Plate viii in print

The Control

Lerner; the economics of control, the index of monopoly power, marginal-cost pricing, and the contested rule for how the surplus should be divided.

The greatest surplus is had when price is set, everywhere, at the cost of one more; the gap by which a price exceeds that cost is the exact measure of the power that withholds it; and as for the sharing of the whole, since none can know whose want a shilling answers more, and since want dulls as means swell, the division that promises the most satisfaction, taking one man with another, is the equal one.

— the argument of this plate, after Abba Lerner, 1944

Every plate of this volume has circled one question without quite answering it: an exchange creates a value beyond its price, and who, in the end, walks away with that value? The surplus is real and measurable; it springs from voluntary trade; it divides between the two parties by their relative power; and the powerful capture it while the blocked destroy it. What remains is to gather these threads into a single account — to state plainly how large the surplus can be made, how its capture by power can be measured, and how, among all the people of a society, it ought finally to be shared. That gathering was the lifework of Abba Lerner, whose treatise on the economics of control set out to write the complete rules by which an economy, of whatever ownership, should be run to wring from its resources the greatest sum of human satisfaction. Lerner did not ask how markets do behave; he asked how an economy should be controlled — by firms, by planners, by the state, by whatever hand holds the levers — and his answer is the fitting close to a volume on the surplus, for it is an answer about how to make the surplus as large as possible and how to divide it as well as possible, the two halves of the whole contest.

The first rule restores, as a universal principle, the result the opening plate drew from Hotelling. The greatest total surplus, that plate showed, is reached when output is carried to the point where the value of one more unit to a buyer has fallen to meet the cost of one more to a seller — the point where price equals marginal cost. Lerner made this the master rule of the whole economy: in EVERY line of production, public or private, the price should be set equal to the marginal cost. The reasoning is the plainest in all of economics. A unit worth more to some buyer than it costs to make is a unit that ought to be made, for making it creates surplus; a unit that costs more than it is worth to anyone ought not to be made, for making it destroys surplus. Setting price at marginal cost, and letting buyers take all they will at that price, ensures that exactly the right units are made — every one whose worth exceeds its cost, and no other. A price held above marginal cost, as a monopolist holds it, chokes off units whose worth exceeded their cost, and the surplus they would have created simply fails to appear. The rule is wholly indifferent to who owns the means of production: a private firm, a public utility, a socialist plant are all to follow it alike, for the surplus does not care whose name is on the deed. This was the principle Lerner shared with Oskar Lange in the great argument of the age over whether a planned economy could match a market — the claim that efficiency is a matter of pricing at marginal cost, achievable under any form of ownership that has the will to enforce it.1

1. The first rule restores Hotelling's result as a universal principle. Greatest surplus comes where the value of one more unit meets the cost of one more — price equal to marginal cost. Lerner made this the master rule: in EVERY line of production, public or private, price should equal marginal cost. The logic is the plainest in economics — a unit worth more than it costs ought to be made, one costing more than its worth ought not, and pricing at marginal cost ensures exactly the right units are made. A price held above marginal cost, as a monopolist holds it, chokes off worth-exceeds-cost units, and their surplus fails to appear. The rule is indifferent to ownership — private firm, public utility, socialist plant follow it alike. This was the principle Lerner shared with Lange: efficiency is a matter of pricing at marginal cost, under any ownership with the will to enforce it.

The second contribution turns the rule into a measure. If pricing at marginal cost is the mark of an industry that creates the most surplus, then the distance an industry stands from that rule is the mark of how much surplus its market power is withholding — and Lerner gave that distance a number. Take the gap between an industry's price and its marginal cost, and express it as a fraction of the price: where the two are equal, as under perfect competition, the fraction is zero; where price stands well above marginal cost, as under monopoly, the fraction is large. This fraction is the degree of monopoly power, the index that bears Lerner's name, and it does two things at once. It measures how much power a seller has over his price — the sliver that Chamberlin's differentiated firm holds, the swath that a true monopolist commands — and in the same stroke it measures how far the market has departed from the surplus-maximizing rule, how much value is going uncreated because the price is held above the cost of one more. The index made precise what the earlier plates had described in words: the power to capture surplus and the destruction of surplus are two faces of one quantity, and that quantity can be read off from the gap between what a thing sells for and what one more of it costs to make.2

