Land scarcity, sustainable uses and environmental policies

We present a dynamic model of land use in a small economy, where land is a fixed resource that can either be used for food consumption, resulting in pollution, or invested in natural capital. Land scarcity imposes a quantity constraint that creates a trade-off between these alternative uses. This constraint shapes the dynamics of the system, influencing its differential equations and leading to a differential–algebraic system of equations (DAE). This approach represents a novelty compared to environmental dynamic models that rely solely on differential equations. Using this analytical framework, we show that shadow prices and stocks are closely interconnected and must be determined simultaneously. We use the DAE system to explore the impact of supranational policies aimed at achieving broader environmental goals on land allocation in the small economy. We derive two main results. First, the relative effectiveness of policy instruments is determined by the pollution intensity of consumption: when pollution intensity is low, incentives that promote land investment in natural capital are more efficient; conversely, when pollution intensity is high, regulatory measures that limit land use for consumption become more effective. Second, although temporary policies do not affect the long-run steady state of the system, they significantly accelerate the transition toward a more sustainable land allocation in the medium term.