dynamics of their vegetative development, and their effects on the soil’s net nutrient balance, sequencing them in ways that capitalize on positive synergies while avoiding negative interactions can increase output or help save input costs (Hennessy 2006). Historically, addition of new crops has been a key driver of productivity growth and the ability of the agricultural sector to release labor for non-agricultural development (Brunt 1999). More recently, synthetic fertilizers, pesticides, and herbicides allow producers to maximize profits by shortening rotations and reducing their diversity (Plourde _et al._ 2013).

Crop rotation affects outcomes via three channels. The first one is the reduction of pest and disease-pressure <mark>(Hilton</mark> _<mark>et al.</mark>_ <mark>2013) by preventing development and a</mark> ccumulation of crop-specific fungi, bacteria and insects that often survive in crop residues (Gentry _et al._ 2013). Proper rotational management can also reduce greenhouse gas emissions (Behnke _et al._ 2018) and capture soil carbon. A second mechanism is to enhance plants’ ability to access nutrients or water through differences in root structure to improve capillarity and aeration of the soil, thus also reducing susceptibility to disease <mark>(Koch</mark> _<mark>et al.</mark>_ <mark>2018).</mark> The underlying dynamics of bacterial, fungal or insect populations and their interaction with climatic conditions can be captured in biological models (Regis Mauri 2019). <mark>A third element is l</mark> egumes’ ability to capture nitrogen <mark>(Archer</mark> _<mark>et al.</mark>_ <mark>2020)</mark> as well as crops’ differential nutrient requirements (Bowles _et al._ 2020). Together with data on prices for inputs and outputs, technical coefficients based on the varietal choice and crop management options (e.g., till- and no-till practices), availability of on-farm resources -most importantly labor in different parts of the growing season- and their shadow prices, as well as any exogenous constraints (e.g., regulation) can then be used to formulate decision-rules for optimum rotational choices at the farm level as a programming model (Boyabatli _et al._ 2019).

Whether such choices are not only individually but also socially optimal requires more detailed analysis. If property rights to land are well defined and can be enforced and the effects of crop rotation remain plotspecific, privately and socially optimal choices will coincide. However, even if property rights are clear, externalities may arise in several respects. Spatial externalities, e.g., because mono-cropping or short rotations can trigger accumulation of insects that may infect neighboring fields or, if a critical mass is exceeded, cause harmful infestation more broadly (Meisner and Rosenheim 2014). Effluents from more intensive use of fertilizer, pesticides, or manure than would be necessary with more diverse rotations may contribute to water pollution. Systematic overuse of chemicals can lead to pests developing resistance, as has been reported for GM crops (Qiao _et al._ 2017) and glyphosphate (Mitchell 2011). Moreover, if property rights are insecure, land users may maximize short-term benefits, e.g., ‘mine’ soil, without regard to long-term sustainability.

If supply is price elastic, modest price changes or subsidies may be sufficient to make farmers shift from monocropping to rotations. Hennessy (2006) shows that, depending on prices for maize and fertilizer, a 4