Cost per Unit of Nutrient

The price per tonne of fertiliser compares nothing at all, because two products at the same price carry different amounts of the thing being bought. The only comparable figure is the cost per unit of actual nutrient, and it is one division away: product price divided by analysis.

Urea at $600 per tonne with 46% nitrogen costs $0.60/0.46 = \$1.30$ per kilogram of N. Ammonium sulphate at $400 per tonne looks cheaper by a third until the 21% analysis is applied, giving $1.90 per kilogram — nearly 50% more expensive for the same nitrogen.

Three adjustments make the comparison honest. Freight is charged on product weight, not nutrient weight, so a low-analysis product carries a proportionally larger haulage cost and the gap widens with distance. Application costs likewise scale with tonnage handled. And products that carry a second useful nutrient deserve credit for it — ammonium sulphate's 24% sulphur is genuinely worth something on a sulphur-deficient soil, and MAP's phosphorus should be valued before its nitrogen is judged.

The figure this feeds is the economically optimum rate, which is not the agronomically optimum one. The last increment of nitrogen pays only while the extra grain it produces is worth more than the nitrogen costs, so the optimum rate falls when fertiliser rises or grain falls. In a year of expensive nitrogen and cheap grain, the profitable rate can sit well below the yield-maximising one.