The hyperbolic discount function

Sounds terrifying, but after reading Utset (2006), it's heaps easier than I think. Reading about this by an economist instead of a lawyer would probably be more terrifying. After writing a paper on the economics of procrastination based on O'Donoghue and Rabin, I finally understand what the hyperbolic discount function is, thanks to Utset.

What it is: economists in general have always assumed that individuals have time-consistent preferences. Basically, what this means is that your long-term preferences e.g. losing weight will be reflected by your short-term preferences e.g. you will take steps to lose weight. In reality, we all know that (i) this assumption is too ridiculously simple (ii) this assumption is unreal. Time-consistent preferences are captured by the exponential discount function, whereby an individual discounts his utility by the same magnitude as time goes on.

Individuals are in fact time-inconsistent in their decisions. I may have a long-term preference to lose weight, but then in the short-term, when it comes to deciding whether or not to eat that bar of Kit Kat, my desire for immediate short-term gratification can override my long-term desire to lose weight. In other words, I give extra weight to the costs and benefits of an action now than later. Such a time-inconsistent behaviour can be modelled by a hyperbolic discount function. The difference between this and the exponential one is that the hyperbolic one further discounts my utility now and in the future by some positive percentage. I won't go into this mathematically, but what this means practically is that in the immediate short-term, I can ignore my long-term preference in favour of my desires now - for example, if you ask me if I would eat the Kit Kat on Jan 1, 2009 on Jan 1, 2009, I'd say YES! But if you were to ask me about if I would eat the same bar of Kit Kat on Jan 1, 2010 on Jan 1, 2009, I'd most probably say I'd skip eating it. So it's quite easy to see time-inconsistency modelled in hyperbolic discount functions.

Voila! It's that simple. And it took so long just to understand it -_- Evidently I'm not strong at mathematics, but I'll be taking quite a big leap in doing a thesis around a topic so full of it.