Free markets and the largest sum of consumer and producer surplus

The terms.

• Consumer surplus is the area below the demand curve and above the price: buyers gain it when they are willing to pay more for a unit than the price they actually pay.
• Producer surplus is the area above the supply curve and below the price. A competitive firm's supply curve is the rising part of its marginal cost curve (from minimum average variable cost in the short run), and the market supply curve is the horizontal sum of the firms' curves; so producer surplus is the excess of the price received over the cost of producing each unit.
• Total surplus is consumer surplus plus producer surplus: a money measure of the well-being that buyers and sellers together get from the market.

What the statement claims. In a free, perfectly competitive market the price moves until quantity demanded equals quantity supplied. The statement says that the quantity traded at this equilibrium is the one at which total surplus is as large as it can be: no other quantity would give buyers and sellers together a bigger gain.

Why the market quantity gives the largest total surplus.

• Buyers. A buyer stays in the market only while her willingness to pay is at least the price; one whose willingness to pay is below the price drops out. The units bought therefore go to the buyers who value them at no less than the price.
• Sellers. A firm produces up to the point where price equals marginal cost, on the rising part of its marginal cost curve, so the units sold are produced by the sellers whose cost of producing them is at most the price.
• Less than the equilibrium quantity. Some units that buyers value above their cost of production would not be traded, and the surplus on them is lost. The SOL's tax example shows this: a tax that cuts output from 20 units to 18 removes the surplus on the 2 lost units, a deadweight loss to society.
• More than the equilibrium quantity. The extra units would cost more to produce than they are worth, so producing them subtracts from total surplus. The SOL's tariff analysis shows the same kind of loss from over-production, when domestic firms are pushed to produce units costing more than the price at which the good could otherwise be had.
• At the equilibrium quantity the value of the last unit to its buyer equals its cost to its seller, so neither more nor less output can raise total surplus.

Example: a guava market. Our own figures. Demand is P = 100 − Q and supply is P = 20 + Q, with P in ₹ per kg and Q in kg. Equilibrium: 100 − Q = 20 + Q gives Q = 40 kg and P = ₹60.

• Consumer surplus = ½ × 40 × (100 − 60) = ₹800; producer surplus = ½ × 40 × (60 − 20) = ₹800; total surplus = ₹1,600.
• If only 30 kg were traded, the 30th kg would be worth ₹70 to a buyer and cost ₹50 to produce; total surplus falls to ₹1,500, a loss of ½ × 10 × (70 − 50) = ₹100.
• If 50 kg were traded, the 50th kg would cost ₹70 but be worth only ₹50; total surplus again falls to ₹1,500, a loss of ½ × 10 × (70 − 50) = ₹100. Only at the market quantity of 40 kg is total surplus at its largest.

Conditions and limits. The statement holds under conditions, and the SOL notes both that markets are usually a good way to organise economic activity and that government can sometimes improve on them:

• Competition. Buyers and sellers must be price takers, as in a perfectly competitive market.
• No externalities. If an activity harms others who are not compensated, such as smoke from a brick kiln damaging crops on nearby farms, the market does not count that harm, and a shared resource is used beyond its efficient level.
• No public goods. Left to the market, public goods are supplied in an inefficient quantity.
• No interference that changes the quantity. A tax drives a wedge between what buyers pay and sellers receive and creates a deadweight loss.
• Efficiency is not equity. Total surplus measures the size of the gains, not how they are shared; the government may still be needed to pursue equality.

Conclusion. In a competitive market with no externalities or public goods, the equilibrium quantity is exactly the one at which the value of the last unit to buyers equals its cost to sellers, so the sum of consumer and producer surplus is maximised; producing less or more lowers it. The statement is therefore true under these conditions, though a maximum total surplus says nothing about whether it is fairly shared.