  The "standard" Merton formulation of optimal investment and consumption
involves optimizing the integrated lifetime utility of consumption, suitably
discounted, together with the discounted future bequest. In this formulation
the utility of consumption at any given time depends only on the amount
consumed at that time. However, it is both theoretically and empirically
reasonable that an individuals utility of consumption would depend on past
consumption history. Economists term this "Habit Formation". We introduce a new
formulation of habit formation which allows non-addictive consumption patterns
for a wide variety of utility specification. In this paper we construct a
simple mathematical description of this habit formation and present numerical
solutions. We compare the results with the standard ones and draw insights
obtained from the habit formation. The consumption path tends to increase with
time and be less sensitive to the market fluctuations, which perfectly reflects
the existence of habit persistence of an investor. At the same time, his
decreasing risk aversion, which seems to be in contradiction with the empirical
evidence, can be explained within the limitations of the model.
