Lesson 05: Market Efficiency, Price Controls & Taxes

Warm-Up

You'd have paid up to $50 for that hoodie; it cost $30. You silently pocketed $20 of value — economists call it consumer surplus. The seller who'd have accepted $18 pocketed $12 of producer surplus. Markets create these gains on every trade — and this lesson is about measuring them, and measuring what's destroyed when governments cap prices, prop them up, or tax transactions. These graph-area questions are among the most point-dense on the whole exam.

Core Concept

Consumer and producer surplus

• Consumer surplus (CS) = willingness to pay − price actually paid. Graphically: the area below the demand curve and above the price, out to the quantity traded.
• Producer surplus (PS) = price received − minimum acceptable price (marginal cost). Area above the supply curve and below the price.
• Total surplus (economic surplus) = CS + PS — the total gains from trade.

[GRAPH: Supply and demand crossing at P = $6, Q = 100. Triangle between demand curve and the P line from Q=0 to Q=100 shaded and labeled "CS". Triangle between the P line and supply curve shaded and labeled "PS". Demand intercept $10; supply intercept $2.]

With linear curves these are triangles: area = ½ × base × height. In the graph above: CS = ½ × 100 × (10 − 6) = $200; PS = ½ × 100 × (6 − 2) = $200; total surplus $400.

At competitive equilibrium, total surplus is maximized — this is allocative efficiency: every unit for which willingness to pay ≥ marginal cost gets produced (up to where P = MC), and no unit for which cost exceeds value does.

Deadweight loss

Deadweight loss (DWL) is total surplus destroyed when the market quantity is not the efficient quantity — trades that would have created value never happen (underproduction) or trades that destroy value happen (overproduction). Graphically, DWL is usually the triangle between the demand and supply curves, between the actual quantity and Q*.

Price ceilings

A price ceiling is a legal maximum price (rent control, anti-gouging laws). It matters only if set below equilibrium ("binding").

[GRAPH: Supply and demand, equilibrium at P = $6, Q = 100. Horizontal line at Pc = $4 below equilibrium labeled "price ceiling". At $4: Qs = 60, Qd = 140; horizontal gap labeled "shortage = 80". DWL triangle between curves from Q = 60 to Q = 100 shaded.]

Consequences of a binding ceiling: - Shortage (Qd > Qs); quantity traded falls to Qs (the short side of the market rules) - Deadweight loss from the lost trades - Non-price rationing: lines, waiting lists, favoritism, black markets - CS may rise or fall; PS unambiguously falls - A ceiling set above equilibrium is nonbinding — no effect

Price floors

A price floor is a legal minimum price (minimum wage, agricultural supports). It matters only if set above equilibrium.

[GRAPH: Supply and demand, equilibrium at P = $6, Q = 100. Horizontal line at Pf = $8 above equilibrium labeled "price floor". At $8: Qd = 60, Qs = 140; gap labeled "surplus = 80". DWL triangle from Q = 60 to Q = 100 shaded.]

Consequences of a binding floor: - Surplus (Qs > Qd); quantity traded falls to Qd - Deadweight loss; sellers compete in non-price ways; government may buy the surplus (farm programs) - In the labor market: a binding minimum wage → surplus of labor = unemployment

Quantity traded always falls under a binding control — whichever of Qd/Qs is smaller governs.

Per-unit taxes and incidence

A per-unit (excise) tax of $T on sellers shifts the supply curve up/left by exactly $T (each unit now needs $T more to be supplied).

[GRAPH: Demand and original supply S₁ at equilibrium ($6, 100). New curve S₂ parallel, vertically $2 above S₁. New intersection with D at Pb = $7.20, Q = 80. Price sellers keep: Ps = Pb − 2 = $5.20. Bracket showing tax wedge $2 between $7.20 and $5.20 at Q = 80. Government revenue rectangle = 2 × 80. DWL triangle between curves from Q = 80 to Q = 100.]

Outcomes: - Buyers pay Pb (higher than old P); sellers keep Ps = Pb − T - Quantity falls → DWL (the tax blocks mutually beneficial trades) - Government revenue = T × new Q (a rectangle) - Tax incidence (who bears the burden) depends on relative elasticities, not on who legally pays: the more inelastic side bears more of the tax. Perfectly inelastic demand → buyers bear all; perfectly elastic demand → sellers bear all. - More elastic curves (either one) → bigger quantity drop → bigger DWL*.

