Abstract: We study the capacity to meet food demand under conditions of climate change, economic and population growth. We take a novel approach to quantifying climate impacts, based on a model of the global economy structurally estimated on the period 1960 to 2015. The model integrates several features necessary to study the problem, including an explicit agriculture sector, endogenous fertility, directed technical change and fossil/renewable energy. We estimate the world economy is more than one trillion dollars smaller, and world population more than 80 million smaller, than would have been the case without climate change. This is despite substantial adaptation having taken place in general equilibrium through R&D and agricultural land expansion. Policy experiments with the model suggest that optimal GHG taxes are high and future temperatures held well below 2°C.