How the invisible hand allocates a good efficiently among buyers and sellers

The invisible hand. In a market economy there is no planner who decides who produces a good and who gets it. The decisions are spread over a great many households and firms, each pursuing its own interest and guided by prices, and the invisible hand of the market leads these separate choices to a good outcome for the economy. The term goes back to Adam Smith: in a perfectly competitive market, a force is at work that moves the price whenever buyers and sellers are out of balance.

How prices reach equilibrium. Each buyer aims at the greatest satisfaction and each firm at the greatest profit, and both take the price as given. If buyers want more than sellers offer at the going price (excess demand), the price rises; if sellers offer more than buyers want (excess supply), the price falls. The price stops moving where the quantity all buyers wish to buy equals the quantity all sellers wish to sell, the equilibrium. The price mechanism in this way settles what is produced, how and for whom.

Efficiency among buyers. At the equilibrium price, only buyers who value a unit at least as much as the price buy it; a buyer whose willingness to pay is below the price stays out. So the good goes to the buyers who value it most. The gap between what a buyer would pay and what she does pay is her gain, and summed over buyers it is consumer surplus, shown on a diagram as the region between the demand curve and the price line.

Efficiency among sellers. A competitive firm produces where price equals its marginal cost, on the rising part of its marginal cost curve, and the market supply is the sum of the firms' supplies. So the units sold are made by the producers who can make them at a cost no higher than the price, while higher-cost producers stay out. Summed over sellers, the excess of the price over each unit's cost is producer surplus; on a diagram it is the region lying between the price line and the supply curve.

Efficiency of the quantity traded. Total surplus, consumer plus producer surplus, measures the combined gain of buyers and sellers. At the equilibrium quantity, the last unit is worth to its buyer about what it costs its seller. Trading fewer units throws away units worth more than they cost: a tax that cuts output below equilibrium creates exactly such a deadweight loss. Trading more would mean units that cost more to make than they are worth to anyone who buys them; the SOL's tariff case shows this kind of loss from over-production. So the free equilibrium makes total surplus as large as it can be.

Example: cricket bats in Meerut. Our own figures. Five buyers would pay at most ₹900, ₹800, ₹700, ₹600 and ₹500 for a bat; five workshops can make one at a cost of ₹400, ₹500, ₹600, ₹700 and ₹800.

• At any price between ₹600 and ₹700, say ₹650, three buyers want a bat (those valuing it at ₹900, ₹800 and ₹700) and three workshops will make one (cost ₹400, ₹500 and ₹600). The market clears at 3 bats.
• Consumer surplus = 250 + 150 + 50 = ₹450; producer surplus = 250 + 150 + 50 = ₹450; total surplus = ₹900, which is also (900 + 800 + 700) − (400 + 500 + 600).
• A worse allocation among buyers: if a bat went to the ₹500 buyer instead of the ₹900 buyer, total surplus would fall by ₹400, to ₹500.
• A worse allocation among sellers: if the ₹800 workshop made a bat instead of the ₹400 one, total surplus would fall by ₹400.
• A wrong quantity: a fourth bat, made at ₹700 for the buyer who values it at ₹600, would cut total surplus by ₹100, to ₹800; stopping at two bats would lose the third bat's ₹100 of surplus (₹700 value minus ₹600 cost). No one directed this outcome: the price alone sorted the buyers and the workshops.

Conditions and limits.

• The market must be competitive, with buyers and sellers taking the price as given.
• Rules must be enforced. Without law and order and secure payment, the invisible hand cannot do its coordinating work.
• Prices must be free to move. When government holds a price away from its market level, it gets in the way of the invisible hand.
• No market failure. A firm that harms others without paying for it is not checked by price (an externality), and a public good is under-supplied if left to the market; here government can sometimes improve on the market.
• Efficiency is not equality. A large total surplus says nothing about how it is shared; government may still be needed to pursue equality.

Conclusion. Through the price, the invisible hand sends each unit to a buyer who values it at least at the price, has it made by a seller whose cost is no more than the price, and fixes the quantity where value and cost meet at the margin. Under competition, enforced rules and no market failure, this allocation makes the sum of consumer and producer surplus as large as possible.