Are spatially specific agricultural input use recommendations more profitable to smallholder
farmers than broad recommendations? This paper provides a theoretical and empirical modeling
procedure for determining the optimal spatial scale at which agricultural researchers can make
soil fertility recommendations. Theoretically, the use of Bayesian decision theory in the spatial
economic optimization model allows the complete characterization of the posterior distribution
functions of profits thereby taking into account spatial heterogeneity and uncertainty in the
decision making process. By applying first order spatial scale stochastic dominance and Jensen’s
inequality; theoretically and empirically, this paper makes the case that spatially specific
agricultural input use recommendations will always stochastically dominate broad
recommendations for all non-decreasing profit functions ignoring the quasi-fixed cost
differentials in the decision itself.
These findings are consistent with many economic studies that find precision agriculture
technologies to be more profitable than conventional fertilizer (regional or national
recommendations based) application approaches. The modeling approach used in this study
however provides an elegant theoretical justification for such results. In addition, seasonal
heterogeneity in maize responses was evident in our results. This demonstrates that broad
recommendations may not only be wrong spatially but also seasonally. Further research on the
empirical aspects of spatio-temporal instability of crop responses to fertilizer application using
multi-location and multi-season data is needed to fully address the question posed initially. The
decision making theory developed here can however be extended to incorporate spatio-temporal
heterogeneity and alternative risk preferences