Positive Mathematical Programming (PMP) has become a popular method for regional production models. The standard approach estimates cost (or production) functions for each land-use activity separately from each other. This means that the same crop grown under two technologies is treated as if it were two separate crops, which may lead to unsatisfying results, for example, if agri-environmental programs are modeled. We present an extended version of PMP that leads to more plausible results than the standard version in such cases. The extended method is applicable to other problems where differences in the elasticity of substitution between activities are important. Copyright 2003, Oxford University Press.