Freight has a charge you pay however far the goods travel, so longer hauls are cheaper per kilometre; a factory halfway between material and market pays that charge twice.
The video builds the intuition; sources and limits are set out in the article. English- and Japanese-captioned versions of the vertical film are still on the to-do list.
Freight rates rarely start from zero and rise in a straight line. Each tonne first pays a charge that is the same however far it travels; only the rest is charged by distance. The further the haul, the cheaper each kilometre on average: tapering rates. On the Chinese state railway’s carload tariff, 100 km costs about 0.26 yuan per tonne-kilometre on average and 1,000 km about 0.11.
Put a factory between a material source and a market and the fixed charge shows its consequence. Let the two be 1,000 km apart, with one tonne of material making one tonne of product at the same rate:
- At the mine, only the product travels: 114.30 yuan per tonne. In the city, only the material travels: also 114.30.
- In the middle, material and product each travel one leg and the fixed charge is paid twice: 130.60. The per-kilometre parts add up to one full trip; the extra 16.30 is the second fixed charge.
- Every interior point costs 130.60, so total cost is low at both ends and higher across the whole interior. As long as the average rate does not rise with distance, the optimum lies at one of the end points: the end-point location theorem.
Which end wins depends on which side carries more weight (strictly, weight times rate). With 1.5 tonnes of material per tonne of product, the mine costs 114 per tonne and the city 171, so the plant stays at the source, as cement works sit by limestone quarries; when the product is heavier (brewing adds water) the plant moves to the market. When material arrives by sea, the land haul starts at the port, so the port acts as the material end, which is one way to read why a steelworks was built in Shanghai, a city without ore or coal.
Limits: only transport cost is compared; rates follow the state railway tariff in force since 2018, and the 1,000 km, one-to-one set-up is illustrative. Real location choices also depend on land, labour, agglomeration and policy.
Japanese classroom version (16:9)
A slower Japanese 16:9 version paced for a lecture, in two parts, with the full derivation, worked numbers and review questions.
Sources: China State Railway freight tariff (in force since 2018); Hoover (1948); the vertical and classroom films use the same calculations.