Every year, the world economy invests a large amount of resources to improve or develop transport infrastructure. How should these investments be allocated to maximize social welfare? In this proposal, I propose to develop and apply new methods to study optimal transport networks in general-equilibrium models of international trade, urban economics and economic geography. The methodology will build on recent work (Fajgelbaum and Schaal, 2017), in which my coauthor and I studied the network design problem in a general neoclassical trade framework.In the first project, I develop a new framework to analyze optimal infrastructure investment in an urban setting. The model features people commuting between residential areas and business districts as well as a choice over the mode of transportation. We plan to evaluate the framework to historical data about specific cities. In the second project, I propose and implement an new algorithm to compute optimal transport networks in the presence of increasing returns to transport, a likely prominent feature of real-world networks. The algorithm applies a branch-and-bound method in a series of geometric programming relaxations of the problem.In the third project, I study the dynamic evolution of actual transport networks using satellite data from the US, India and Mexico. In the spirit of Hsieh and Klenow (2007), I use the model to measure distortions in the placement of roads between rich and poor countries.In the fourth project, I study the inefficiencies and welfare losses associated with political economy frictions among governments and planning agencies. I use the model to identify inefficiencies and relate them to measures of institutions and political outcomes.In the final project, I propose a new explanation behind the Zipf’s law distribution of city sizes. I show that Zipf’s law may result from particular topological properties of optimal transport networks that allocate resources efficiently in space.