Difficulty: Intermediate to Advanced | Prerequisites: Short-run and long-run cost curves, consumer theory (demand curves, utility).
This is the final layer of the course. Perfect competition and monopoly are the two polar market structures: one with many firms, zero market power, and price equal to marginal cost; the other with a single firm, full market power, and a deadweight loss from restricting output. Elasticity ties demand responsiveness to revenue. Revealed preference tests whether observed consumer behaviour is consistent with rational choice. Risk and insurance round out the course by introducing decisions under uncertainty. Collectively, these topics account for 8 of the 27 exam questions, plus 1 each for elasticity, revealed preference, and risk.
A perfectly competitive firm is a price taker that produces where P = MC and earns zero economic profit in the long run. A monopolist restricts output so that MR = MC, charges P > MC, and creates deadweight loss. Price elasticity of demand links percentage changes in quantity to percentage changes in price and determines what happens to total revenue. Revealed preference uses observed choices to test whether a consumer behaves rationally. Risk-averse consumers value certainty equivalents below expected value, and the gap is the risk premium they would pay for insurance.
Perfect competition
A market structure with many buyers and sellers, identical products, complete information, and free entry and exit. No single firm can influence the market price.
Price taker
A firm that accepts the market price as given. Its demand curve is a horizontal line at the market price, meaning demand is perfectly elastic.
Breakeven price
The price at which the firm earns zero economic profit. It equals the minimum of ATC. Below this price the firm makes losses in the short run.
Shutdown price
The minimum of AVC. If the market price falls below this, the firm produces nothing in the short run because it cannot even cover its variable costs.
Short-run supply curve (competitive firm)
The portion of the MC curve that lies above the minimum of AVC. Below that price, quantity supplied is zero.
Monopoly
A market with a single seller. The monopolist faces the entire downward-sloping market demand curve and has the power to set price above marginal cost.
Monopoly quantity (Q^M)
The output level where MR = MC. The monopolist restricts output relative to the competitive level to push the price up.
Monopoly price (P^M)
The price read off the demand curve at Q^M. Always higher than the competitive price because output is restricted.
Deadweight loss (DWL)
The loss in total surplus (consumer surplus plus producer surplus) caused by the monopolist producing less than the competitive quantity. It is the triangle between the demand curve and the MC curve, from Q^M to Q^C.
Consumer surplus (CS)
The area below the demand curve and above the price, up to the quantity purchased. It measures the total net benefit to consumers.
Producer surplus (PS)
The area above the MC curve (or supply curve) and below the price, up to the quantity sold. It measures the firm's gain from trading.
Price elasticity of demand (PED)
The percentage change in quantity demanded divided by the percentage change in price. Formally, e = (dQ/dP)(P/Q). It is typically negative, but often expressed in absolute value.
Weak Axiom of Revealed Preference (WARP)
If bundle A is chosen when bundle B is affordable, then bundle B must never be chosen when bundle A is affordable. A violation means the consumer's behaviour is inconsistent with utility maximisation.
Certainty equivalent
The guaranteed amount of money that gives the consumer the same utility as a risky gamble. For a risk-averse consumer, the certainty equivalent is less than the expected value of the gamble.
Risk premium
The difference between the expected value of a gamble and its certainty equivalent. It measures how much the consumer would pay to eliminate risk. Risk premium = E[W] - CE.
Willingness to pay for insurance (WTP)
The maximum amount a risk-averse consumer would pay to fully insure against a risk. Equal to the risk premium.
Assumptions: many buyers and sellers, identical (homogeneous) products, complete information, free entry and exit.
A perfectly competitive firm faces a perfectly elastic (horizontal) demand curve at the market price P.
Why P = MR: since the firm can sell any quantity at the market price, the revenue from one additional unit is just P. More formally, MR = P(1 - 1/|e|), and if |e| = ∞ (perfectly elastic), then MR = P.
Profit maximisation: set MR = MC. Since MR = P, the rule becomes P = MC.
Short-run supply curve: the upward-sloping portion of the MC curve that lies at or above the minimum of AVC. If P < min(AVC), the firm shuts down and produces zero.
Short-run profit: π = (P - ATC) × Q. If P > ATC, the firm earns positive profit. If P = ATC, it breaks even. If AVC < P < ATC, it operates at a loss but continues producing because it covers its variable costs.
Breakeven price: the price equal to the minimum of ATC. At this price, economic profit is exactly zero.
Competitive output and price (Q^C, P^C): used as the benchmark when comparing to monopoly. Q^C is where the supply curve (or MC) intersects the demand curve. P^C = MC at that quantity.
A monopolist is the sole seller and faces the entire downward-sloping market demand curve.
Key relationship: because the demand curve slopes downward, the monopolist must lower the price on all units to sell one more unit. This means MR < P. Specifically, MR = P(1 - 1/|e|).
Profit maximisation: set MR = MC, then read the price off the demand curve at that quantity. The result is Q^M (monopoly quantity) and P^M (monopoly price).