2. The second contribution turns the rule into a measure. If pricing at marginal cost marks the surplus-maximizing industry, the distance from that rule marks how much surplus market power withholds — and Lerner gave it a number. Take the gap between price and marginal cost as a fraction of price: zero where they are equal (perfect competition), large where price stands well above marginal cost (monopoly). This is the degree of monopoly power, the index bearing Lerner's name. It measures at once how much power a seller has over his price — Chamberlin's sliver, the monopolist's swath — and how far the market has left the surplus-maximizing rule. Power to capture surplus and destruction of surplus are two faces of one quantity, read off from the gap between what a thing sells for and what one more costs.
⁂

With the rule and the index, half the contest is settled, and settled cleanly. We know how large the surplus can be made — as large as possible when price equals marginal cost everywhere, when no power withholds output and no barrier blocks a worthwhile trade — and we know how to measure the power that falls short of this and the loss it imposes. But all of this concerns the SIZE of the surplus, not its DIVISION. To say that the surplus is largest under marginal-cost pricing is to say nothing about who should receive it; a vast surplus may be heaped on a few or spread among the many, and the rules of efficiency are silent on which. Here Lerner turned to the harder and more dangerous half of the question, the half that the rest of the volume has approached only obliquely through the bargaining of the parties — the question of how the surplus, which becomes in aggregate the whole income of a society, ought to be divided among the people who compose it. And here he made the boldest argument of his career.3

3. With the rule and the index, half the contest is settled cleanly. We know the surplus is largest when price equals marginal cost everywhere, no power withholding and no barrier blocking, and we know how to measure the power that falls short and the loss it imposes. But this concerns the SIZE of the surplus, not its DIVISION. That the surplus is largest under marginal-cost pricing says nothing about who receives it — a vast surplus may be heaped on a few or spread among many, and efficiency is silent on which. Lerner turned to the harder, more dangerous half: how the surplus, which becomes a society's whole income, ought to be divided among its people. Here he made the boldest argument of his career.

The obstacle is the one the volume on utility met at its summit, in the plate on comparing one person's satisfaction with another's. To say how income should be divided for the greatest good, one must be able to weigh the satisfaction a dollar brings to one person against the satisfaction it brings to another — to say whether the shilling taken from the rich man and given to the poor adds more to the poor man's happiness than it subtracts from the rich man's. But such comparisons between separate minds, the utility volume showed, rest on no firm ground; there is no instrument that reads off the intensity of one person's wanting and sets it beside another's, and a generation of economists had concluded that interpersonal comparison of satisfaction is a thing science cannot perform. Lerner granted the point in full. We cannot know, he agreed, whose want a given dollar answers more deeply; we cannot pick out the man who would squeeze the most joy from a fortune from the man who would barely notice it. But he argued, with great ingenuity, that we do not NEED to know in order to say what division is best — that ignorance itself, properly reasoned from, points to a definite answer.4

4. The obstacle is the one the utility volume met at its summit, in the plate on comparing one person's satisfaction with another's. To say how income should be divided for the greatest good, one must weigh the satisfaction a dollar brings one person against another — whether the shilling taken from the rich adds more to the poor man's happiness than it subtracts from the rich man's. But such comparisons between separate minds rest on no firm ground; no instrument reads off one person's wanting and sets it beside another's, and a generation concluded that interpersonal comparison is beyond science. Lerner granted this fully. We cannot know whose want a dollar answers more deeply. But he argued that we need not know to say what division is best — that ignorance, properly reasoned from, points to a definite answer.

The argument runs so. Suppose a fixed total of income is to be divided between two people, and suppose two things about them. First, that for each, the satisfaction got from income grows, but grows ever more slowly — that the marginal utility of income diminishes, each added dollar bringing a little less than the dollar before, which is among the most widely shared of all the premises of economics. Second, that we are wholly ignorant of which of the two has the greater capacity for satisfaction — that, knowing nothing, we must treat it as equally likely that either is the keener vessel of joy. Then, Lerner showed, the division that maximizes the EXPECTED total of satisfaction — the best bet, in our ignorance — is the EQUAL division. For consider any unequal split, and consider shifting a dollar from the richer share toward the poorer. We do not know which person values the dollar more; but because marginal utility diminishes, the dollar is, on the average of all we do not know, worth more in the poorer hand than in the richer, since the poorer hand holds less. The expected gain from the shift therefore exceeds the expected loss, and this remains true of every shift toward equality until the shares are equal, at which point no further shift can be expected to help. Out of pure ignorance of who is who, joined to the diminishing of marginal utility, equality emerges as the division that promises the most satisfaction, one person with another. It was a remarkable feat of reasoning — to wring from a confessed inability to compare persons a firm conclusion about the best division among them — and it remains one of the most discussed arguments in the literature of distribution.5

