Demand for agricultural products is an important problem in global change economics. Food consumption will shape and be shaped by global change through interactions with bioenergy and afforestation, two critical issues in meeting international goals. We develop a model of food demand for staple and nonstaple commodities that evolves with changing incomes and prices. The model addresses a long-standing issue in estimating food demands, the evolution of demand relationships across large changes in income and prices. We discuss the model, some of its properties and limitations. We estimate parameter values using pooled cross-sectional-time-series observations and Bayesian Monte Carlo method and cross-validate the model by estimating parameters using a subset of the observations and test its ability to project into the unused observations. Finally, we apply bias correction techniques borrowed from the Earth system modeling community and report results. We find that the demand for food rises rapidly as income initially increases from zero. Demand for staples peaks at under $1000 per person per capita. Nonstaple food demands increase steadily with income. While staples are an inferior good at per capita incomes greater than $1000, we see no evidence that there is a range of per capita income for which staples are Giffen goods.