An awareness is growing that Africa lacks profitable land despite its abundance in agriculture-suitable land. The key in assessing the availability of economically meaningful cropland is the responsiveness of cropland supply to land returns. Knowledge about this parameter at a fine-resolution is sparse due to unknown site-specific prices. Using gridded data from Sub-Saharan Africa and spatial econometric analysis, this paper quantifies the elasticities of cropland supply and land transformation. A computable general equilibrium model with these updated parameters is applied to study the much-debated land use change effect of agricultural innovation in Africa. We find that literature concerning land use in Africa has significantly overstated the ease of land transformation and masked its geographical disparity. Because of the low-land supply elasticities at current prices, barring major investments in market access, the effects of broad-based technological progress in agriculture are unlikely to incentivize major land expansion.