Abstract
National borders govern trading opportunities and eligibility for public services. There is suggestive evidence that post-colonial border design has harmed African long-term development through these two channels. This paper offers a spatial model of borders that tracks their welfare consequences through trade and public goods provision. It features four key forces: the benefits of economic and fiscal integration, and the costs of preference heterogeneity and span of control. To evaluate inefficiencies of border configurations, I set up an optimal borders problem whose solution provides a benchmark and develop a strategy to make it tractable. I calibrate parameters of the spatial model and use the proposed method of solving the optimal borders problem on African data. Africa could gain at least 28% in welfare with optimal borders. The primary shortcoming of current borders is their geographic position, not the number of countries.

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