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[1] Following suitable treatment, municipal wastewater can be used for agricultural irrigation; the potential benefit to the agricultural sector is especially significant in arid and semiarid regions, where fresh water is scarce. The analysis focuses on a region which consists of a principal (a wastewater “producer” (a city)), and two competitive agents (water users (two groups of farmers' associations)), who make decisions under conditions of asymmetric information. First, we develop an optimization model aimed at maximizing the principal's profits from conveying treated wastewater without damaging the farmers' reservation utilities or profits. The analysis determines the treated-wastewater allocation, income transfers, and profit allocation among the three assumed economic entities. Contracts composed of transfer payment–wastewater combinations are studied in a mechanism design setting in which the city has incomplete information on the farmers' demand for treated wastewater. The theoretical analysis is applied to the situation in the Sharon region of Israel. The empirical results show that regional cooperation is profitable for all of the involved economic entities.

Economic optimization of a resource which is space dependent and displays irregular spatial variation was investigated. The resource (yield) of an entire field is regarded as a random variable which depends on a random function on the one hand, and a control variable on the other hand. The study focuses on the question of how economically efficient levels of relevant control variables may vary as a function of random spatial variability of resources, taking into account the decision maker's attitude to risk. A general approach to cope with the above question is developed, and the effects of uncertainty on the levels of the optimal control variables are investigated by comparing a deterministic case with two uncertainty levels of decision making: risk neutral and risk averse. Following the general methodology, expectation value and variance of average yield are first approximated by Taylor series expansion and then closed-form solutions are obtained for a specific, exponential, yield production function. Subsequently, we illustrate the general analysis for the example of irrigated corn, the only control variable being water quantity, and with corp yield a spatial random function in the plane. The results suggest that the impact of random soil properties on optimum level of water application might be substantial. Hence it is generally worthwhile to account for spatial variability in optimizing level of irrigation or similar control variables.

A methodology to infer the spatial distribution of the statistical moments of a stationary normal random spatial function based on a finite set of measured values is described. The uncertainty of estimation of the parameters characterizing the probability density function (pdf) is incorporated in the process of inferring and conditioning. Relationships generalizing the traditional approach of stochastic interpolation and simulation have been derived. They yield: (i) an estimate of the conditional expectation; (ii) an estimate of the conditional multivariate normal (MVN) covariance and variance; and (iii) a new quantity, the variance of the estimated variance. The method is illustrated for a two-dimensional synthetic example with both estimated mean and variance regarded as random. A set of 60 points was generated within a square of sides equal to unity from a MVN population with zero mean, unity variance and exponential covariance with a linear integral scale of 0.3. Contour maps of the inferred expected values and variances are drawn and compared with maps of kriged values and maps of kriged variances. Contour maps of variances of estimation of the variance are given to demonstrate the uncertainty of variance estimates. The unconditional and conditional statistical moments of the space average (block value), , were also evaluated. The reduction of the uncertainty of the inferred random variable as the number of measured points increases is demonstrated with the same synthetic example.

Linear programing models, deterministic in the short run and stochastic (random rainfall) in the long run, aimed at guiding annual decision making with regard to crop mix and saline irrigation water mixing from various sources within a farm framework, are presented. The short-run model incorporates the physical, biological, and economic relationships involved in one endogenous system and enables an in depth analysis of them but is limited to a single year. The long-run model considers the effects of the short-run decisions on the future but several relationships are incorporated exogenously. The short run model's results are utilized for the determination of some of these predetermined relationships. The models are applied to a potential farm situation in southern Israel. The results provide priorities in the allocation of water and soil plots of varying salinity levels and empirical estimates of the shadow prices and the rates of substitution between the limited resources.