Interactive graphs for learning about hyperbolic discounting

Would you rather have 100 pounds in 12 months’ time, or 110 pounds in 13 months’ time? Most of us would take the latter option and wait just a month longer for 10% more money.

But now, move everything forward by 12 months: would you rather have £100 right now, or wait a month for £110? Suddenly an extra month seems a long time to wait: many of us would rather take the hundred.

This is an example of what’s called a preference reversal. The choice is essentially the same, but merely by transposing the choice in time, we can affect which option people prefer. Even if £110 seems more attractive to you in both cases, there will still be a similar reversal when we fine-tune the times and amounts of money.

In economics, the word discounting is used for the principle that money in the future is worth less than the same amount right now. One theory to explain the above preference reversal is hyperbolic discounting; a theory which takes ideas from the psychology of perception. Hyperbolic discounting is very different from the traditional theory which assumes a constant discount rate, which could be called exponential discounting. Discounting has implications for investment, finance and government policy. I’m told that the procedure used by professional government economists is built on (but different from) the hyperbolic theory.

Inspired by Daniel Kahneman’s Nobel Memorial Prize acceptance speech, I’ve programmed a couple of interactive learning objects which allow you to compare the properties of hyperbolic and exponential discounting. By tweaking the sliders, you can see for yourself why preference reversals are possible in one, but not the other.

They are Creative Commons licensed, so you are welcome to adapt them for educational use so long as you give credit.

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