ECON5001 · Microeconomic Theory
Perfect Competition & Market Equilibrium
This is where the cost theory pays off and the first market structure appears. Perfect competition — many sellers, a homogeneous good, free entry — makes every firm a price-taker whose only choice is how much to produce. That single decision turns the cost curves of Chapter 6 into a supply curve: the firm produces where p = MC on the rising branch, supplies along MC above minimum AVC (the shutdown point), and earns producer surplus equal to revenue minus variable cost. Summing firms gives the short-run industry equilibrium; free entry and exit then drive long-run price down to minimum average cost, where economic profit is zero. The competitive equilibrium maximises total surplus, so it is allocatively efficient — and a quantity tax breaks that efficiency by a measurable deadweight-loss triangle. The exam rewards solving cleanly: optimise the firm, separate producer surplus from profit, clear the market, and let entry compete profit to zero.
What this chapter covers
- 011. Price-taking firm — max π = py − c(q); FOC p = MC on the rising branch
- 022. Short-run supply — MC above AVC; shutdown at min AVC (fixed cost is sunk)
- 033. Shutdown vs exit — p < min AVC (short run) vs p < min AC (long run)
- 044. Producer surplus — PS = TR − VC = area above supply, below price
- 055. PS is not profit — PS = π + F in the short run (they differ by fixed cost)
- 066. Short-run industry equilibrium — sum n firm supplies, set Qs = Qd
- 077. Long-run equilibrium — free entry/exit ⇒ p = min AC, zero economic profit
- 088. Welfare & tax — TS = CS + PS maximised at (p*, Q*); tax wedge, DWL, incidence
Profit maximisation, producer surplus and profit
- +2Marginal cost is MC = c′(q) = q + 6. The price-taker's rule is P = MC: 20 = q + 6, so q* = 14.
- +1Shutdown check. Average variable cost is AVC = (0.5q² + 6q)/q = 0.5q + 6, whose minimum (at q = 0) is 6. Since P = 20 > min AVC = 6, the firm produces rather than shutting down.
- +2Producer surplus = revenue − variable cost. TR = 20 × 14 = 280; VC = 0.5(14²) + 6(14) = 98 + 84 = 182. So PS = 280 − 182 = 98 (check the triangle: ½ × (20 − 6) × 14 = 98).
- +1Profit = PS − fixed cost = 98 − 40 = 58. Subtract F only after PS, never before.
Key terms
- Price-taker
- A firm so small relative to the market that it treats the price p as fixed and cannot influence it. Its marginal revenue equals the price (MR = p), so its only decision is the quantity q that maximises π = pq − c(q).
- p = MC supply rule
- The price-taking firm's first-order condition for profit maximisation: produce where price equals marginal cost, on the upward-sloping branch of MC. The other (falling-branch) intersection is a profit minimum, so always pick the rising branch.
- Short-run supply curve
- The portion of the marginal-cost curve that lies above minimum average variable cost. Below min AVC the firm shuts down (produces zero and loses its fixed cost F), so the supply curve has a floor at the shutdown point.
- Shutdown point vs exit
- Shutdown is a short-run choice to produce zero when p < min AVC (fixed cost is sunk, still paid). Exit is a long-run choice to leave the industry when p < min AC (once fixed costs become avoidable). A firm with min AVC ≤ p < min AC keeps producing at a loss in the short run.
- Producer surplus (PS)
- Revenue minus variable cost, PS = TR − VC, equal to the area above the supply (MC) curve and below the price line. In the short run PS = π + F (it exceeds profit by the fixed cost); in the long run, with no fixed cost, PS = π.
- Zero-profit (free entry/exit) condition
- In long-run competitive equilibrium, free entry and exit drive economic profit to zero, so price equals the minimum of long-run average cost (p = min LRAC). Each firm produces at efficient scale, and the number of firms adjusts to clear the market.
- Allocative efficiency
- The competitive equilibrium maximises total surplus (CS + PS) because at Q* the marginal willingness to pay equals marginal cost, so every mutually beneficial trade occurs. This is the First Welfare Theorem applied to a single market.
- Deadweight loss / tax incidence
- A per-unit tax t opens a wedge P_b = P_s + t, cuts the quantity traded, and destroys surplus equal to the welfare triangle DWL = ½ t (Q* − Q_t). The burden (incidence) falls more heavily on the more inelastic side of the market, regardless of who is legally taxed.
Perfect Competition & Market Equilibrium FAQ
When should a competitive firm shut down?
In the short run, shut down when the price falls below minimum average variable cost (p < min AVC), because every unit then loses money even before fixed cost, and the firm is better off producing zero and eating the sunk fixed cost −F. If min AVC ≤ p < min AC the firm makes a loss but keeps producing, because shutting down would forfeit the whole of F. Exit (leaving the industry) is a separate long-run decision, made when p < min AC.
What is the difference between producer surplus and profit?
Producer surplus is revenue minus variable cost (PS = TR − VC); profit subtracts fixed cost as well (π = TR − VC − F). So in the short run they differ by exactly the fixed cost: PS = π + F. A firm can have positive producer surplus but negative profit — that is the short-run loss case where it still produces because price covers its variable costs. If a question asks for profit, remember to subtract F after computing PS.
How do I find the long-run competitive equilibrium?
Use the two-line ritual. First, the long-run price equals minimum average cost, found by setting MC = AC and solving for the efficient scale q*, then p_LR = AC(q*). Second, plug p_LR into market demand to get total quantity, and divide by each firm's output: n = Q_d(p_LR)/q*. Free entry competes any short-run profit away until price falls to min AC, where economic profit is zero.
Why is the competitive equilibrium efficient?
Because it maximises total surplus (consumer surplus plus producer surplus). At the competitive quantity Q*, price equals marginal cost, so the marginal unit is valued by buyers at exactly what it costs to produce — every mutually beneficial trade has occurred and none of the harmful ones. This is the First Welfare Theorem from the exchange chapter, now seen in a single market. Any deviation (a tax, a quota, market power) shrinks total surplus and creates a deadweight loss.
Does it matter whether a tax is levied on buyers or sellers?
No — and this is a favourite exam trap. The economic incidence (who really bears the tax) and the size of the deadweight loss depend only on the relative elasticities of demand and supply, not on which side the statute names. The more inelastic side bears more of the burden; if one side is perfectly inelastic it bears the whole tax and there is no deadweight loss. Legal incidence is not economic incidence.
Exam move
Treat perfect competition as a four-move routine you can run on any problem, because the exam tests clean execution under time pressure rather than definitions. (1) Optimise the firm: set p = MC on the rising branch, then run the shutdown check (is p ≥ min AVC?). (2) Compute surplus carefully — producer surplus is revenue minus variable cost, and profit is PS minus fixed cost, so never quote one when the question asks for the other. (3) Build the short-run market by horizontally summing the n firms' supply curves (Qs = n·y(p)) and setting Qs = Qd. (4) For the long run, find p = min AC by solving MC = AC for the efficient scale, then get the firm count from n = Q_d(p_LR)/q*. Finish by checking welfare: total surplus is maximised at the competitive equilibrium, and a per-unit tax adds a deadweight-loss triangle whose burden is set by elasticities. Drill each move on a numerical problem until the setup is automatic, and keep a running list of the two traps that cost the most marks — confusing producer surplus with profit, and using AC instead of AVC for the shutdown test.
