I do have one doubt, however. Some folks show data that indicates that too much fertilizer is used currently. Rising - perhaps dangerous - levels of nitrates in river systems (e.g., the Mississippi River) are well beyond that which can be blamed on (under-regulated) livestock manure concentrations in the river system's upstream watershed. Implication is that fertilizer on grain-growing land is dispensed too liberally.

This behavior would certainly fit the bottom-line model of the large-scale farms for which the question would simply be is the cost of the fertilizer for the number of units used less than the market price of the product given maximized grain yield.

In other words your interest in this subject - and your model(s) - seem to start from the ecological perspective. Is potential over-use of ammonia-based products a part of your analysis?

paul spencer