An ability to quantify the impacts associated with different emissions scenarios across a broad range of economic and environmental outcomes would be helpful for guiding policy on energy and greenhouse gas emissions. One outcome of particular interest, especially for food insecure populations, are effects on agricultural productivity. In this study we use empirical models of the relation between climate and CO2 concentration on the one hand, and changes in crop yields on the other, to characterize the differential impacts on the future productivity of two major crops of two level of forcings: those associated with RCP4.5 and those associated with RCP8.5. This study is part of a larger project on the Benefits of Reducing Anthropogenic Climate changE (BRACE). We consider differential effects on maize and wheat yields at the global scale from expected changes in mean temperature and precipitation under the two scenarios. We also characterize differential levels of exposure to damaging heat extremes. Several time horizons are considered, characterizing expected impacts over the short, middle and long terms over the 21st century.