Optimal Consumption Under a Habit-Formation Constraint
نویسندگان
چکیده
We propose a new optimal consumption model in which the degree of addictiveness habit formation is directly controlled through constraint on admissible consumption. In particular, we assume that individual unwilling to consume at rate below certain proportion 0<α≤1 of her habit, exponentially-weighted average past rates. α=1 prohibits process decrease and corresponds completely addictive model. α=0 makes habit-formation moot non-addictive 0<α<1 leads partially models, with level increasing α. contrast existing literature, our cannot be incorporated objective function infinite marginal utility, alters analysis corresponding control problem. Assuming invests risk-free market, formulate solve an infinite-horizon, deterministic problem maximize discounted CRRA utility individual's consumption-to-habit subject said constraint. derive policies explicitly terms solution nonlinear free-boundary problem, analyze detail. Impatient individuals (or, equivalently, those more habits) always above minimum rate; thus, they eventually attain wealth-to-habit ratio. Patient less habits) if their ratio threshold, it otherwise. By consuming patiently, these maintain greater than acceptable level. Additionally, prove path hump-shaped initial either: (1) larger high threshold; or (2) low threshold agent risk seeking (that is, averse). Thus, provide simple explanation for hump observed by various empirical studies.
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ژورنال
عنوان ژورنال: Social Science Research Network
سال: 2021
ISSN: ['1556-5068']
DOI: https://doi.org/10.2139/ssrn.3844760