Constraints on resources, growth in demand, and a slowdown in agricultural productivity raise concerns that food prices may rise substantially over the next decades. The impacts of such higher prices on the poor and the required mitigating policy responses to this problem remain unclear. This paper uses a global general equilibrium model, projections of global growth and microeconomic household models, to project potential implications for incomes, food production and poverty. We find that higher agricultural productivity would generally lower poverty, with different impacts depending where the productivity growth occurs, while protection policies that reduce imports would generally raise poverty.