People say money does not equal happiness, and I agree, but there is got to be some relationship between the 2.
What they really meant when they say $ != H is that they are not directly proportional.
I think I have finally figured out how they are related.
If we all agree that constant money doesn’t make anyone happy, obviously the function for happiness must involve d$/dt.
The first guess would be
But that is not accurate. If you give a hobo $10, he will be very happy. If you give Bill Gates $10, he will call the security to remove you from his vicinity.
The difference between the hobo and Bill is how much money they already have, so let’s add that to the equation. What if happiness is proportional to the ratio of d$/dt to current money?
That makes more sense. For example, if Bill has $100 billion and the hobo has 100 cents, giving them $50 billion and $0.50 respectively will make them equally happy.
Now, how much money do we need to maintain a constant happiness?
This is a separable first order differential equation.
Well, that’s bad news. In order to have constant happiness in life, your $ needs to grow exponentially. We can barely keep it linear.
But all is not lost. The diff eq has 2 variables. d$/dt and $. Changing d$/dt is a lot more difficult. So let’s start giving money away!