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Flat Payoff Functions and Site-Specific Crop Management
1D. Pannell, 2M. Gandorfer, 3A. Weersink
1. School of Agriculture and Environment University of Western Australia Perth WA 6009, Australia
2. Institute for Agricultural Engineering and Animal Husbandry Bavarian State Research Center for Agriculture Vöttinger Str. 36, D-85354 Freising, Germandy
3. Dept of Food, Agricultural and Resource Economics University of Guelph, Guelph, ON, Canada N1G 2W1

Within the neighbourhood of any economically “optimal” management system, there is a set of alternative 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 judgments 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).

Keyword: Payoff function, curvature, nitrogen managment