• Environmental policy;
  • land use;
  • national park management;
  • spatial externalities;
  • Wirtinger's inequality

Abstract Growing demand for cropland products has placed intense pressure on the ability of land resources to support nature, straining public budgets to purchase environmental goods. Fixing overall agricultural output, two environmental policy options are whether to (i) promote more agricultural extensification and nature-friendly farming practices or (ii) produce intensively on some land and leave the rest wild. Microeconomic models of the topic have not accounted for widely recognized spatial externalities regarding fragmented reserves. This article does so, using Wirtinger's inequality to also identify a third policy possibility. This is that ecological services can follow a smoothly varying spatial path chararacterized by harmonic functions. We use the results to rationalize the core and periphery national park structure put in place around the world, that is, versions of our third policy possibility have been implemented.