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Global export subsidies are known to be welfare reducing. This paper demonstrates that a small targeted subsidy can increase the welfare of the subsidizing country by exploiting differences in excess demand elasticities. Targeted export subsidies can also increase the subsidizing country's welfare by exploiting transportation cost differences, excess supply elasticities of competitors, or excess demand elasticities of markets supplied by competitors when markets are shared. An empirical model of the world wheat market illustrates the theoretical conclusions. An optimal targeted subsidy scheme causes a small increase in U. S. welfare but with major disruptions in world trade flows.

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