Stochastic efficiency optimisation analysis of alternative agricultural water use strategies in Vaalharts over the long- and short-run
The main objective of this research was to develop models and procedures that would allow water managers to evaluate the impact of alternative water conservation and demand management principles in irrigated agriculture over the long-run and the short-run while taking risk into account. One specific objective was to develop a generalised whole-farm stochastic dynamic linear programming (DLP) model to evaluate the impact of price incentives to conserve water when irrigators have the option to adopt more efficient irrigation technology or cultivate high-value crops over the long-run. The DLP model could be characterised as a disequilibrium known life type of model where terminal values were calculated with a normative approach. MOTAD (Minimising Of Total Absolute Deviations) was used to model risk. Another specific objective 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 in the short-run. 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 short-run 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 inter- and intra-temporal matrixes of gross margins necessary to incorporate risk into the long-run and short-run water use optimisation models. A new procedure (standard risk aversion) was developed to standardise values of absolute risk aversion with the objective of establishing a plausible range of risk aversion levels for use with stochastic efficiency analysis techniques. A procedure was developed to conduct stochastic efficiency with respect to a negative exponential utility function using standard risk aversion. The standardised risk aversion measure produced consistent answers when the risk premium was expressed as a percentage of the range of the data. Long-run results showed that the elasticity of irrigation water demand was low. Overall risk aversion and the individual farming situation will have an important impact on the effectiveness of water tariff increases when it comes to water conservation. Although the more efficient irrigation technology scenario had a higher net present value when compared to flood irrigation, the ability to pay for water with the first mentioned scenario was lower because the lumpy irrigation technology needs to be financed. Failure to take risk into account would cause an over- or underestimation of the shadow value of water, depending on whether water was valued as relatively abundant or scarce. The conclusion was that care should be taken when interpreting the derived demand for irrigation water (elasticity) without knowing the conditions under which they were derived. Cognisance should also be taken of the fact that higher gross margins per unit of applied water would not necessarily result in greater willingness to pay for water when the alternatives were evaluated on a whole-farm level. The main conclusion from the short-run 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. The modelling framework and the models that were developed in this research provide powerful tools to evaluate water allocation problems that are identified while busy implementing the National Water Act. Only through the application of these type of models linked to hydrological models will a better understanding of the mutual interaction amongst water legislation, water policy administration, technology, hydrology, human value systems and the environment be gained to enhance water policy formulation and implementation.