Using an overlapping generations model, this paper describes interactions between naïve and sophisticated hyperbolic discounters in general equilibrium. The naïfs, who overestimate their future propensity to save and hence over-forecast the future equilibrium asset prices, are exploited through capital transactions by sophisticates, who correctly forecast the future asset prices by incorporating the naïfs' mis-forecasts. Due to the capital losses, the naïfs fall into bankruptcy when they are highly present-biased, highly patient, and small in proportion. Under permissive conditions, the equilibrium is shown to be globally stable and Pareto inefficient in the ex-post sense.
Bankruptcy Hyperbolic discounting Naïf Sophisticate General equilibrium