Equilibrium and Efficient Land-Use Arrangements under Spatial Externality on a Lattice

Alexander E. Saak
October 2004  [04-WP 376]

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Saak, A.E. 2004. "Equilibrium and Efficient Land-Use Arrangements under Spatial Externality on a Lattice." Working paper 04-WP 376. Center for Agricultural and Rural Development, Iowa State University.


Many cases of externalities in agricultural production, such as pesticide drift, cross-pollination, and offensive odors, are attributable to the incompatibility of neighboring land uses and exhibit distance dependence. We characterize equilibrium spatial patterns of externality-generating and -receiving land uses on a two-dimensional lattice with noncooperative, profit-maximizing producers. In equilibrium, generators or recipients form one or more neighborhoods with certain geometric properties, depending on how an externality dissipates with distance and whether there is an externality generated outside the region's boundaries. Efficient land-use arrangements maximize social welfare subject to the implementability constraints stipulating that no farm-level activity, except for land use, can be directly controlled by the social planner. We characterize efficient land-use arrangements when the return to recipient land use decreases linearly with the length of the border shared with incompatible land uses. Under these assumptions, we find circumstances in which an efficient activity arrangement belongs to the set of the Nash equilibrium outcomes. Also, efficient arrangements in a more general case are discussed.

Keywords: graph partitioning, land-use arrangement, spatial externality, supermodular game.