5. The argument: a fixed income is divided between two people. Suppose, first, that satisfaction from income grows ever more slowly — marginal utility diminishes, each dollar bringing less than the last, among the most widely shared premises in economics; and second, that we are wholly ignorant of which has the greater capacity for satisfaction, treating either as equally likely. Then the division maximizing the EXPECTED total of satisfaction — the best bet in our ignorance — is the EQUAL one. Consider shifting a dollar from richer share to poorer: we do not know who values it more, but because marginal utility diminishes it is, on the average of all we do not know, worth more in the poorer hand. Expected gain exceeds expected loss until the shares are equal. From pure ignorance plus diminishing marginal utility, equality emerges as the division promising the most satisfaction.
⁂

The argument is bold, and like all bold arguments it stands on premises that may be denied, each of which marks a real and respected line of objection. The first is that it assumes the two people are drawn from the same distribution of natures — that our ignorance is perfectly symmetric. If in truth people differ in their capacity for satisfaction, and if some of those differences can be discerned, then equal division is no longer best: more should go to those who can do more with it. Lerner half-conceded this, allowing that income should be adjusted for differences in need that we can see — the sick, the burdened, those with many to feed — and the concession opens a door, for once we admit that some capacities are knowable, the clean symmetry that drove the argument begins to fray. The second objection cuts deeper. The whole argument speaks of a total of satisfaction and its mathematical expectation, and so assumes that satisfaction can after all be added across persons — the very interpersonal comparison the argument set out to do without. A strict ordinalist, who holds that one mind's pleasure simply cannot be placed on the same scale as another's, will say that there is no such thing as the expected total of satisfaction to be maximized, and that the argument, for all its ingenuity, smuggles back in the comparison it claimed to have banished. The third objection is the most practical and, in the end, the most telling.6

6. The argument stands on premises that may be denied, each a respected line of objection. First, it assumes the two are drawn from the same distribution of natures — that ignorance is perfectly symmetric. If people differ in capacity for satisfaction, and some differences can be discerned, equal division is no longer best: more should go to those who do more with it. Lerner half-conceded, allowing adjustment for visible need — the sick, the burdened — and the concession frays the clean symmetry. The second cuts deeper: the argument speaks of a total of satisfaction and its expectation, assuming satisfaction can be added across persons — the very comparison it set out to avoid. A strict ordinalist denies any such total exists to maximize. The third objection is the most practical, and the most telling.

It is that the argument holds the total income fixed while it is divided, as though the size of the surplus and its division were independent — and they are not. How a surplus is shared shapes how large a surplus there is to share. If income is to be divided equally no matter what each person does, the spur to work harder, to save, to take the risk of the new venture, to acquire the rare and costly skill, is dulled, for none of the extra reward of effort is kept by the one who makes the effort. An enforced equality may shrink the very pie it divides, leaving each with an equal slice of a smaller whole, and possibly a slice smaller in absolute terms than the unequal world would have given. The division that is best for satisfaction, taking the pie as fixed, may be far from the division that is best once we allow that the pie's size answers to the division. This is the famous tradeoff between equity and efficiency — between sharing the surplus well and making it large — and it is the reason no society divides its income equally, and the reason Lerner himself, for all his argument, treated equal division as a goal to be approached only so far as the preserving of incentives allows. The surplus, it turns out, will not sit still to be divided; the act of dividing it reaches back and changes its size, and the rule for the best division must reckon with that reaching-back, which no clean theorem can fully capture.7

7. The third objection: the argument holds total income fixed while dividing it, as though size and division were independent — and they are not. How a surplus is shared shapes how large it is. If income is divided equally whatever each does, the spur to work, save, take risk, acquire costly skill is dulled, for none of effort's reward is kept by the one who makes it. Enforced equality may shrink the pie, leaving each an equal slice of a smaller whole. The division best for satisfaction, taking the pie as fixed, may be far from the best once the pie's size answers to the division. This is the tradeoff between equity and efficiency — sharing the surplus well versus making it large — the reason no society divides income equally, and why Lerner treated equal division as a goal to approach only so far as incentives allow.

