Why do equal increases in fertilizer sometimes produce smaller increases in crop yields?

In the context of farm management, the phenomenon where equal increases in fertilizer produce progressively smaller increases in crop yields is explained by the law of diminishing returns.12

This economic principle dictates that if you continue to increase one input—such as fertilizer—while keeping other production factors constant, you will eventually reach a point where each additional unit of input results in a smaller gain in output than the previous unit. Beyond this optimal threshold, further applications of fertilizer become less efficient and may even hamper the production process.31

For farmers, the goal is to identify the most profitable application rate that balances the cost of nutrients against the expected value of the crop. Applying fertilizer beyond this point is not only economically inefficient but also environmentally irresponsible, as excess or ill-timed application can lead to water pollution through runoff, creating a negative externality that impacts the broader environment.12