This is the translation of the Leibnitz Module of the RTM, which follows the Bresson Module.

# Leibnitz Module

## (a) Thoughts on the Relativity of Prices (N)

Let’s assume that for a short time compared to life expectancy (a few years), the prices of some known values are relatively stable in the M/N frame of reference. Given this hypothesis, simulate:

- create the spreadsheet of a Libre Currency in both Quantitative and Relative (UD) frames while the population is composed of N individuals

including I1, I2 and I3 ; N is a variable represented in a column, during 80 years, one line per month (80×12 lines) as well as a newcomer I4 who enters when N varies, - on a short period of time, express the relative price in the frame M/N during a few years of an economic value V ; translate the quantitative price in UD,
- express during the same period the price of V compared to the accounts of every individual,
- simulate cases where “N increases strongly” and “N decreases strongly” in a few years, create the charts of the prices of V (which remains quite stable in the quantitative frame), in the 3 units as well as relative to the 4 individuals,
- Compare and interpret the results.

## (b) Reflections on the formula of the UD when N is unstable

- In the same spreadsheet, simulate two strong local variations of N (10 times growth/reduction) during a small period of time (2 years), N remains stable otherwise,
- add I4 who is a newcomer during the variation of N,
- express for the 4 individuals the variations of the price of V (which we will assume is still stable in the quantitative frame) in the 3 units (quantitative, UD, M/N) and relative to the accounts of each individual, during a period of 20 years around the variations of N (before and after),
- try to find a possible range for the UD’s formula between minimal and maximal values by studying the case of the 4 individuals,
- Compare and interpret.

## (c) Studying different UD formulas

- In the same spreadsheet, simulate two strong local variations of N (x 10) on a short period (2 years), N remains stable otherwise,
- Simulate for the 4 individuals different formulas for the UD that can be studied in a 20 year interval before and after the variation of N,
- simulate the same formulas when N is stable in another spreadsheet,
- compare each formula graphically by comparing it to M/N when N is stable,
- calculate for each of these formulas the standard deviation with the stable case,
- Compare and interpret the results.

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