A primitive preliminary simulation of a taxation system suggested in r/math a week and a half ago: progressive taxes based on net worth, not income.

On May 2nd, pathjumper submitted a post which proposed a progressive tax system dependent on net worth, not income. He suggested a few other things too but this was the only one I could decipher well enough. Unfortunately pathjumper acted an ass in both of the posts he made (the original was in r/reddit.com) so nothing ever came of it. Well today I was bored so I decided to see if I could figure out some of the base implications of a system such as this.

I have no background in economics (I took one micro class in college...) so I'm sure there are some obvious improvements/corrections that can be made to this sim, and I'd love to hear about them in the comments, along with any other ideas or suggestions.

THE MODEL

For lack of a better role model I essentially borrowed the progressive brackets from the modern U.S. system, fit a curve to them, shifted it sideways a bit, then picked out some new brackets from that curve. This is what I ended up with.

 ------------------------------
|  net worth ($)        |  %   |
 ------------------------------
|  0 - 50,000           |  0   |
|  50,001 - 63,000      |  15  |
|  63,001 - 92,500      |  22  |
|  92,501 - 159,300     |  26  |
|  159,301 - 310,800    |  30  |
|  310,801 - 654,600    |  34  |
|  654,601 - 1,435,000  |  38  |
|   > 1,435,000         |  42  |
 ------------------------------

After that, I create "people" with all combinations of three qualities:

• Initial net worth is one of a number of values evenly spaced from $40,000 to $3,000,000.

• Yearly income is one of a number of values evenly spaced from $10,000 to $1,500,000.

• Percentage of income spent is one of a number of values evenly spaced from 50% to 100%.

In the specific model in this post, I have 6 different net worths, 7 different yearly incomes, and 4 different spending percentages, giving me a total of 6*7*4 = 168 people. I assume yearly incomes and spending percentages are fixed. Forever.

At the end of each year, I tax their net worth before adding their profit (income - money spent).

CONCLUSION

I can draw one sure conclusion from the simulation: eventual net worth is not dependent on initial net worth. In other words, wealth does not transfer from parent to child. See the results below for an illustration.

THE DATA

First I'd like to apologize for how gigantic these images are.

This bar graph shows the initial data of the model. There is a legend on the far right. Each set of three bars (purple, green, and orange) represents one person. The purple bar represents their net worth, the green bar represents their yearly income, and the orange bar represents their yearly spending.

This bar graph shows the results after simulating for 30 years. Regardless of initial net worth, the net worth at the end of 30 years is the same for everyone with the same income and spending. Here is the same graph, sorted by net worth.

Here is an animation covering the first 15 years of the simulation.

I noticed a little instability in the net worth for those who end up near the tax cutoff ($50,000), so I ran the simulation again to look specifically at more people down there. In the images below, initial net worth and income range from $10,000 to $100,000 each.

This bar graph shows the initial data for this new set of people.

This bar graph shows the results after simulating for 30 years on this new set. As before, eventual net worth depends only on income and spending. Here is the same graph, sorted.

Here is an animation covering the first 15 years of the simulation for this new set.

MISC. DISCUSSION

First it is interesting that those who spend all of their income are punished severely in this model. Those who save money trade standard of living (eating out all the time, vacations) for net worth (a better house, maybe?). See this image. The third and fourth blocks of people from the left have equal net worth, but one makes far more than the other. This is balanced by the people earning more spending that much more per year (bathing in pure gold). So at least this part of the model has a tiny bit of sensibility.

There's a pretty firm cap on the lower class at the bottom of the minimum tax bracket, while the wealth of the rich appears to be unbounded. This seems highly un-Marxist to me--perhaps pathjumper should rethink his endorsement.

Originally I added each person's profit before taxing net worth but you know your model is broken if you always end up with net worths less than yearly incomes.

WHERE TO GO FROM HERE?

The tax brackets need some serious help, and it would probably be worth discussing how a given bracket could be 'better'. If someone would like to take a stab at making another set of brackets I'd be happy to run the simulation(s) again to see what changes.

It might also be of interest to run the simulation with a sample of people representative of the actual distributions of net worths, ncomes, and spending percents in some country. I'd definitely appreciate it if anyone would take the time to cook up such a set, or at least one that's 'good enough'. This might reveal how the model would affect the distribution of wealth in said country.

I'd be happy to post my Mathematica code but I've had bad experiences here with line breaks messing it up in the past. Let me know where to dump it.

Thoughts?