In this paper, we analyze the long-term distributive impact of climate change through rising food prices. We use a standard incomplete markets model and account for non-linear Engel curves for food consumption. For the calibration of our model, we rely on household data from 92 developing countries, representing 4.5 billion people. The results indicate that the short-term and long-term distributive impact of climate change differs. Including general equilibrium effects change the welfare outcome especially for the poorest quintile. In the presence of idiosyncratic risk, higher food prices increase precautionary savings, which through general equilibrium affect labor income of all agents. Furthermore, this paper studies the impact on inequality for different allocations of productivity losses across sectors. When climate impacts affects total factor productivity in both sectors of the economy, climate impacts increase also wealth inequality.