How flat is flat? Measuring payoff functions and the implications for site-specific crop management

Within the neighbourhood of any economically “optimal” management system, there is a set of alternative management systems that are only slightly less attractive than the optimum. Often this set is large; in other words, the payoff function is flat within the vicinity of the optimum. This has major implications for the economics of variable-rate site-specific crop management. The flatter the payoff function, the lower the benefits of precision in the adjustment of input rates spatially within a crop field. This paper is about how we can best measure the flatness of payoff functions, in order to assist with judgements about the likely benefits of site-specific crop management. We show that two existing metrics — the relative range of an input for which the payoff is at least 95% as large as the maximum payoff (IR95) and the relative curvature (RC) of the payoff function — are flawed. We suggest an alternative metric: the standard deviation of the slopes of site-specific payoff-functions at the optimal uniform input rate (SDS). The SDS is highly correlated with the benefits from variable-rate precision management.