An important question in economics is how people choose between different payments the future. The classical normative model predicts that a decision maker discounts later payment relative to an earlier one by exponential function of time them. Descriptive models use nonexponential functions fit observed behavioral phenomena, such as preference reversal. Here we propose discounting, consistent ...

Does the existence of secondary markets for durable goods affect price and allocation on primary markets? We study competitive equilibria for durable goods where the possibility of future trade on secondary markets does not affect consumer behaviour in the primary market, provided consumers are exponential discounters. If consumers are hyperbolic discounters, however, secondary markets are no l...

We use experimental matching data from the 2000 Bank of Italy Survey of Household Income and Wealth to compare the relative frequencies of hyperbolic and exponential discounters. Among 3,235 Italian respondents, less than one-fourth exhibited hyperbolic discounting; this finding is both statistically significant and robust across a wide variety of economic, social, and demographic characteristi...

Hyperbolic discount functions induce dynamically inconsistent preferences, implying a motive for consumers to constrain their own future choices. This paper analyzes the decisions of a hyperbolic consumer who has access to an imperfect commitment technology: an illiquid asset whose sale must be initiated one period before the sale proceeds are received. The model predicts that consumption track...

The amount of money a person was willing to forgo in order to give 75 dollars to another person decreased as a hyperbolic function of the perceived social distance between them. Similar hyperbolic functions have previously been shown to describe both time and probability discounting.

Experiments on static intertemporal choice …nd evidence of particularly extreme impatience toward immediate rewards. While this is often taken as support for hyperbolic discounting, it could also arise because the most likely participants in experiments are also those with the most immediate need for money. We conduct a calibration exercise and …nd that the extreme impatience observed in experi...

A robust …nding in experiments on time preference is the magnitude effect: subjects tend to be more patient towards larger rewards. Using a calibration theorem, we argue against standard curvature-based explanations for the …nding. We axiomatize a model of preferences over dated rewards that generalizes the standard exponential discounting model by permitting the discount factor to depend on th...

This paper introduces the concepts of amount and speed of a discounting procedure. Exponential discounting sequesters both concepts into a single parameter that needs to be disaggregated in order to characterize nonconstant rate procedures. The inverse of the present value of a unit stream of benefits provides a natural measure of the amount a procedure discounts the future. We propose geometri...