Linear and quadratic models of the southern Murray-Darling basin.

Linear programming (LP), a well-established technique for modelling agricultural and other systems, has been extensively used to model irrigation systems in Australia. The models constructed have been used to assess the effects of changing water charges on farm incomes, water use, and the effects of trade in water allocations. An LP model that reflects actual farm behaviour requires a large amount of data. Moreover, demand and supply functions estimated with LP models are necessarily stepped rather than smooth. Howitt has suggested a way of escaping from these problems of LP models. His positive programming approach replaces an LP model with a simpler quadratic programming model. In this paper, Howitt's approach is used to develop a quadratic programming model from an existing LP model of irrigated agriculture in the southern Murray-Darling basin of Australia. A comparison of the quadratic and linear models indicates that the quadratic programming model is smaller and simpler to specify and that it produces similar results to the linear model, in terms of cropping, trade, and demand for irrigation water. The choice of modelling technique depends on the problem and the available resources. Positive programming can be a valuable addition to the farm modellers' arsenal.