How market prices share an industry's output among its plants at least cost

The question: who should produce how much. An industry's output is usually produced in many plants, some new and cheap to run, some old and costly. For a given total output, the allocation is efficient when that total is produced at the lowest possible total cost: no reshuffling of output between plants could produce the same amount more cheaply. The question is how a competitive market reaches such an allocation without anyone directing it.

What the invisible hand is. In a market economy there is no central planner; decisions are taken by numerous households and firms, each following its own interest and guided by prices, and the invisible hand of the market leads these separate decisions to a desirable overall outcome. In a competitive market the invisible hand is the force that moves the price whenever demand and supply are out of balance until the market clears, and prices carry the signals that coordinate what and how much is produced.

Step 1: every plant faces the same price. Under perfect competition each plant's owner is a price taker: the firm cannot affect the market price and can sell as much as it wants at it, so its marginal revenue equals that price. Every plant in the industry, whatever its costs, therefore faces one and the same price.

Step 2: each plant produces where price equals its marginal cost. Marginal cost is the increase in total cost from producing one more unit. A profit-maximising firm produces the output at which price equals its marginal cost, on the rising part of the MC curve, provided the price covers its average variable cost. Two consequences follow:

• Low-cost plants produce more. A plant whose marginal cost rises slowly reaches the market price only at a large output, so it produces a large share. A technical improvement that lowers a plant's marginal cost makes it supply more at the same price.
• High-cost plants produce little or nothing. A plant whose minimum average variable cost is above the market price produces nothing. Market supply is the sum of what each firm supplies at the going price, so at a low price only the cheaper producers are in the market, and costlier ones join only when the price rises far enough.

Step 3: why this allocation costs the least. Because every plant equates the same price to its own marginal cost, the marginal costs of all producing plants end up equal to one another. This is exactly the condition for producing the industry's total output at least cost. Suppose instead that one plant's marginal cost were ₹30 and another's ₹20. Moving a small amount of output from the first plant to the second would save about ₹30 a unit and add about ₹20, cutting total cost by about ₹10 a unit with no change in total output. Where marginal costs rise smoothly, such savings exist whenever marginal costs differ, and vanish only when they are equal. Put another way, at the market price the last unit each plant produces costs no more than the price, and the next unit any plant could add would cost more than the price, so no plant can take over another plant's output more cheaply. Where output comes in whole units, as in the example below, the marginal costs of the last units need not be exactly equal, but the same test holds: every tonne produced costs less than the price and every tonne left out costs more. No plant needs to know any other plant's costs: each responds to the price alone, and the price does the coordinating.

Example (our own). Three spinning mills in Tamil Nadu sell yarn in a competitive market. The marginal cost of each successive tonne a week, in ₹ thousand, is:

At a price of ₹21 thousand a tonne. Mill A produces every tonne whose marginal cost is below 21, that is 6 tonnes; mill B produces 2 tonnes; mill C, whose cheapest tonne costs 25, produces nothing. Industry output is 8 tonnes at a total variable cost of 90 + 32 = ₹122 thousand. Every other way of making 8 tonnes costs more: 5 tonnes in A and 3 in B costs 70 + 54 = 124; 7 in A and 1 in B costs 112 + 14 = 126; an equal split of 4 tonnes each in A and B costs 52 + 80 = 132. The price has steered output to the cheapest 8 tonnes on offer.

If demand rises and the price goes to ₹23 thousand. Mill A adds its 7th tonne (cost 22) and mill B its 3rd (cost 22), so output rises to 10 tonnes; these are the two cheapest extra tonnes available, and both cost less than 23, while the next ones (A's 8th at 24, mill C's first at 25) cost more and are not produced. The extra output is again obtained as cheaply as possible.

The long run. With free entry and exit and identical firms, competition drives the price to the minimum of the firms' average cost, so in the long run each firm also produces at its lowest cost per unit.

Conditions. The result rests on competition and price-taking, and on the government enforcing property and contracts, without which the invisible hand cannot coordinate. It concerns the costs that firms themselves bear: a plant that pollutes a river imposes costs on others that it does not pay, so its own marginal cost understates the cost to society.

Conclusion. The invisible hand allocates production among plants through a single market price. Each plant, pursuing its own profit, produces up to the point where its marginal cost equals that price; high-cost plants produce little or nothing, low-cost plants produce more, and marginal costs are equalised across plants, which is the condition for producing the industry's output at the lowest total cost.