We structurally estimate a two-sector Schumpeterian growth model with endogenous population and finite land reserves to study the long-run evolution of global population, technological progress, and the demand for food. The estimated model closely replicates trajectories for world population, GDP, sectoral productivity growth, and crop land area from 1960 to 2010. Projections from 2010 onward show a slowdown of technological progress, and, because it is a key determinant of fertility costs, significant population growth. By 2100, global population reaches 12.4 billion and agricultural production doubles, but the land constraint does not bind because of capital investment and technological progress.