Multi-Sector Sustainability in Agroecosystem Environments: Using Value Function Iteration for Numerical Solutions

Using the numerical technique of value iteration, this paper imposes several sustainability constraints on a simple multi-sector agroecosystem model, and provides analysis of the costs tradeoffs within and between generations. Results show that internalization of a stock externality is insufficient for intergenerationally equitable welfare paths, while sustaining a physical resource over time in the interests of equitability can result in a less equitable distribution of welfare across generations. Furthermore, a value sustainability constraint imposed on the social welfare maximization problem acts as a welfare transfer mechanism from the productive sector to the sector affected by the externality, but implies growth in profits for the productive sector and declining utility for the non-productive sector.