On the Spatial Allocation of Public Goods

We wish to find an optimal solution to an economic problem concerning allocation of a public good by some central, governing body, over a spatial dimension. In particular, this government is cost minimizing, so it wishes to provide the minimal amount of the public good necessary to achieve its desired outcome, while at the same time considering its dual of maximizing the benefit of the limited amount of good which it provides. This paper puts forth a straightforward, easily-implementable algorithm using only some linear algebra and graph theory to solve this problem with suitable generality for varied applications in public economics and beyond. In short, this algorithm, given a static, planar graph and a utility function solves for the constrained optimal placement of public good units so as to satisfy the above, using eigenvalue centrality and Fiedler partitions. These reduce large, difficult placement problems to those easily solvable using standard iterative methods. We then validate this algorithm for fire hydrant placement in a real life neighborhood according to city codes and geographic properties. The algorithm performs accurately and does so at a polynomial time complexity.No embargoAcademic Major: Economic