Suppose we express the amount of land under cultivation as the product of four factors: Land= (Land / food ) x (Food/ K Cal) x (Kcal/person) x(population)
The annual growth rates for each factor are 1 the land required to grow a unit of food 1 percent due to greater productivity per unit of land 2 the amount of food grown per calorie of food eaten by a human 0.5 percent because with affluence people consume more animal products which greatly reduces the efficiency of land use 3 the per capita calorie consumption 0.1 percent and 4 the size of the population 1.5 percent At these rates how long would it take to double the amount of cultivated land needed? At that time how much less land would be required to grow a unit of food?