Non-linearity in Marginal LCA: Application of a Spatial Optimization Model

Typical applications of LCA assume that the magnitude of life-cycle impact grows proportionally to the volume of demand, while in reality the additional impact due to marginal increase in demand may differ from the average impact. In the literature, the calculation of marginal life-cycle impacts often involves the use of optimization models, where typically the total economic costs are minimized. However, modeling spatially explicit marginal responses of a system involving multiple producers and consumers has not been discussed in LCA literature. In this paper, we demonstrate a spatial optimization technique for modeling marginal responses of a multi-producer, multi-consumer system. Our model determines the optimal production-by-location mix and associated environmental stressor at minimum systems cost. We demonstrate the model using a case study on blue water consumption by potato. We collected state-by-state data on potato yield, cost of potato production, and water use for irrigation, as well as interstate transportation costs. We also estimated the marginal increase in demand for potato following USDA’s recommended diet. The results show that the cradle-to-gate blue water consumption of potatoes based on 2016 demand was 96 m3/tonne potato, which changes non-linearly along with the growth of potato demands. In order to meet the USDA’s recommended diet, the additional demand on potato (530,000 tonne per year) would result in a 29% lower blue water consumption per tonne of potato (68 m3/tonne) as compared to the average result of the current production system. In addition, we tested the model to analyze the marginal impacts under two scenarios: (1) high fuel tax and (2) high water price. The results indicate that water pricing is more effective than a fuel tax increase in reducing the marginal blue water consumption of potato based on our scenarios of the recommended diet demand. The results demonstrate that our model can be used to understand the non-linear behavior of marginal effect over demand crease, and for testing alternative policy scenarios involving a system with multiple producers and consumers across regions.