Plants in Space

To decide the number, size, and location of its plants, a firm balances the benefit of delivering goods from multiple plants with the cost of setting up and managing these plants and the potential for cannibalization among them. Modeling the decisions of heterogeneous firms in an economy with a vast number of distinct locations involves a large combinatorial problem. Using insights from discrete geometry, we study a tractable limit case of this problem in which these forces operate at a local level. Our analysis delivers predictions on sorting across space. Compared with less productive firms, productive firms place more plants in dense, high-rent locations and fewer plants in markets with low density and low rents. We present evidence consistent with these and several other predictions, using US establishment-level data.