Numéraire
Volume II · The Rent · The Prices
Plate the Sixth, of twelve

The Location

Von Thünen's isolated state and Alonso's city: the rent not of fertile soil but of accessible position — Ricardo's differential transposed into space, sloping down from every center as a gradient of price. The rent of nearness, made by the nearness of others; and the question of the earned and the seized, asked now of the ground beneath the city.

in print · published

The volume turns now from whether rent is deserved — the great matter of the unearned increment — to where rent comes from; and the first and most literal answer is space itself. The volume's own emblem, the spot that others must pass through, is most exactly the central location: the place near which everyone wants to be, and pays to be. This plate takes up locational rent — the rent not of fertile soil but of accessible position — through the two who founded its theory: Johann Heinrich von Thünen, who in 1826 derived the rent of land from distance alone, and William Alonso, who a century and a third later turned von Thünen's farmland into the modern city. It will show that the same differential the volume opened with reappears in space, as a gradient of price sloping down from every valued center; that the rent of nearness is created, strangely, by the nearness of others; and that the question of earned-or-extracted returns, on the ground beneath the city, with peculiar force.

Begin with von Thünen, a Mecklenburg landowner who, in 1826, set down one of economics' first great thought-experiments. Imagine, he said, an isolated state: a single city planted in the middle of a featureless plain of perfectly uniform fertility, with no river, no road, no rival town to disturb the picture — the city the one and only market for everything the plain can grow. On such a plain, one thing alone varies from place to place: the distance to the city, and so the cost of carting produce in to market. And from that single variable von Thünen drew an entire spatial order — concentric rings of cultivation about the city, each given over to whatever crop the balance of land rent against carriage cost made it fittest to bear. Close in, where land was dear but the journey short, went the perishable and the heavy: the market-garden, the dairy. Farther out went the grains, which bore their carriage more cheaply. Farther still went the grazing herds, which walked themselves to market and wanted no cart at all. The famous von Thünen rings — the first demonstration that economic activity arranges itself across space according to the cost of distance.

And at the heart of the rings lay a new kind of rent. The rent of any plot, von Thünen saw, was what its produce fetched at market, less the cost of growing it, less the cost of carrying it there. Land beside the city paid a high rent, for little was consumed in carriage and much was left to the landlord; land far out paid little, for the long haul devoured the surplus; and at the farthest margin, where the cost of carriage just swallowed all that the crop would fetch, the rent fell away to nothing. This was location rent — the rent of nearness — and it was Ricardo's differential lifted clean out of the soil and set down in space. Where Ricardo's rent had measured the advantage of the fertile field over the barren, von Thünen's measured the advantage of the near field over the far. The nearer land was the better land; the edge of cultivation was the no-rent margin; and the rent declined, plot by plot, with every mile from the center. Rent, von Thünen showed, is paid not only for what the land can grow but for where the land is.

Where Ricardo's rent measured the advantage of the fertile field over the barren, von Thünen's measured the advantage of the near field over the far.

For more than a century von Thünen's rings stood as a curiosity of agricultural economics — until, in 1964, William Alonso saw that the very same logic governed the modern city, and turned the farmland into downtown. Replace the market town with the central business district — the dense knot of offices and shops to which the whole city commutes — and replace the competing crops with competing households and firms, and von Thünen's rings become the structure of the metropolis. Each bidder for land, Alonso saw, faces the farmer's old trade-off afresh: to sit near the center is to pay a high rent but a low cost of commuting; to sit far is to pay little rent but to spend long and dear in travel. Each household and each firm therefore carries a bid-rent curve — the most it will pay for land at each distance from the center, holding its own welfare fixed — and the land at every point falls to the highest bidder upon it. The result is the monocentric city: a surface of land rent sloping down from the center like the side of a hill, with the uses that prize nearness most — the bank, the office tower, the great store — heaped upon the summit, and rent and density and the very height of the buildings all declining together toward the rim. The city, Alonso showed, simply is a gradient of price.

And the gradient is not a mere pattern but a machine — one that sorts the city's uses to their proper places with no hand to plan it. For the bid-rent contest sets each activity down where it most values being: the use that gains most from the center, and would therefore pay most to sit upon it, outbids all the rest for the central ground, so that the center fills with whatever most needs the center, while whatever needs it less is pushed, by its own unwillingness to outbid, out toward the cheaper rim. The high rent of downtown is precisely what ensures that downtown goes to the bank and the department store and not to the car park or the cow pasture — that the scarce accessibility of the center is rationed to those who prize it most. Here, as everywhere in this volume, the rent does allocative work: the gradient of price is the city's way of deciding, through ten thousand separate bids and no central will at all, what shall stand where. The rent of nearness is the price that arranges the city.

