This volume began with a paradox and a banishment. The paradox was that water, on which life depends, is nearly free, while diamonds, which we could do without, command fortunes; and the banishment, by which the paradox was dissolved, was the setting-aside of the whole. Value, the marginal revolution taught, does not answer to the total usefulness of a thing — not to all the water in the world, which is beyond price — but to the usefulness of one more unit of it, the last and least-needed drop, which is worth almost nothing where water is plentiful. To explain price, the discipline learned to stop looking at the whole and to look only at the margin; and the lesson was so fruitful, and resolved so much, that the whole was not merely set aside but very nearly forgotten. This last plate is about the circumstances under which the whole comes back. For there is a large and growing class of things to which the margin's central premise simply does not apply, and in their domain the very quantity the margin taught us to ignore turns out to be the one that governs everything.
The premise in question has run, mostly unspoken, beneath every plate of this volume, and it is worth dragging into the light. It is the premise of diminishing returns: that one more of a thing is worth less than the one before. The whole apparatus depends upon it. The gradient of marginal utility slopes downward because each successive unit of a good sates the want a little further and is prized a little less. The marginal product of a factor falls because each added worker has less of the other factors to work with. The cost of one more unit tends to rise as a firm strains against its capacity. Everywhere the same shape recurs — the increment shrinking as the total grows — and it is this shape that gives the marginal apparatus its most cherished properties: a demand curve that slopes down, a supply curve that slopes up, a single point at which they cross, a unique optimum to be found by pushing each activity to the margin where its diminishing benefit meets its rising cost. Diminishing returns is not one assumption among many in the theory of the margin. It is the assumption upon which the orderly determinacy of the whole construction rests.
Now suppose it fails. Suppose that, over some range that matters, one more of a thing is worth not less than the last but more — that returns, instead of diminishing, increase. This is no idle hypothesis; it describes a great and expanding share of modern economic life. A factory with heavy fixed costs makes each unit more cheaply the more it produces, as the last plate observed; a worker or a firm grows more productive at a task the more often it is performed, sliding down a learning curve; a body of knowledge, once created, can be used by any number of people at no further cost, so that the return to it rises without limit as it spreads. In all these cases the increment grows rather than shrinks: the hundredth unit costs less than the tenth, the experienced hand outpaces the novice, the second user of an idea gets it for nothing. And the moment returns increase, the cherished properties desert the apparatus. The advantage now feeds upon itself — the larger grows cheaper and so grows larger still — and the gentle, self-correcting tendency of the diminishing-returns world, in which expansion raises costs and so checks itself, gives way to a self-reinforcing one, in which success breeds success and the leader pulls away.
Where returns increase, the second unit is easier than the first, and the thousandth easier still; the advantage feeds upon itself, and the rule that more grows harder — the rule on which the whole apparatus was built — runs exactly backward.
The purest and most consequential form of increasing returns is the one that attaches not to making a thing but to joining a network, and it has reshaped the modern economy more than any other. A single telephone is a useless ornament; a second makes a pair worth having; and every further telephone added to the system raises the value of every telephone already in it, for each new subscriber is someone all the others can now call. The value of the network grows with its size — and here is the decisive twist — so that the worth of one more member is not fixed, as a diminishing marginal utility would have it, but rises with the number of members already joined. The same logic governs the language more people speak, the marketplace more buyers and sellers frequent, the software platform more developers build upon, the standard more devices obey. In each, the good becomes more valuable the more widely it is held, and the wish to join is keenest where the most have joined already. This is the network effect, and it stands the diminishing-returns world on its head: the value of one more member, instead of tapering as the network fills, climbs with every member the network already has.
