On the economic theory of crop rotations: value of the crop rotation effects and implications on acreage choice modeling

Crop rotations are known to have two main kinds of economic effects: direct effects on potential yields and on the productivity of different inputs, and indirect effects on economically optimal input levels, especially pesticides and fertilizers. The main objective of this article is to uncover the mechanisms through which crop rotation effects affect the acreage choices of forward-looking farmers, in a dynamic programming framework. Whereas most models considering acreage choices with crop rotation effects are based on discrete choice models at the plot level, our model considers a farm level strategy. This implies that our theoretical modeling framework is closely related to the models commonly used for empirically investigating farmers’ acreage choices, either in the multicrop econometric literature or in the mathematical programming literature. We provide original results aimed at characterizing the properties of optimal acreage choices accounting for crop rotation effects and constraints in an uncertain context. Using a stochastic programming approach together with a Lagrangian approach we show that optimal dynamic acreage choices can be formally characterized as static acreage choices with contingent renting/lending markets for acreages with specific preceding crops. The crop rotation constraint Lagrange multipliers provide the renting/lending prices of acreages with specific crop histories. The results presented in the article are mainly theoretical. Our modeling framework can easily be implemented in practice since it mainly considers quadratic programming problems and their solution functions.