Handout On ‘Saving and Growth with Habit Formation’

where h is the stock of habits, c is the instantaneous flow of consumption, ρ is the coefficient of relative risk aversion, and γ indexes the importance of habits. If γ = 0 then only the absolute level of consumption is important (the standard CRRA model), while if γ = 1, then consumption relative to the habit stock is all that matters. For values of γ between zero and one, both the absolute and the relative levels are important. For example, if γ = .5, then a person with consumption of 2 and habit stock of 1 would have the same utility as a person with both consumption and habit stock equal to 4. Finally, we assume 0 ≤ γ < 1 and ρ > 1. The stock of habits evolves according to