies, Nash equilibrium and the prisoner's dilemma. ECON10004 tests this as Market Structure 2, sitting after perfect competition (Ch 8) and before factor markets, because it is the live policy lens on real Australian market power.
What this chapter covers
- 01Where market power comes from: barriers to entry (resource, government/patent, natural monopoly)
- 02The single seller faces market demand = AR
- 03Why marginal revenue is below price: the output vs price effect, and the linear MR = a − 2bQ rule
- 04Profit maximisation: MR = MC for Q*, then read P* off demand; the markup and Lerner index
- 05Price discrimination (1st/2nd/3rd degree) and natural monopoly
- 06The welfare cost: P = MC benchmark, transfer vs deadweight loss, and that monopoly has no supply curve
- 07Regulating a monopoly: P = MC vs P = AC pricing
- 08Game theory: payoff matrix, dominant strategy, Nash equilibrium, the prisoner's dilemma and cartel instability
The full monopoly solve (EX 9A)
- +1Marginal revenue. TR = P×Q = (16 − Q)Q = 16Q − Q². Using the linear rule (a = 16, b = 1): MR = 16 − 2Q.
- +1Marginal cost. TC = Q², so MC = dTC/dQ = 2Q.
- +1Set MR = MC. 16 − 2Q = 2Q ⇒ 16 = 4Q ⇒ Q* = 4.
- +1Read the price off demand (not MR or MC): P* = 16 − Q* = 16 − 4 = $12. Sense-check: P* = 12 > MC = 2×4 = 8. ✓
- +1Revenue, cost, profit. TR = P*×Q* = 12×4 = 48; TC = Q*² = 16; π = TR − TC = 48 − 16 = $32.
Key terms
- Marginal revenue (MR)
- The extra revenue from selling one more unit. For a monopolist MR < P (always, for Q > 0) because selling more requires cutting the price on every unit already sold — the output effect (+P) plus the price effect (−). For linear demand P = a − bQ, MR = a − 2bQ: same intercept, twice the slope.
- Lerner index
- A measure of market power, L = (P − MC)/P, the markup as a fraction of price. It runs from 0 for a competitive firm (P = MC) toward 1 as power grows. A firm sets a bigger markup when demand is less elastic, so inelastic demand plus high entry barriers imply a large L.
- Deadweight loss (DWL)
- The surplus destroyed because a monopolist restricts output below the efficient Qc. The units between Qm and Qc are worth more to buyers than they cost to make yet are never produced. It equals the triangle ½×(Qc−Qm)×(Pm−MC at Qm), gained by no one — distinct from the transfer of surplus to the firm.
- Natural monopoly
- A market where economies of scale make average cost keep falling over the whole relevant range, so one large firm supplies more cheaply than many small ones. Arises from technology (high fixed costs, network industries), not strategy. The policy answer is not to break it up but to regulate the price.
- Nash equilibrium
- A combination of strategies where each player is best-responding to the other, so no one can do better by changing their move alone. It is the standard prediction for a game's outcome — stable, but not necessarily efficient, as the prisoner's dilemma shows.
Monopoly and Game Theory FAQ
Do I read the monopoly price off MR, MC, or demand?
Off demand — always. MR = MC only gives you the profit-maximising quantity Q*. The firm then charges the highest price the market will bear for Q*, which is found by plugging Q* into the demand curve and reading straight up. A reliable sense-check is that P* must exceed MC; if your price isn't above MC, you read it off the wrong curve. Charging P = MC (the competitive rule) or reading the price off MR are the two traps the exam baits every year.
When I make demand into MR, do I double everything?
No — you keep the demand intercept a and double only the slope coefficient b. For P = 16 − Q the marginal revenue is MR = 16 − 2Q, not 32 − 2Q and not 16 − Q. The MR line shares the demand intercept but has twice the slope, so it lies below demand everywhere (except at Q = 0) and turns negative at half the demand quantity. Get the coefficient on Q right and the rest of the question falls out.
Why doesn't a monopoly have a supply curve?
A supply curve maps each given price to a single quantity supplied. A monopolist doesn't respond to a given price — it chooses the price by picking a point on demand. So there is no supply curve to draw. Producer surplus is still well defined, though: it's the area above MC and below the price line out to Qm. Stating 'monopoly has no supply curve' is a frequent short-answer mark.
If the Nash equilibrium is stable, why isn't it the best outcome?
Because stability and group welfare are different questions. A Nash equilibrium is a cell no player wants to deviate from alone, but a better cell can exist that everyone prefers — it just isn't stable. In the prisoner's dilemma both confessing is Nash, yet both staying silent pays more; each player could grab a bigger individual payoff by deviating from the cooperative cell, so it can't hold. Individually rational choices produce a collectively bad outcome. This is also why cartels are unstable: each member gains by cheating.
Exam move
Marks are won by following one fixed chain and never improvising. For the solve: write MR from the linear rule (a − 2bQ), differentiate TC for MC, set MR = MC for Q*, then read P* up to demand and sense-check P* > MC. For welfare: after Qm, Pm, set P = MC for the competitive Qc, Pc, then compute the DWL two ways — as |ΔCS| − ΔPS and as the triangle ½×(Qc−Qm)×(Pm−MC at Qm) — and they must agree. On every diagram, markers award the shading: shade the profit rectangle for monopoly and the DWL triangle for welfare, and label Qm/Qc, Pm/Pc. For game theory, check dominance first (it's the fastest route to Nash), name the prisoner's dilemma explicitly, and be ready to say why cartels can't sustain the cooperative cell.