Set Lerner's rules beside the rest of the volume, and the long contest over the surplus resolves into a clear, if unfinished, account. The surplus is brought into being by voluntary exchange, each party gaining what it values more for what it values less. Its size is greatest when, in every market, price is set at the cost of one more, so that every worthwhile trade is made — the rule of the economics of control. Between the two parties to any trade it is divided by their relative power, the terms turning against whoever wants the exchange more, so that the surplus flows to the one who can walk away. Where a seller has gathered market power — measured now by Lerner's index, the gap of price above cost as a fraction of price — he draws the division toward himself and destroys a part of the surplus outright in the trades his high price forbids. And over all of this stands the state, the third party in the contest, which can tax the surplus for its own purposes, can break or bridle the market power that captures and destroys it, can hold the great fixed-cost industries to marginal-cost pricing as Hotelling urged, and can redistribute the income that the surplus becomes toward whatever division it judges right. So the answer to the question that has run through the volume — who walks away with the surplus? — is that it is contested at every step. Buyers and sellers split it by their elasticities; the powerful capture it by their power; the state claims and reapportions what it can; and a part of it, wherever power or barrier intervenes, walks away with no one at all, vanishing into the trades that were never made.8

8. Set Lerner's rules beside the volume, and the contest resolves into a clear if unfinished account. The surplus is born of voluntary exchange; its size is greatest when price equals the cost of one more in every market; between the two parties it divides by their relative power, flowing to whoever can walk away; where a seller has market power — measured by Lerner's index — he draws the division toward himself and destroys part outright. Over all stands the state, the third party, which can tax the surplus, bridle the power that captures it, hold fixed-cost industries to marginal-cost pricing, and redistribute the income it becomes. So: who walks away with the surplus? It is contested at every step — split by elasticities, captured by power, claimed by the state, and partly lost to the trades never made.

What Lerner's economics of control finally teaches is to hold two questions apart that the heat of argument forever runs together. How LARGE should the surplus be? On this, economics speaks with one voice and a clear answer: as large as it can be made, which means as large as it is when every value-creating trade is carried out, when price equals the cost of one more, when no power withholds and no wall blocks. This is the domain of theorem, where reasoning compels assent. How should the surplus be DIVIDED? On this, economics can clear the ground, can expose bad arguments and trace the consequences of each division, can even — as Lerner showed with his argument from ignorance — push reason further into the question than one would have thought possible; but it cannot deliver a final answer, because the answer turns on comparisons between persons that the science cannot make and on a weighing of fairness against plenty that is, at the last, a matter of judgment and of politics rather than of proof. The value beyond the price is created jointly, made largest by competition, captured by power, and divided by a contest that economics can illuminate brilliantly and decide not at all. On that division the argument remains open, as it must; and with the surplus thus accounted for — its creation, its measure, its maximization, and the limits of what can be said about its sharing — the volume closes, and with it the family of the Quantities, whose four elements, the margin, the surplus, the utility, and the stock, are now complete.

Abba Lerner gathered the threads of the surplus into a single program of control. His first rule, generalizing Hotelling's, holds that the total surplus is greatest when price is set at marginal cost in every industry, under any form of ownership; his index of monopoly power, the gap of price above marginal cost taken as a fraction of price, measures in one number both how much market power a seller holds and how much surplus that power withholds and destroys. To the harder question of how the surplus, become a society's income, should be divided, he brought his celebrated argument from ignorance: that since we cannot know whose want a dollar answers more, and since the marginal utility of income diminishes, the division that maximizes expected satisfaction is the equal one — an argument as bold as it is contested, vulnerable to the differences among persons it assumes away, to the ordinalist's denial that satisfaction can be summed across minds at all, and above all to the incentive effects that make the size of the surplus depend on its division. Drawing the volume together, Lerner shows the contest over the value beyond the price to be unending and many-sided — created by exchange, maximized by competition, captured by power, taxed and reapportioned by the state, and partly lost to the trades that power and barrier forbid. The size of the surplus, economics can settle; its division it can only illuminate. And so the family of the Quantities is complete, and the argument remains open.