P > MC: since MR = MC and P > MR, it follows that P > MC. This is the source of the inefficiency.
Comparing to perfect competition:
Q^M < Q^C (monopolist produces less)
P^M > P^C (monopolist charges more)
Consumer surplus is smaller under monopoly.
Producer surplus may be larger under monopoly (the monopolist captures part of what was consumer surplus).
Deadweight loss = the triangle between the demand curve and MC, from Q^M to Q^C. This is surplus that neither consumers nor the monopolist capture.
Calculating surplus areas: draw the demand curve, MC curve, and MR curve. CS = triangle above P^M and below demand, from 0 to Q^M. PS = area below P^M and above MC, from 0 to Q^M. DWL = triangle between demand and MC, from Q^M to Q^C.
Formula: e = (dQ/dP)(P/Q), or equivalently, e = (%ΔQ) / (%ΔP). Demand elasticity is negative for a downward-sloping demand curve, but is often discussed in absolute value |e|.
Elastic vs inelastic:
|e| > 1: elastic. A 1% price increase causes more than a 1% drop in quantity.
|e| < 1: inelastic. A 1% price increase causes less than a 1% drop in quantity.
|e| = 1: unit elastic.
Relationship with total revenue (TR = P × Q):
If demand is elastic (|e| > 1), a price decrease raises TR.
If demand is inelastic (|e| < 1), a price decrease lowers TR.
If demand is unit elastic (|e| = 1), TR is at its maximum.
Relationship with marginal revenue: MR = P(1 - 1/|e|).
When |e| > 1: MR > 0.
When |e| = 1: MR = 0.
When |e| < 1: MR < 0.
A profit-maximising monopolist always operates on the elastic portion of the demand curve (where MR > 0).
Core idea: if a consumer chose bundle A when bundle B was affordable, then A is "revealed preferred" to B. We write A R B.
WARP (Weak Axiom of Revealed Preference): if A is revealed preferred to B, then B must not be revealed preferred to A. In other words, if the consumer chose A when B was in the budget set, then in any other situation where the consumer chose B, A must not have been in the budget set.
Testing for a WARP violation:
For each observation, compute the cost of every other observed bundle at that observation's prices.
If the chosen bundle costs at least as much as another observed bundle (meaning the other bundle was affordable), then the chosen bundle is revealed preferred.
Check whether any pair of observations has A revealed preferred to B and B revealed preferred to A. If so, WARP is violated.
What you can infer: if A is revealed preferred to B, then U(A) ≥ U(B). You can also identify bundles that must be on a lower indifference curve, narrowing down the consumer's preference ordering from observed behaviour alone.
Expected value: E[W] = p₁W₁ + p₂W₂, where p_i is the probability of outcome i and W_i is the wealth in that outcome.
Expected utility: E[U] = p₁U(W₁) + p₂U(W₂). A risk-averse consumer has a concave utility function (U'' < 0), so E[U(W)] < U(E[W]).
Certainty equivalent (CE): the guaranteed wealth level that gives the same utility as the gamble. Solve U(CE) = E[U]. For a risk-averse consumer, CE < E[W].
Risk premium: RP = E[W] - CE. It is the amount the consumer would sacrifice to eliminate the risk entirely. A larger RP means the consumer is more risk-averse.
Willingness to pay for insurance: the maximum premium a risk-averse consumer would pay for full insurance equals the risk premium. If the insurance costs less than RP, the consumer buys it.
Graphical intuition: with a concave utility function, draw a chord between U(W₁) and U(W₂). The expected utility is on the chord at E[W]. The certainty equivalent is where the utility curve reaches that same height. The horizontal gap between CE and E[W] is the risk premium.
\text{Competitive firm profit: } \pi = (P - ATC) \times Q\text{Monopolist's MR (linear demand } P = a - bQ\text{): } MR = a - 2bQ\text{MR and elasticity: } MR = P\left(1 - \frac{1}{|e|}\right)\text{Price elasticity: } e = \frac{dQ}{dP} \cdot \frac{P}{Q}\text{Deadweight loss (linear): } DWL = \frac{1}{2}(P^M - MC(Q^M))(Q^C - Q^M)\text{Risk premium: } RP = E[W] - CE\text{WARP test: bundle A revealed preferred to B if } P_A \cdot A \geq P_A \cdot B \text{ and A was chosen}Students often think a competitive firm can set its own price. It cannot. The firm takes the market price as given. Its only decision is how much to produce.
Students sometimes think the monopolist chooses a point on the MR curve. The monopolist sets quantity where MR = MC, but charges the price on the demand curve at that quantity, not MR.
Students often confuse the sign of elasticity with its magnitude. Demand elasticity is negative, but when comparing to 1 (elastic vs inelastic), use the absolute value.
Students sometimes think "inelastic demand" means quantity does not change at all. It means quantity changes less than proportionally to price, not that it stays fixed.
