The demand- and supply-side drivers connected to the “shared socioeconomic pathways” (SSP) will impact future agriculture. Assessing the projected impacts of those drivers on regional and global agriculture requires approaches that goes beyond the traditional biophysical sciences’ methods and tools. The present work uses a static partial equilibrium model for global agriculture that incorporates into the analysis the effects of economic responses to scarcity affecting regional and global agricultural production and land use. By 2050, agricultural output will expand, but at different rates depending on the region and on the SSP-productivity scenario. Yield gains will consolidate as a major driver, but cropland expansion will still play an important role, especially in Sub-Saharan Africa. The SSP1 (Sustainability), fast technological development scenario, offers a promising perspective to increase global agricultural output and reduce pressures for cropland expansion. Under SSP1 scenario, food insecurity would drop the most, to 2.8% of world population by 2050. Achieving the Sustainability scenario will require an articulated global effort to strengthening agricultural R&D expenditures accompanied by a well-designed strategy to translate science into problem-solving knowledge and technologies that could be successfully transferred and adopted by farmers to boost productivity gains over the next three decades.