But whose creation is this rent? Here the volume's question returns, in the city, with a peculiar sharpness. For the value of the central location — the accessibility the downtown owner charges others for — is not in the least his own doing. It is the creation of everyone else: of all the others who have chosen to cluster there, of the workers who pour in each morning and the customers who throng the streets, of the roads and rails and pipes the public laid, of the very existence of the city assembled round the spot. The owner of the central acre has done nothing but hold the deed while the city gathered itself about him; and the rent he gathers in is the cash value of his neighbours' proximity — the toll upon a nearness that they, and not he, brought into being. This is Mill's unearned increment in its purest and most visible form, for nowhere is it plainer than in urban land that the worth of the spot is made by the community and merely captured by the owner. The rent of nearness is made by the nearness of others; and the man who owns the nearness grows rich, as Mill said of all landlords, in his sleep.

The rent of nearness is made by the nearness of others; and the man who owns the nearness grows rich in his sleep.

Two things the modern city presses upon the clean old model. The first is that the gradient has flattened and split. The monocentric city of a single peak was the creature of costly transport; and as the cost of moving — by motor-car, by motorway, by wire — has tumbled, the gradient has slumped and spread, and the one center has given way, in the great modern metropolis, to many: the edge city, the scattered office park, the polycentric sprawl that von Thünen's tidy rings will not describe. Accessibility still commands its rent, but to many centers now, and along a gentler slope; and amenity — the pleasant street, the good school, the fine view — has joined accessibility among the things the city's rent is paid for, so that people now bid for nearness not to work alone but to beauty, and to one another. The second qualification, and the more troubling, is that the rent gradient of the desirable city is no longer purely natural. Where the law forbids the building — where zoning caps the height and freezes the use and walls the old neighbourhood against the newcomer — the supply of central space is held artificially short, and the locational rent is swollen, past anything mere nearness would fetch, into something nearer the monopoly rent of a later plate: a scarcity not of nature's making but of the ordinance's. Much of the crushing rent of the great cities of our age is locational rent steepened by the planner's hand — the natural premium upon nearness, multiplied by a manufactured shortage of the right to build.

Return, then, to the volume's emblem, which the city makes literal. The whole of this volume is about the price of the spot that others must pass through; and there is no spot more exactly that than the center of a city — the place made valuable by the very fact that everyone wishes to be near it, and priced to the hilt accordingly. Von Thünen found the gradient upon his imaginary plain; Alonso found it running through the real metropolis; and between them they showed that the value of land is, in the last reckoning, very largely the value of its location — that rent is a price of nearness, sloping downward from every center that people have reason to approach. The rent of nearness does the city's work, sorting its uses to their places by ten thousand unplanned bids. But it is a rent the owner did not earn, for the nearness he charges for is his neighbours' doing and never his own — the unearned increment of the last plate, made visible in every downtown deed. And in our own day it is a rent that policy has bent and swollen, the natural premium upon the center compounded by the artificial scarcity of the leave to build upon it. Whether the rent of the spot is the just price of a real and useful nearness, or the unearned toll upon a position the owner merely holds — and how much of it is the one, and how much the other, and how much again the pure manufacture of the law — is the volume's question, asked now of the ground beneath the city. As the table says of every price within it, the argument remains open.

A note on the plate's sources

  1. Johann Heinrich von Thünen, The Isolated State (1826) — location rent, and the concentric rings of land use.
  2. William Alonso, Location and Land Use (1964) — the bid-rent curve, and the monocentric city.
  3. Edwin S. Mills (1967) and Richard F. Muth (1969) — the monocentric model formalized.
  4. Walter Christaller, Central Places in Southern Germany (1933) — the spatial hierarchy of towns and markets.
  5. Enrico Moretti, The New Geography of Jobs (2012) — the divergence of cities in the modern economy.
  6. Edward L. Glaeser & Joseph Gyourko, “The Impact of Building Restrictions on Housing Affordability” (2003) — the rent of the desirable city, steepened by the law.
  7. Edward L. Glaeser, Triumph of the City (2011) — the city of amenities and of many centers, and the limits of the single peak.