Would you eat 2 day old sushi? How about a 9 month old Mallo Cup?

When you think about whether a leftover is safe to eat, you’re mentally doing the same discounting calculation done in basic finance classes.

An interesting example of this came up yesterday.

I eat just about anything. My friend does not.

So, my friend offers to split a Mallo-Cup. A Mallo-Cup that was shipped from an internet site about 9 months ago. The bit of wrapper that was impregnated in the chocolate added depth. My friend then declined to not eat “sushi” — in quotes because it contained no raw ingredients — because it had been made fresh about 42 hours previously.

Afterwards, I wondered which was safer … and if there’s a bit of rationality paradox here. Because, when you think about it, we rarely think about how to discount packaged candy. There’s lot of apocryphal stories about people saving leftover candy from one Halloween to the next, right? But, we always think about discounting leftover sushi, even if it’s cooked.

Now, I’ll admit that I wouldn’t normally eat 2 day old sushi no matter how well it’s cooked, but I did. I’d like to think I’d never eat 3 day old sushi ... but frankly, I’ve never been tested on that count. So, what’s the appropriate discount rate? I’d say perhaps 20% per day.

What that means is that if I valued the sushi when made at $10, that it was worth $6.40 to me after 2 days, because I took 20% off its value, twice.

**Days** | **Value of Sushi** |

0 | $10.00 |

1 | $ 8.00 |

2 | $ 6.40 |

3 | $ 5.12 |

If you’d put less value on 2 day old sushi, this just means you have a higher discount rate.

But, for the moment, let’s take that 20% discount rate seriously. And, let’s take the method — called exponential discounting — seriously too.

Just to ballpark that, a 20% daily discount rate for 2 days gets you to the same present value as a 0.165% daily rate applied for 270 days (9 months). So, $10 worth of 9 month old Mallo Cups would have the same value as $10 worth of 2 day old sushi if discounted at that lower rate.

What’s really interesting is the present values that such a discount rate implies for really old Mallo Cups. For example, it then takes 420 days for them to lose half their value. Going further:

**Days** | **Value of Mallo Cups** |

0 | $10.00 |

270 | $6.40 |

420 | $5.00 |

1394 | $1.00 |

I probably wouldn’t eat a Mallo Cup that’s almost 4 years old. But the calculations show that they’d still have positive value … so someone probably would eat them.

I’d go further and claim that most people would put a higher value on a 9 month old Mallo Cup than is shown in the table. If that’s the case, they’d put value on them for far, far longer than shown here.

All of this makes me think that perhaps with leftovers, we don’t use exponential discounting (as shown in textbooks) but rather hyperbolic discounting. In this form, we initially discount things very rapidly, and then more slowly after that.

So, for (even cooked) “sushi”, we discount very heavily for the first few days, so that perhaps the “sushi” has almost no value after 3 days. After that, we discount more normally, but from such a heavily discounted starting point that the value is always minute.

Alternatively, we might discount Mallo Cups hyperbolically, but those first few steps aren’t that large. This makes some sense. Think about how hard it is to resist the candy on the counter that you just bought, and how much easier it can be if it sits there for a few days. Perhaps this is because you’ve mentally discounted it a bit.

There’s another feature here that makes me think that hyperbolic discounting is the norm for leftovers. Do you really have any idea how old the packaged food you bought is? I mean, yes, it may have a freshness date on it, but those are mostly for store use, not personal use. And no one ever asks when that freshness date was actually applied. Especially on something like candy.