  We consider a class of economic growth models that includes the classical
Ramsey--Cass--Koopmans capital accumulation model and verify that, under
several assumptions, the value function of the model is the unique viscosity
solution to the Hamilton--Jacobi--Bellman equation. Moreover, we discuss a
solution method for these models using differential inclusion, where the
subdifferential of the value function plays an important role. Next, we present
an assumption under which the value function is a classical solution to the
Hamilton--Jacobi--Bellman equation, and show that many economic models satisfy
this assumption. In particular, our result still holds in an economic growth
model in which the government takes a non-smooth Keynesian policy rule.
