A few weeks ago I learned about the “Simple Economy” simulation on NetLogo thanks to a presentation by Bill Rand at the Santa Fe Institute. I shared the program with the boys when I got home from the conference – that project is here:

Today I revisited the project with my younger son, though in Mathematica rather than in NetLogo.

First we explored the original problem -> 500 people start with $100 and play a game. At each step of the game they give $1 to one of the 500 people selected at random (assuming they have more than $1). How does the distribution of the money evolve over time?

Then, as in the prior project, we talked about what happens when you give away 1% of your money at each step rather than $1:

At the end of the last video I asked my son to design a new experiment. Here’s what he decided to do:

(i) If you are below $50 you have to give only 50 cents
(ii) If you are above $200, you have to give $3, and
(iii) Otherwise you give $1.

We talk through how to code his idea:

After we finished coding we discussed what he thought would happen, but in this video we didn’t yet see what would happen since the simulation was taking a bit longer to run that we’d guessed:

Here are the results of the simulation. My son explains where his guess was right and where it was wrong:

Finally, we wrapped up by looking at some of the individuals and how their money evolved over time:

This “simple economy” model is super fun to play with both on Netlogo and on your own. It still feels like such an unusual result to me, but I’m really enjoying hearing my kids talk about the results of the original model and the modifications that we are playing around with.