From this self-reinforcement two phenomena follow that the marginal apparatus, built for a self-correcting world, has no proper place for. The first is the tipping point. Where each adopter makes the thing more attractive to the next, there is a critical mass below which it languishes and above which it suddenly takes off: the network too small to be worth joining stays small and dies, while the one that crosses the threshold explodes into ubiquity, the very same feedback driving collapse on one side of the line and runaway growth on the other. Thomas Schelling showed how thresholds of just this kind, operating in the small decisions of individuals, produce the abrupt and surprising tipping of whole populations. The second phenomenon is lock-in. Once a standard has pulled ahead, the network effect chains everyone to it: people adopt it because others have, and the others stay because everyone else does, so that the standard entrenches itself regardless of its merit. The classic illustration is the QWERTY keyboard, which Paul David and Brian Arthur made the emblem of a deep and unsettling possibility — that the arrangement which prevails may not be the best, but only the one that history and chance allowed to get ahead first, with the world locked in behind it. The market, in this telling, does not reliably select the fittest. It selects, and then freezes, whatever crossed the threshold soonest.
The standard that prevails need not be the best, only the one that got ahead; for past a certain threshold each adopts it because the others have, and the market, far from selecting the fittest, locks in whatever chance and history put first.
And with the tipping point and the lock-in, the whole returns to the centre of the story from which the margin had banished it. For everything that matters in an increasing-returns world is a property not of the increment but of the totality. Whether a network is worth joining depends on how large it already is — on the whole, not the next member. Whether a thing tips or dies depends on whether the total has crossed the critical mass — a fact about the whole system, invisible to any inspection of the marginal unit. Which standard locks in depends on the entire history of who adopted what and when — the accumulated whole, not the present margin. The quantity the marginal revolution taught the discipline to ignore, in order to see that water is cheap though water is precious, turns out to be exactly the quantity that decides which network thrives, which technology wins, which city or firm or platform pulls away from its rivals and leaves them behind. The volume opened by showing that the whole could not explain the price of a glass of water. It closes by showing that nothing but the whole can explain the triumph of a telephone network, a software platform, or a global standard. The margin banished the whole to resolve a paradox; the whole returns to resolve the paradoxes the margin cannot.
It would be a mistake, and a mirror of the original overreach, to conclude from this that the margin was wrong, or that the whole should now be restored to the throne from which the marginalists deposed it. The truth is that there are two worlds, and the discipline needs both of its eyes to see them. In the vast world of diminishing returns — most of consumption, most of agriculture, most of ordinary competitive industry, the smooth and divisible and self-correcting domain — the margin reigns, and reigns rightly; there the value of one more is what governs, the equilibrium is unique, and the market does tend toward the efficient outcome the marginal apparatus describes. In the smaller but swelling world of increasing returns — networks and platforms and standards, knowledge and software and scale-bound industry, the self-reinforcing domain that the digital age has pushed toward the centre of the economy — the whole reigns, and there the marginal intuitions mislead: the outcome is not unique, the market need not find the best, and being larger is not a burden checked by rising costs but an advantage that compounds. The error the discipline must guard against is not the margin itself but its imperialism — the habit, bred of the marginal revolution's very success, of carrying the marginal picture into the one domain where the whole, and not the increment, holds the truth.
And so this volume, the first of the second family, comes to its close. The Margin set out to honour the quiet revolution that remade economics from its foundations — the discovery that what governs a price is never the total or the average but the value of one more — and across twelve plates it has followed that idea from the paradox it dissolved and the revolution it launched, through the gradient and the equimarginal rule, the scissors and the cost and the product, the rate of substitution and the three-word rule, to the limits where the smooth calculus falters: the indivisible lump, the as-if fiction, and at the last the threshold beyond which the whole comes home. The finding of the volume is the one the table makes of all its primitives in turn — that the margin is a profound and powerful truth, sovereign across the greater part of economic life, and yet a partial one, silent or misleading in the territory beyond its proper bounds. The value of one more is the hinge on which the modern subject turns; it is not the whole of the subject. There remains a quantity that the margin itself creates but cannot, on its own, perceive: the surplus an exchange leaves behind, the whole of the benefit a price secures, recovered by summing all the margins that lie above it. To that surplus, and to the next volume of the table, the argument now turns. As the table says of every quantity, first to last: the argument remains open.