We study the interactions between global population, technological progress, per capita income, the demand for food, and agricultural land expansion over the period 1960 to 2100.We formulate a two-sector Schumpeterian growth model with a Barro-Becker representation of endogenous fertility. A manufacturing sector provides a consumption good and an agricultural sector provides food to sustain contemporaneous population. Total land area available for agricultural production is finite, and the marginal cost of agricultural land conversion is increasing with the amount of land already converted, creating a potential constraint to population growth. Using 1960 to 2010 data on world population, GDP, total factor productivity growth and crop land area, we structurally estimate the parameters determining the cost of fertility, technological progress and land conversion. The model closely fits observed trajectories, and we employ the model to make projections from 2010 to 2100. Our results suggest a population slightly below 10 billion by 2050, further growing to 12 billion by 2100. As population and per capita income grow, the demand for agricultural output increases by almost 70% in 2050 relative to 2010. However, agricultural land area stabilizes by 2050 at roughly 10 percent above the 2010 level: growth in agricultural output mainly relies on technological progress and capital accumulation.