Gulching

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I’m reading Atlas Shrugged for the first time, and I’ve been thinking about the economic tradeoffs involved in a movement like Galt’s Gulch or seasteading, where you take an initial charge in order to achieve higher long-term growth rates due to more efficient government.

I decided to model the costs of Gulching as an initial cost to wealth, and the gains as a higher exponential growth rate. To make the graphs easier (by making it wealth-invariant, and thus not having that extra variable), I modeled the initial cost as simply being a fraction of wealth. For growth rates, I used 3% for the US (roughly what it actually is, and what we expect for spending 40% of GDP on govt), and either 6% or 8% for GG (the new society) – this is what we expect spending 0 – 10% of wealth on government, and what we see for high-growth societies today. I’ll first show the graphs, then talk about the assumptions and their impact. (Sorry for the messy screen capture graphs, I couldn’t figure out how to save graphs as images w/ Apple’s Numbers software.)

For timescale, I used the average adult lifetime of 54 years, which is an average lifespan of 72 years minus 18 years before adulthood. The next 2 graphs show the relative growth rates of wealth over these 54 years, at 8% for GG and 3% for USA.


Costs 75% of wealth to gulch

Costs 90% of wealth to gulch

You can see that even if you lose 3/4 of your wealth by gulching, you end up much richer over your lifespan. Even if you lose 9/10 of your wealth, you still manage to beat someone who stays home, in your last years. The lesson here is that even over one adult human lifespan, the differences in growth between big and small government countries dominates losing even a large fixed fraction of your wealth. You can see why people were willing to pay significant initial costs to get to the USA back when it was the land of opportunity for immigrants from around the world.

Next, we look at a different figure: the breakeven time. How long does it take until you have caught up? Here we show curves for both 8% growth (blue) and 6% (green), as well as a horizontal yellow line at 54 years. The Y-axis is years until break-even. The X-axis is what fraction of your wealth you have left, so 2 = 1/2 is lost, 4 = 3/4 is lost, 10 = 9/10 is lost. When green or blue are below yellow, that means you catch up before you die.

This is kinda confusing, it is saying things like “If gulching costs 3/4 of your wealth, at 6% growth you still catch up in about 45 years, at 8% in 25 years”, and “At 6% growth, if you lose more than 4/5 of your wealth, you don’t catch up in your lifetime. But even at 9/10 loss, your children still easily catch up in their lifetimes. At 8% growth, even with a 9/10 loss, you still catch up in your lifetime”

A few thoughts on some of the assumptions:

* A one-time initial cost of a fixed fraction of wealth is convenient for making starting wealth irrelevant, but it is not right. In reality, I think we should expect to pay a constant cost to gulch, or perhaps some combination of a constant cost and a maintenance cost which is a small fraction of wealth. A constant cost makes the gains increase over time (as we get wealthier and the constant cost becomes a lower fraction of wealth), and makes them greater for the richer than the poorer.
* Exponential growth of wealth is a good assumption, however note that a maintenance cost proportional to wealth, as mentioned above, is actually a decrease in this exponent.
* The growth rates seem pretty reasonable to me, as long as the society trades with the rest of the world (a small, isolated society would be vastly poorer and have slower growth rates). On the one hand, a geographically isolated society is more expensive to live in and will grow slower. On the other hand, jurisdictional arbitrage will tend to pull wealth into even an isolated society if it is the most attractive jurisdiction (see the Cayman Islands, Bermuda, the Bahamas…) Also, the relative growth rates change the timespan, but not the answer: growth wins, period.

Thoughts:

* Several people on my LJ pointed out that a problem with this analysis is that it assumes that wealth at death is the metric we want to maximize, when in reality, we care about wealth throughout life. Unfortunately, what is good for us is bad for our children and species.
* This analysis shows the interplay between seasteading and life-extension. The longer and healthier our lives, the more it becomes worth making short-term sacrifices for long-term gains, and the better aligned our individual and species interests are.

4 comments

  1. DanB 4:13 am

    Very interesting.  I would be interested in seeing more of these kinds of models.

    An additional factor to consider is the effect of increase in population. At the beginning, it may cost a lot (risk/money/lifestyle reduction) for people to move to a seastead. But as the population grows, these risks will decrease substantially. So at some point the choice will be much closer to "do you give up 10% of your wealth to live in a society with 8% growth rates?" – basically a no brainer.

    Note also that the standard % growth of GDP applies to the society as a whole. Individuals presumably experience much faster wealth growth during their productive years.

     

     

  2. Arthur B. 9:33 pm

    Growth rate ? Do you mean price index adjusted GDP ? This is a moslty meaningless number… Do you mean average stock market return ? Do you mean the typical interest rate ? If there are free capital flows, why not invest your money in the seastead and stay on land then ?

    Many people’s wealth – especially young people – is not in cash or financial assets but in their potential for labor over their lifespan. The value of labor is much higher where there is a lot of capital available. Seasteads may have lower tax rate but they have less capital. Sure you can have computer and intellectual labors, but then you’re tied to other land based industries which are highly taxed. You still pay taxes when you consumme anything produced in a taxed economy.

    All in all, this shows that exponential grow really fast… yeah it’s nice but it’s by no mean an account of the economics of Gulching. For most people, the relevant economic factor is not so much the grow rate but the effect on your net salary.

  3. Lasse Birk Olesen 10:26 pm

    "when in reality, we care about wealth throughout life."

    With (1-cost)*1.08^years being how much you earn in GG and 1.03^years being how much you earn in USA, I integrated these two functions and made a graph which shows how much you can afford to pay to move at a certain age in life and still expect to have earned the same amount of money at age 72: http://liberator.dk/content/files/seastead/ggvsusa.html

    With all the usual reservations, I think it looks promising with people in their 20’ies able to pay 70-85% and people in their 30’ies able to pay 60-70%.

  4. NathanS 2:50 am

    Just an update on the above post.  Finding the area under the curve (wealth throught your lifetime, not just at the end) is fairly simple.

    Integral of A^X = (A^X) / lnA

    Gulch:

    Integral from 0 to 54 years of 1.08^x is going to = (1.08^54 – 1) / ln(1.08) = 816.11.

    USA:

    (1.03^54 – 1) / ln(1.03) = 133.09.

     

    133.09 / 816.11 = .163 = 16% of wealth is required at the start to have the same amount of average wealth over a lifetime

     

    This method of comparison strongly favors money you have earlier in your lifetime, rather than using wealth at the end of life as the standard.  I think this more closely models human behavior and needs.

     

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