Question: Suppose we express the amount of land under cultivation as the product of four factors:
Land = (land/food) x (food/kcal) x (kcal/person) x (population)
The annual growth rates for each factor are:
1) the land required to grow a unit of food, -1% (due to greater productivity per unit of land)
2) the amount of food grown per calorie of food eaten by a human, +0.5%
3) per capita calorie consumption, +0.1%
4) the size of the population, +1.5%.
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?