Augmented discounting: interaction between ageing and time–preference behaviour

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Abstract
Discounting occurs when an immediate benefit is systematically valued more highly than a delayed benefit of the same magnitude. It is manifested in physiological and behavioural strategies of organisms. This study brings together life–history theory and time–preference theory within a single modelling framework. We consider an animal encountering reproductive opportunities as a random process. Under an external hazard, optimal life–history strategy typically prioritizes immediate reproduction at the cost of declining fertility and increasing mortality with age. Given such ageing, an immediate reproductive reward should be preferred to a delayed reward because of both the risk of death and declining fertility. By this analysis, ageing is both a consequence of discounting by the body and a cause of behavioural discounting. A series of models is developed, making different assumptions about external hazards and biological ageing. With realistic ageing assumptions (increasing mortality and an accelerating rate of fertility decline) the time–preference rate increases in old age. Under an uncertain external hazard rate, young adults should also have relatively high time–preference rates because their (Bayesian) estimate of the external hazard is high. Middle–aged animals may therefore be the most long term in their outlook.