We develop a framework to study optimal transport networks in general equilibrium spatial models. We model a general neoclassical economy with multiple goods and factors in which arbitrarily many locations are arranged on a graph. Goods must be shipped through linked locations, and transport costs depend on congestion and on the infrastructure in each link, giving rise to an optimal transport problem in general equilibrium. The framework nests neoclassical trade models, such as Armington or Hecksher-Ohlin, and allows for labor mobility. The globally optimal transport network is the solution to a social planner's problem of building infrastructure in each link. We provide conditions such that this problem is globally convex, guaranteeing its numerical tractability. We also study and implement cases with increasing returns to transport technologies in which global convexity fails. We match the model to data on actual road networks and economic activity at high spatial resolution across 25 European countries, and then compute the optimal expansion and reallocation of current roads within each country. We find larger gains from road expansion and larger losses from misallocation of current roads in lower-income countries. The optimal expansion of current road networks reduces regional inequalities.
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