  In this paper we use a dynamic programming approach to analytically solve an
endogenous growth model with internal habits where the key parameters
describing their formation, namely the intensity, persistence and lag structure
(or memory), are kept generic. Then we show that external and internal habits
lead to the same closed loop policy function and then to the same (Pareto)
optimal equilibrium path of the aggregate variables when the utility function
is subtractive nonseparable. The paper uses new theoretical results from those
previously developed by the dynamic programming literature applied to optimal
control problems with delay and it extends the existing results on the
equivalence between models with internal and external habits to the case of
finite memory.
