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Governments use their countries’ economic strength from existing financial and trade relationships to achieve geopolitical and economic goals. We refer to this practice as geoeconomics. We build a framework based on three core ingredients: limited contract enforceability, input-output linkages, and externalities. Geoeconomic power arises from the ability to jointly exercise threats across separate economic activities. A hegemon, like the United States, exerts its power on firms and governments in its economic network by asking these entities to take costly actions that manipulate the world equilibrium in the hegemon’s favor. We characterize the optimal actions and show that they take the form of mark-ups on goods or higher rates on lending, but also import restrictions and tariffs. Input-output amplification makes controlling some sectors more valuable for the hegemon since changes in the allocation of these strategic sectors have a larger influence on the world economy. This formalizes the idea of economic coercion as a combination of strategic pressure and costly actions. We apply the framework to two leading examples: national security externalities and the Belt and Road Initiative.