Money and Happiness. Diff Eq.

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.
f4

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!

8 thoughts on “Money and Happiness. Diff Eq.”

  1. Haha this is confirmed by Bill Gates’ actions!
    First he increased his money exponentially to be happy. Then he realised that it wasn’t working out anymore so he started giving money away!

  2. Well, I am still happy, even though I am not gaining money exponentially, nor am I giving away lots of money. This must mean money is only one of the many factors involved with happiness.
    If I don’t give away much money, yet I am still happy, that means the other factors must be very large!

    One more thing: If I am losing money, does that mean my d$/dt is negative? If so, then in order to maintain constant happiness I must have negative money!
    That would make sense, since people want to borrow money when they lose large amounts, like when they gamble and such. The equation is sound!

  3. Hi,
    Interesting thoughts! I believe it’s not possible to make a general statement on whether money makes people more or less happy.

    Money comes with a whole set of new elements that may have good or bad impact on our happiness, and depending on how susceptible we are to every one of them, the conclusion will go one way or the other (i.e. different from person to person). I recently made an effort to provide a more comprehensive picture of what these ad- and disadvantages are. I invite you to have a
    look at Money and Happiness and tell me what you think!

    Thank you, Nick

  4. So two things. This is a piecewise function please add that because you cannot divide by zero and everyone knows money can very well be $ = 0; Therefore your function needs to be peacewise.

    Secodly, according to your theory I can void all increase in money the d$/dt as you put it just by making my $ -> 0 thereby making H -> infinity. Appart from that it is a worthy attempt I would love to see more of your theories.

    1. hahaha that is true, but I was hoping our $ won’t approach 0 =P

      how did you find my blog?! and thanks for dropping by!

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