In subsequent posts, I intend to expand this proof of concept to include economies with growth, and eventually with inflation, trade, and progressive redistribution models.
Effectively this simulation demonstrates that in any economy, taxation and redistribution is necessary to prevent members of society from dropping out of said economy, or more succinctly, dying.
Population
Starting Wealth
Average Trade
Tax Rate
Tax Period
In this simulation, we assume that each person in the economy trades with another member, and that in each pairing one profits at the expense of the other.
Bad economists will argue that all trades are inherently profitable for all parties involved, but they are bad economists. In reality, each participant winds up with goods or services they may value more, but if we accept he existence of money and markets, these goods and services have a value for which they can be traded, and profit is defined as the increase in the market value of an entity's assets.
Following that, the simulation also assumes that everyone starts out with the same starting wealth. Obviously, this does not represent real conditions in an economy, nor does it purport to. In fact these idealized conditions represent a perfect economy, and any deviation from them only amplifies the random-walk effects of the simulation. Future iterations will include the ability to create and edit individuals within simulations, but for right now, as a proof of concept this demonstrates the math.
In the simulation, there are a two other variables, tax rate and tax period. Tax Rate represent the amount of profit (expressed as a percentage) recaptured and redistributed by an idealized government entity. Again, inefficiency in this government entity can be modeled, but only enhances the downward trajectory of the unfortunate individuals that are already "losing". Tax Period is how many trade periods occur between tax events. A tax event is when the government entity assesses profit, claims taxes, and redistributes wealth.
What this leaves us with is a probability that a participant in the model economy will reach insolvency by a period n.
This probability of an individual will reach insolvency for systems without taxation can be expressed roughly as:
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where w is the starting wealth and t is the average trade.The probability that one individual in the population will reach insolvency is simply
pq
where q is the total number of individuals in the economy, and the probability that a percentage (x) of them will reach insolvency by time n can be approximated as
px
for all x such that xq > 1.
Taxation and efficient redistribution of course lowers this probability, but modeling its effects are complicated, and the subject of further discussion. For now, play with the colorful lines, and see if you learn something.
