 There is some evidence that the standard discounted utility model does not adequately represent human behaviour. For a simple example, consider a person who prefers one apple today to two apples tomorrow, but yet (today) prefers two apples in 51 days to one apple in 50 days. Although this is a plausible preference pattern, it is incompatible with the exponentially discounted utility model. It can however be accounted for in a bifactorial model with a declining discount rate. Pioneered by Ainslie (1992), psychologists and behavioural economists have therefore proposed to replace Samuelson’s exponential discounting model with a model of hyperbolic discounting. The hyperbolic model discounts the future consumption with a parameter inversely proportional to the delay of the consumption, and can therefore cover examples like the above. 