With WARP, students sometimes check only one direction. You must check both: if A is revealed preferred to B, verify that B is not also revealed preferred to A.
Students sometimes think a risk-averse consumer avoids all risk. Risk aversion means the consumer would pay a premium to avoid risk, not that they never take gambles.
⚠️ 2 questions on perfect competition. Expect to find the profit-maximising quantity, compute short-run profit, identify the breakeven price, or describe the supply curve.
⚠️ 3 questions on monopoly. The standard problem: given a demand curve and MC, find Q^M, P^M, CS, PS, and DWL. Comparing to the competitive outcome (Q^C, P^C) is almost certain.
⚠️ 1 question on price elasticity. Know all three links: to total revenue, to MR, and how to calculate it from a demand function.
⚠️ 1 question on revealed preference. Expect a table of price-quantity observations and a question asking whether WARP is violated, or what you can infer about the consumer's preferences.
⚠️ 1 question on uncertainty and risk. Calculate the certainty equivalent, risk premium, and WTP for insurance given a utility function and a two-outcome gamble.
True or false: a perfectly competitive firm's short-run supply curve is its entire MC curve. (False: only the portion above the minimum of AVC.)
Fill in the blank: a monopolist maximises profit by setting ______ = ______. (MR = MC.)
True or false: if demand is inelastic, a price increase raises total revenue. (True.)
Fill in the blank: the risk premium equals E[W] minus ______. (the certainty equivalent.)
True or false: WARP is violated when bundle A is revealed preferred to B and bundle B is revealed preferred to A. (True.)
Q: A monopolist faces demand P = 100 - 2Q and has MC = 20. Find Q^M, P^M, Q^C, P^C, and the deadweight loss.
A: MR = 100 - 4Q. Set MR = MC: 100 - 4Q = 20, so Q^M = 20. P^M = 100 - 2(20) = 60. For the competitive outcome, set P = MC: 100 - 2Q = 20, so Q^C = 40. P^C = 20. DWL = (1/2)(60 - 20)(40 - 20) = (1/2)(40)(20) = 400.
Q: A competitive firm has TC = 50 + 2Q^2. The market price is P = 20. Find the profit-maximising quantity and short-run profit.
A: MC = dTC/dQ = 4Q. Set P = MC: 20 = 4Q, so Q* = 5. Profit = TR - TC = 20(5) - (50 + 2(25)) = 100 - 100 = 0. The firm breaks even.
Q: Demand is Q = 200 - 4P. At P = 30, what is the price elasticity of demand?
A: dQ/dP = -4. At P = 30, Q = 200 - 120 = 80. e = (-4)(30/80) = -1.5. Demand is elastic at this price.
Q: A consumer has U(W) = W^(1/2). They face a gamble: W = 100 with probability 0.5 and W = 36 with probability 0.5. Find the certainty equivalent, risk premium, and WTP for insurance.
A: E[U] = 0.5 × sqrt(100) + 0.5 × sqrt(36) = 0.5(10) + 0.5(6) = 8. CE: sqrt(CE) = 8, so CE = 64. E[W] = 0.5(100) + 0.5(36) = 68. Risk premium = 68 - 64 = 4. WTP for insurance = 4.
Q: In observation 1, prices are (P_X, P_Y) = (1, 2) and the consumer chooses (4, 3). In observation 2, prices are (2, 1) and the consumer chooses (3, 4). Is WARP violated?
A: Cost of bundle 2 at observation 1 prices: 1(3) + 2(4) = 11. Cost of bundle 1 at observation 1 prices: 1(4) + 2(3) = 10. Since 10 < 11, bundle 2 was not affordable when bundle 1 was chosen. So bundle 1 is not revealed preferred to bundle 2. Cost of bundle 1 at observation 2 prices: 2(4) + 1(3) = 11. Cost of bundle 2 at observation 2 prices: 2(3) + 1(4) = 10. Since 10 < 11, bundle 1 was not affordable when bundle 2 was chosen. Neither is revealed preferred to the other. WARP is not violated.
Perfect competition and monopoly build directly on the cost curves from the Production and Costs notes (Doc 3): the firm's MC curve is its supply curve in competition, and the starting point for the monopolist's profit-maximisation problem. Consumer surplus and deadweight loss tie back to demand curves derived from consumer theory (Doc 1). Elasticity connects to the MR formula used in monopoly pricing. The welfare comparison between competition and monopoly connects to Pareto efficiency (Doc 2): competitive equilibrium is efficient; monopoly is not.
Price taker, price setter, market power, market structure, homogeneous products, free entry, zero economic profit, long-run equilibrium, shutdown decision, marginal revenue, total revenue test, elastic demand, inelastic demand, unit elastic, Lerner index, allocative efficiency, welfare loss, surplus analysis, revealed preference axiom, SARP, GARP, rational consumer, expected utility theory, von Neumann-Morgenstern, risk aversion, risk neutrality, risk loving, concave utility, fair insurance, actuarially fair premium, expected value.