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# Predictions for Euro Mixing

A question of some interest is that for the speed of the mixing process and the time when the coin mixture in Europe
will be "complete". It is clear that new emissions of coins as well as coin collectors disturb the process.
The "progress" of the mixing progress until April 2010 in Germany is shown in the following time series.

• The true values are a bit smoothed. The increase of the proportion of foreign 1--coins is clearly visible;
it is approaching now the value of 40%.
The origin 0 of the time axis is January 1, 2002.

Predictions on the coin mixing process can be made by means of a simple mathematical model. It leads to the formula
a(t) = a - a exp(-bt),
where
t = time in years after 2002,
a = percentage of non-German 1- coins in Europe,
a(t) = percentage of non-German 1- coins in Germany at time t.
The parameter b was estimated based on the assumption that in summer 2007 (t = 5.5) there were
25% foreign 1- coins in Germany.

Using this model, for 2018 50% foreign 1- coins are expected in Germany,
while in the 2030s a state close to total mixing can be expected --
if then the Euro still exists.

The model above is based on the assumption that the coin numbers in all countris are fixed over the time.
This is, however, not true, there is the tendency that the numbers increase.
In a joint paper with Professor Seitz and Dr. T๖dter the effect of variable coin numbers was studied.
We came to the conclusion that the percentage of foreign 1- coins in Germany
will hardly ever cross the 50% level.

It is interesting to study the mixing process in the smaller countries.
I got data from Slovenia, where the Euro was introduced in 2007.
My colleague Dr. Ida Erzen reported on 31% Slovenian coins in a sample of 215 coins of different sorts.

Last change: June 2010