  We prove a verification theorem for a class of singular control problems
which model optimal harvesting with density-dependent prices or optimal
dividend policy with capital-dependent utilities. The result is applied to
solve explicitly some examples of such optimal harvesting/optimal dividend
problems. In particular, we show that if the unit price decreases with
population density, then the optimal harvesting policy may not exist in the
ordinary sense, but can be expressed as a "chattering policy", i.e. the limit
as $\Delta x$ and $\Delta t$ go to $0$ of taking out a sequence of small
quantities of size $\Delta x$ within small time periods of size $\Delta t$.
