Habit formation and indeterminacy in overlapping generations models

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I introduce habit formation into an otherwise standard overlapping generations economy with pure exchange populated by three-period-lived agents. Habits are modeled in such a way that current consumption increases the marginal utility of future consumption. With logarithmic utility functions, I demonstrate that habit formation gives rise to stable monetary steady states in economies with hump-shaped endowment profiles and reasonably high discount factors. Intuitively, habits imply adjacent complementarity in consumption, which in turn explains why income effects are sufficiently strong in spite of the logarithmic utility. The three-period horizon further strengthens the income effect.