The Search — The Spread, Plate ii

The volume's question grows sharpest at its simplest case. Set aside the dealer's inventory and the menace of the better-informed; imagine only a buyer who wants a thing and a seller who has it, each content with a price the other would take. They should trade and be done — yet they may not, because the two cannot find each other. The market is not a room in which all the willing stand together; it is a scattered country, its traders dispersed and arriving at different times, each looking for a counterparty who is also looking. This plate is about that looking — the search by which buyers and sellers are matched — and why a third who shortens it should be paid: not as a toll on a meeting that would have happened anyway, but for arranging one that might not have happened at all.

Begin with how meetings occur. A trade requires that a particular buyer and a particular seller encounter one another, and such encounters arrive not all at once but at a rate — quick when many look, slow when few.¹ The economics of search captures this with a matching function: the number of new trades struck in a span of time depends on how many buyers and how many sellers are searching, much as a production function turns labor and capital into output. The inputs are the two sides; the output is meetings. What the function insists, against the frictionless picture, is that matching is itself an activity with a technology and a pace — that even when every buyer would gladly trade with some seller, the meetings come only gradually, and the market clears not in an instant but over time, if ever at all.

1. The matching function is usually taken to have constant returns: double both sides together and the meetings double, the rate at which any one trader is matched unchanged. This lets the model speak of a single market tightness — the ratio of one side to the other — as governing how long each waits.

A market that matches only gradually is never, at any instant, one in which all who would trade have traded. At every moment some buyers are still looking and some sellers still waiting, coexisting without yet having met — willing partners who simply have not been introduced.² This standing pool is no sign that the price is wrong or that anyone holds out; it is the ordinary condition of a market with search, the residue of a matching that takes time. The same shape appears wherever search governs: in the labor market the theory first described, vacant jobs and idle workers sit side by side, the unemployment not a glut of unwanted labor but the population in the midst of looking. The market does not empty; it churns, new meetings struck against new searchers arriving.

2. This is the insight that made the framework famous in its first home, the study of unemployment — and it carries to any market of dispersed buyers and sellers, the unmatched a working condition rather than a failure to explain away.

Now ask what price the two agree on once they meet. They are not in a crowded exchange where competition pins the terms; having found each other after looking, to walk away is to return to the search — more waiting, more cost, more uncertainty. Each therefore holds a threat blunted by that prospect, and each will take terms worse than a frictionless market would give: the buyer a higher price, the seller a lower one, rather than resume the hunt.³ They split the gains of their meeting in a bargain the search itself has shaped, and the result is a wedge between what the buyer pays and what the seller in effect receives, once the cost and risk of searching are counted. That wedge is a spread, appearing with no middleman in sight: the price of the friction itself, levied on the two who managed to cross it.

3. How the surplus is divided turns on each side's patience and how quickly the search can be resumed — on who holds the better outside option. The frictions do not merely delay the trade; they bend its terms, the same meeting yielding a different price to an eager buyer than to a patient one where alternatives abound.

⁂

The matching technology carries a consequence the traders never intend. Because meetings are produced from the two sides together, any trader who enters makes matching easier for the other side: one more buyer a chance for every seller, one more seller a prospect for every buyer.⁴ A thick market matches quickly; a thin one slowly, each searcher languishing for want of partners. But no single trader, deciding whether to enter or how hard to look, counts the help his presence gives everyone else; he weighs only his own chances. So the searching is uncoordinated, and the market can settle thinner than would serve it best, each staying away because the others do, a sparseness that feeds on itself. The market's depth is a shared good the searchers, each minding only his own crossing, undersupply.

4. This is why activity clusters — why trade of a given kind concentrates in one market, one district, one hour. Each trader goes where the others are, because that is where matching is fastest, and the concentration, once begun, sustains itself: the thickness that makes a market attractive is made by the very traders it draws.

Into this difficulty steps the figure the volume is named for. A third party who places himself permanently in the market — holding a stock, keeping a book of who wants what, quoting always a price at which he will deal — turns the two-sided search into a one-sided one: a trader no longer hunts for a counterparty but simply finds the middleman, who is always there.⁵ The scattered crossings collapse into a single reliable point of contact, the thickness the searchers could not coordinate now supplied by one who profits from it. He is, in the later plates' language, the maker of the market; his spread is neither toll nor tribute but the price of the matching he performs — of converting a country that must be searched into a counter at which one may arrive. What looked like a parasite skimming a meeting he did not make is the one who makes it possible.

5. The middleman does not abolish the friction; he absorbs it, gathering into himself the searching the traders would each have done. The later plates take up what he must be paid for — the waiting he spares, the stock he carries, the risk that those he trades with know more.

So the volume's opening suspicion meets its first answer. The third is paid to introduce a buyer and seller because the introduction is real work and the meeting is not assured: left to themselves, the two might search long and dearly, or never meet, and the wedge between their prices would open anyway, levied by the friction rather than the firm. Upon that foundation the rest of the volume builds: The Immediacy will price the waiting the maker spares, The Inventory the stock he carries across the gap in time, The Informed the hazard of dealing with those who know more. But beneath each lies the plainer fact set down here — that buyers and sellers, however willing, must be found before they can be served, and that the finding, not the standing in the way, is the first thing the spread is paid for.