Stochastic efficiency analysis of deficit irrigation with standard risk aversion

Abstract

The main objective of this research was to develop an expected utility optimisation model to economically evaluate deficit irrigation within a multi-crop setting while taking into account the increasing production risk of deficit irrigation. The dynamic problem of optimising water use between multiple crops within a whole-farm setting when intraseasonal water supply may be limited was approximated by the inclusion of multiple irrigation schedules into the optimisation model. The SAPWAT model (South African Plant WATer) was further developed to quantify crop yield variability of deficit irrigation while taking the non-uniformity of irrigation applications into account. Stochastic budgeting procedures were used to generate appropriately correlated matrixes of gross margins necessary to incorporate risk into the water use optimisation model. Special care was taken to represent risk aversion consistently between the alternatives through the use of a new procedure to standardise values of absolute risk aversion. The model was applied to study the impact of increasing levels of risk aversion on the profitability of deficit irrigation under limited water supply conditions. The main conclusion from the analyses was that although deficit irrigation was stochastically more efficient than full irrigation under limited water supply conditions, irrigation farmers would not willingly choose to conserve water through deficit irrigation and would be expected to be compensated to do so. Deficit irrigation would not save water if the water that was saved through deficit irrigation were used to plant larger areas to increase the overall profitability of the strategy. Standard risk aversion was used to explain the simultaneous increasing and decreasing relationship between the utility weighted premiums and increasing levels of absolute risk aversion and was shown to be more consistent than when constant absolute risk aversion was assumed.