Formulation and Spatial Aggregation of Agricultural Production Relationships within the Land Use Change (LUC) Model

Land Use Change (LUC) Project at IIASA in which the Centre for World Food Studies participates, is currently engaged in the development of a case study for China (Fischer et al., 1996). Its focus on land use and land cover change makes it necessary to ensure that geographic detail and statistical information on conditions prevailing within these regions be preserved to the extent possible. This raises two issues that are addressed in this paper. First, while it is not practical to formulate a regional optimization model with a very large number of sub-regions, over two thousand in the case of China, one would like to avoid the loss of information associated with aggregation. For a generalized version of the Mitscherlich-Baule yield function that is commonly used in agronomy the paper describes a consistent aggregation procedure over sub-regions, which leads to simple aggregate functions at regional level, but has the special property that, once the regional model has been solved, all results can be recovered fully at sub-regional level. Secondly, agronomy studies commonly use yield functions in which the per hectare yield of a particular crop depends on inputs per hectare. Unfortunately, in the case of China, as for most countries, input use is not available by crop and only recorded for a particular geographical unit. The paper proposes a more crude formulation whose parameters, however, can be estimated by cross-section on the basis of available data.