MODULE 03Welfare & efficiency

Consumer & Producer Surplus

Default · quota 30 · $320 DWLAll modules

Module 03 · Theory

Consumer Surplus, Producer Surplus, and Efficiency

Mankiw · Ch. 7 · Consumers, producers, and the efficiency of markets

A demand curve is a willingness-to-pay schedule: at each quantity, it shows the value of the marginal unit to buyers. A supply curve is a marginal-cost schedule: it shows what it costs sellers to produce the next unit. The space between the two curves is the surplus the market creates.

Consumer surplus

Consumer surplus is the area below demand and above the price. Buyers who would have paid more than the market price keep the difference. When the price falls, the existing buyers gain on every unit and new buyers enter, so consumer surplus grows.

Producer surplus

Producer surplus is the area above supply and below the price. Sellers who would have accepted less than the market price keep the difference. It is not profit in an accounting sense: fixed costs are omitted, so producer surplus measures the gain from trading at the market price.

Total surplus is maximized at equilibrium

At the intersection, every unit whose value exceeds its marginal cost is produced, and no unit whose cost exceeds its value is produced. Total surplus is CS + PS. Move away from that quantity and some mutually beneficial trades disappear.

A quota creates deadweight loss

A binding quota limits quantity to Q_t < Q*. The demand price at that quantity becomes the single price buyers pay, while the marginal cost of the last unit is lower. The vertical gap between the two curves is the lost gain from each prevented trade. The triangle between Q_t and Q* is deadweight loss.

Quota rent

Sellers receive the quota price, not their marginal cost. The rectangle between the quota price and marginal cost is quota rent. In this single-price model it is counted inside producer surplus, which is why a quota can raise PS even as it destroys total surplus.

Formulas

P_d = 100 − Q

P_s = 20 + 0.6Q

Q* = 50, P* = $50

DWL = ½ (Q* − Q_t)(P_t − MC_t)

At Q_t = 30: P_t = $70, MC = $38, CS = $450, PS = $1,230, and DWL = $320. Total surplus plus DWL always returns to $2,000.

Try this

01Start at the efficient quantity of 50. Deadweight loss is zero and total surplus reaches its maximum of $2,000.
02Cut the quota to 30. The price rises to $70, quantity falls by 20, and $320 of surplus disappears.
03Cut it to 10. Producers still collect a large quota rent, but DWL jumps to $1,280.
04Set the quota to zero. CS and PS vanish and the entire $2,000 becomes deadweight loss.

Live welfare$1,680 total · DWL $320

Quota

Consumer surplusProducer surplusDeadweight lossQuota

Click the plane or drag the indigo handle at the bottom edge to change the quota. Focus the handle and use the arrow keys (Shift for larger steps; Home and End for the extremes).

Live readout

Who gets the surplus

Restricted output

Consumer surplus

$450

willingness to pay − price

Area below demand and above the price buyers pay.

Producer surplus

$1,230

price − marginal cost

Area above supply and below the price sellers receive.

Total surplus

$1,680

CS + PS

The welfare the market actually delivers.

Deadweight loss

$320

surplus destroyed

The gap between demand and supply from Q_t to Q*.

Welfare identity

Total surplus plus deadweight loss stays at the efficient total.

$2,000

Quota price / marginal cost

Buyers pay the demand price; the last unit costs less to make.

$70 / $38

Quantity traded

20 units below the efficient quantity.

30units

Quota rent

The rectangle between the quota price and marginal cost, counted inside PS.

$960