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Intermediate Microeconomics Unit 7: Perfect Competition and Welfare

Competitive firms take prices as given and set price equal to marginal cost; free entry drives profits to zero, and the resulting equilibrium maximizes total surplus, which is why taxes and price controls create deadweight loss.

Covers: Profit maximization and P = MC, Shutdown rule and short-run supply, Long-run equilibrium and industry supply, Consumer and producer surplus, Taxes, subsidies and incidence, Price controls and deadweight loss, Pareto efficiency and the welfare theorems

Study guide

A perfectly competitive firm is a price taker, so its marginal revenue equals the market price. It maximizes profit by producing where P = MC on the rising part of the MC curve. In the short run, fixed costs must be paid whether or not the firm produces, so it compares price with average variable cost: if P is below minimum AVC it shuts down, otherwise it produces even if it makes a loss. The firm's short-run supply curve is therefore its MC curve above minimum AVC, and the market supply curve is the horizontal sum of all firms' supply curves.

In the long run firms can enter or exit. Economic profits attract entrants, which shift supply right and lower price; losses cause exit, which raises price. With identical firms, long-run equilibrium has price equal to minimum long-run average cost and zero economic profit. The number of firms equals market demand at that price divided by each firm's efficient output. In a constant-cost industry, long-run supply is horizontal at min LRAC. If expansion bids up input prices, the industry has increasing costs and an upward-sloping long-run supply curve.

Welfare is measured by surplus. Consumer surplus is the area under demand above price; producer surplus is the area above supply below price, equal to revenue minus variable cost. In a competitive equilibrium, every unit whose value exceeds its marginal cost is traded, so total surplus is maximized. A per-unit tax drives a wedge between the price buyers pay and the price sellers keep; the burden falls more on the less elastic side, regardless of who legally pays. Revenue is the tax times the new quantity, and the deadweight loss is the triangle of lost trades, which grows with the square of the tax.

Price controls also destroy surplus. A binding ceiling below equilibrium creates a shortage, a binding floor above equilibrium creates a surplus, and in both cases the quantity traded falls to the short side of the market. Subsidies overshoot, producing units that cost more than buyers value. More generally, an allocation is Pareto efficient if no one can be made better off without hurting someone else. In an exchange economy, efficiency requires equal MRSs across consumers, the contract curve of the Edgeworth box. The first welfare theorem says competitive equilibria are Pareto efficient; the second says any efficient allocation can be reached with lump-sum transfers and markets.

Key ideas

• A price taker produces where P = MC with MC rising.
• Shut down in the short run if P < min AVC; exit in the long run if P < min ATC.
• Long-run competitive equilibrium has P = min LRAC and zero economic profit.
• Producer surplus equals revenue minus variable cost; profit is producer surplus minus fixed cost.
• Tax incidence depends on relative elasticities, not on who legally pays.
• Taxes, subsidies and binding price controls create deadweight loss by changing the quantity traded.
• Competitive equilibria are Pareto efficient; efficiency in exchange requires equal MRSs.

Formulas and rules

Common mistakes

• Shutting down whenever price is below ATC instead of below AVC.
• Assuming the side that legally pays a tax bears its burden.
• Computing tax revenue with the pre-tax quantity.
• Forgetting that a price ceiling above equilibrium (or floor below it) has no effect.
• Equating Pareto efficiency with fairness or equal shares.

Before the test, make sure you can

• Find a competitive firm's profit-maximizing output and profit.
• Apply the shutdown rule and derive short-run supply.
• Solve for long-run price, output per firm and number of firms.
• Compute consumer surplus, producer surplus and deadweight loss.
• Calculate tax incidence, revenue and DWL for linear supply and demand.
• Analyze binding price ceilings, floors and subsidies.
• Test whether an allocation is Pareto efficient and state the two welfare theorems.

Words to know

Price taker

A firm too small to affect the market price; its MR equals P.

Profit-maximizing rule (competition)

Produce where P = MC, on the rising part of the MC curve.

Shutdown price

The minimum of AVC; below it, the firm produces nothing in the short run.

Short-run supply curve

The firm's MC curve above minimum AVC.

Long-run equilibrium

With free entry, P = min LRAC and economic profit is zero.

Constant-cost industry

An industry whose input prices do not change with industry output; long-run supply is horizontal.

Increasing-cost industry

An industry in which expansion raises input prices; long-run supply slopes upward.

Producer surplus

The area above supply and below price; revenue minus variable cost.

Consumer surplus

The area below demand and above price.

Deadweight loss

The loss of total surplus from trades that would have been mutually beneficial but do not happen.

Tax incidence

How the burden of a tax is divided between buyers and sellers.

Price ceiling

A legal maximum price; binding when set below equilibrium, causing a shortage.

Price floor

A legal minimum price; binding when set above equilibrium, causing a surplus.

Pareto efficiency

An allocation where no one can be made better off without making someone worse off.

Contract curve

In an Edgeworth box, the set of Pareto-efficient allocations, where MRSs are equal.

First welfare theorem

Under standard conditions, a competitive equilibrium is Pareto efficient.

Second welfare theorem

With convex preferences, any Pareto-efficient allocation can be reached as a competitive equilibrium after lump-sum transfers.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.