A per-unit subsidy is the mirror image: supply shifts down/right by the subsidy, quantity rises past the efficient level, buyers pay less, sellers receive more, government spends subsidy × Q, and there's DWL from overproduction (units whose cost exceeds their value get made).

Tariffs (preview)

A tariff is a tax on imports. With a world price below domestic equilibrium, a tariff raises the domestic price toward (but below) the no-trade level: domestic production ↑, consumption ↓, imports shrink, government collects tariff revenue, and two DWL triangles appear (overproduction by high-cost domestic firms + lost consumption). Full treatment typically appears with the ceiling/floor toolkit — the mechanics are the same area-hunting.

Worked Examples

Example 1 (easy): Surplus areas

Demand: P = 20 − Q. Supply: P = 4 + Q. Find equilibrium, CS, and PS.

Solution: 20 − Q = 4 + Q → Q* = 8, P* = 12. - CS = ½ × 8 × (20 − 12) = $32 - PS = ½ × 8 × (12 − 4) = $32 - Total surplus = $64.

Interpretation: Heights come from the intercepts: demand chokes at $20, supply starts at $4.

Example 2 (medium): Binding ceiling

Same market. Government caps price at $8. Find quantity traded, the shortage, and the DWL.

Solution: At P = 8: Qs = 8 − 4 = 4; Qd = 20 − 8 = 12. - Quantity traded = 4 (short side). - Shortage = 12 − 4 = 8 units. - DWL = area between curves from Q = 4 to Q = 8: at Q = 4, demand height = 16, supply height = 8, gap = 8 → DWL = ½ × (8 − 4) × 8 = $16*.

Interpretation: The DWL triangle's base runs along the quantity axis (from Qtraded to Q*); its height is the demand–supply gap at the traded quantity.

Example 3 (AP-style): Tax incidence

A $3 per-unit tax is imposed on sellers of a good with very inelastic demand and elastic supply. (i) Who bears more of the tax? (ii) What happens to DWL if demand were instead very elastic?

Solution: - (i) Buyers bear more: inelastic demanders can't dodge the tax, so the price to buyers rises by most of the $3, while elastic sellers escape by cutting output. - (ii) With elastic demand the quantity drop is bigger → DWL is larger (and buyers bear less).

Interpretation: Mantra: the inelastic side gets stuck with the bill; elasticity anywhere magnifies deadweight loss.

Example 4 (AP-style): Reading a tax graph

After a $2/unit tax, buyers pay $7.20, sellers keep $5.20, and quantity falls from 100 to 80. Compute: government revenue, buyer share, seller share, and DWL (pre-tax price was $6).

Solution: - Revenue = 2 × 80 = $160 - Buyer burden = (7.20 − 6.00) × 80 = $96; seller burden = (6.00 − 5.20) × 80 = $64 (sum = $160 ✓) - DWL = ½ × (100 − 80) × 2 = $20

Interpretation: Burdens must sum to revenue — a built-in arithmetic check the graders love to see.

Common Mistakes

1. Putting the ceiling above equilibrium (or the floor below). Binding ceiling = BELOW equilibrium; binding floor = ABOVE. Draw the horizontal line on the correct side or the whole part scores zero.
2. Using Qd for quantity traded under a ceiling. Sellers won't supply more than Qs — the short side always wins.
3. Claiming the buyer pays the whole tax because "the tax was on sellers." Legal incidence ≠ economic incidence; elasticities decide.
4. Wrong DWL triangle. DWL sits between the curves, spanning from the restricted quantity to the efficient quantity — not the shortage/surplus gap along the price line.
5. Forgetting subsidies cause DWL too. Any wedge that moves quantity away from Q* — up or down — destroys surplus.

Practice Problems

11. (FRQ-style) The competitive market for rental apartments in Bayville is in equilibrium at $1,500/month and 40,000 units. The city imposes a rent ceiling of $1,200/month. At $1,200, landlords supply 32,000 units and renters demand 50,000 units. (a) Draw a correctly labeled supply-and-demand graph showing the equilibrium and the rent ceiling. (b) Identify the quantity of apartments actually rented and the size of the shortage. (c) Shade or identify the area of deadweight loss and explain why it exists. (d) Identify one non-price rationing mechanism likely to emerge. (e) If the ceiling were set at $1,700, what would happen? Explain.