Geographically-explicit, dynamic partial equilibrium model of regional primary value chains – Mathematical formulation and application to forestry in the Northland region of New Zealand

Abstract

This paper lays out the mathematical foundation of the Primary Value Chains (PVC) model, which is a geographically-explicit, dynamic partial equilibrium model of regional value chains. The model identifies the optimal value chains in a region by linking spatially-distributed resources, technologies and markets. Specifically, the model identifies: the equilibrium price-quantity bundles, optimal harvest schedules, market destinations, individual processing plant locations, and transportation routes. Results of a regional case study in the forestry sector in the Northland region of New Zealand are presented to showcase the model’s capabilities. The model was used to determine the impact of investments in new capacity of traditional and new high-value technologies on the optimal use of the forest resource and the region’s overall profitability. The model’s discrete representation of space simplifies the generation of maps to present results in a simple graphical manner. The model’s structure is flexible enough to easily include other regions, cropping or farming systems, transportation alternatives, processing technologies and destination markets.