The von Thünen Model and Bid-Rent Arithmetic

The assumptions

Von Thünen's isolated state assumes: one central market; a flat, featureless plain; uniform soil, climate and fertility; uniform transport cost in every direction; and farmers who are profit-maximizing and fully informed. The assumptions are not a weakness — they are the device that isolates distance as the only variable, so any observed pattern must be caused by distance alone.

The rings

From the market outward: market gardening and dairying (perishable, heavy, high yield per hectare); forest (in his day fuel and timber were bulky and consumed constantly); field crops and grain, with fallow rotations further out; and livestock ranching at the edge, where animals could walk themselves to market.

The arithmetic

Land rent per hectare for a given crop is

$$R = y(p - c) - y\,t\,d$$

where $y$ is yield per hectare, $p$ the market price per tonne, $c$ the production cost per tonne, $t$ the transport cost per tonne per kilometre, and $d$ the distance to market. The intercept $y(p-c)$ is the rent at the market gate; the slope is $y\,t$ — yield multiplied by transport rate. At any distance, the land goes to whichever use bids the highest rent, so the intersections of the bid-rent lines are the ring boundaries.

Distortions

Relax "uniform transport in all directions" and add a navigable river or a railway: along that corridor the effective transport cost per kilometre falls, so each bid-rent line flattens along the corridor and the rings stretch into elongated ovals — they do not disappear. Add a second market and you get a second, smaller set of rings. Add refrigeration, containerisation and air freight and the model scales globally: fresh flowers grown in Kenya for Amsterdam are still von Thünen logic, with air freight cost substituting for kilometres.