Envelope theorem

Okay kiddo, so let's imagine you have a big pile of candy and you want to eat as much as you can. But you can only eat one piece at a time. So, you start eating and you realize that for every piece of candy you eat, you feel a little bit happier.

Now let's say you are very good at math and you want to figure out how much happier you will be if you can eat just one more piece of candy. That's where the envelope theorem comes in.

The envelope theorem helps you figure out how much your happiness will increase when you eat one more piece of candy without having to eat it first. It does this by looking at the "envelope" or the maximum amount of happiness you can get by eating all the candy in the pile.

So, even if you don't eat all the candy, the envelope theorem helps you figure out how much happier you would be if you did eat all of it. This makes it easier for you to make decisions about how much candy you want to eat without having to actually eat it all first.

Now, this might sound a bit silly when we're talking about candy, but the envelope theorem is actually used a lot in economics and finance to help people make decisions without having to try out all the different options first. It helps us understand how much we can gain from a certain choice without having to actually take that choice.

So, in summary, the envelope theorem helps us figure out how much we can gain from different options without having to actually try them out first, just like how it helps us figure out how much happier we will be if we eat one more piece of candy without having to eat it first.