...by Daniel Szego
 "On a long enough timeline we will all become Satoshi Nakamoto.." Daniel Szego

## Wednesday, January 10, 2018

As we have mentioned in our previous blog there is a possibility and sometimes the need as well to create a token that has a actually a monetary base and an extended money supply as well that can be achieved in the most easy way with the help of a simple multiplicator value. However in certain situations, there might be the need to have something as multiply multiplication.

So let we further refine our model, let be M0 the monetary basis and M1 = M0 * m is an extended monetary supply where m is a multiplication number. Let we define an M2 refined and extended monetary supply in a way that:

- let G={g1, g2, ... gn} a set of groups, in a way that
- for each A={a1, a2, ... ak} possible addresses, there is maximum one gi group in which the address is member
- let |G|={|g1|,|g2|, ... |gn|} the number of addresses that are associated to a given group
- besides, let we have for each group a {m1, m2, ... mk} multiplicator value.

If so, we can define the M2 refined extended monetary supply:

M2 = M1 * Sumi (|ai| * mi) / Sumi (|ai|)

It is practically a measure for creating an average of different multiplicator values weighted by the size of the groups.