Is there enough fertile soil to feed a planet of growing cities?

We analyze a scaling law for the consumption of agricultural soil by cities. The nonlinear dependence of the size of the city on the number of inhabitants gives rise to an equation for population dynamics. We found the asymptotic limit of the solution for this equation, given by the carrying capacity in terms of number of inhabitants that can be fed. The carrying capacity as a function of the scaling law exponent is computed numerically, showing that the exponent must be very small to ensure a food sustainability. We suggest a bound for the value of this exponent and analyze the reliability of the scaling law for major cities.