Utility functions on divisible goods

Okay, so imagine you have a big bag of candy. There are different types of candy in the bag, like gummy bears, lollipops, and chocolate bars. You really like all types of candy, but you have a favorite - gummy bears! You also have some friends who really like candy too, but they each have their own favorite type.

A utility function is like a way to measure how much you like something. For example, you might rate gummy bears as a 10, lollipops as a 8, and chocolate bars as a 6. Your friends might rate their favorite candies differently.

Now, let's pretend that the candy is divisible, which means you can split it into smaller pieces. So, if you have a gummy bear, you can cut it into little pieces and share it with your friends. This way, everyone gets a little bit of their favorite candy.

But here's the thing - you and your friends have different utility functions for the candy. This means that each of you values the candy differently. When you decide how to divide the candy, you need to take into account everyone's preferences.

For example, if there are only a few gummy bears left in the bag, you might want to save them for yourself because you value them the most. But if there are a lot of lollipops and your friend really likes lollipops, you might give them more lollipops instead.

In the end, you want to make sure that everyone is happy with how the candy is divided. So, by using utility functions, you can figure out the best way to divide the divisible goods among your friends.