Who are the privileged individuals - past and present - that emit money? Do they not distort the ability of each one to say "this has value, and this has none"? Is this not alienating? Is this not undemocratic?

Should we not - wherever we live, and whatever our time - receive an equal freedom to assign value through the emission of money?

The Relative Theory of Money (RTM) leads to a simple solution to this problem: regular increase in the money supply following a rate established by the RTM, the new money being uniformly emitted by each individual of the community. This corresponds to a system providing an Universal Dividend through money creation.

These emissions could be managed by a central bank, or better, by a decentralized electronic cash system, such as Duniter or OpenUDC.

About this application

This web application deals with the Relative Theory of Money (RTM) designed by Stéphane Laborde, hoping not to misrepresent its spirit.

All the results presented here can be easily reproduced in a spreadsheet program such as LibreOffice Calc.

Suggestions:

you can skip to Step 3 and play, for example, on the first sliding cursor located at the bottom; in this way, you can add lines and see the evolution of results over time;

you can also click the table and, thanks to the arrow keys on the keyboard, move from one cell to another; this comments area will then be updated to describe the selected cell.

Money Supply at year 0: 10 000 000

The field is prefilled with the value 10 000 000, it is the number of millions of euros in the Eurozone in 2010.

Number of Individuals: 330

The field is prefilled with the value 330, it is the number of millions of citizens of the Eurozone in 2010.

For simplicity, we assume that the population is constant over time.

Life expectancy (in years) of individuals in the community: 80

In the Relative Theory of Money, life expectancy is used to determine the minimum and maximum rate of the Universal Dividend.

“Those who have quitted the world, and those who have not yet arrived at it, are as remote from each other as the utmost stretch of mortal imagination can conceive. What possible obligation, then, can exist between them — what rule or principle can be laid down that of two nonentities, the one out of existence and the other not in, and who never can meet in this world, the one should control the other to the end of time?”

This rate is set by the community and represents the increase in the money supply which occurs every year. No other form of creation is provided by this monetary system. In particular, to use the terminology of Irving Fisher, it is a “100 % money” system (to sum up, money can not be lent more than once, and a debt can not pretend to be real money).

How to assign its value

The money can be seen as a ballot paper which gives a mandate to a whole generation of individuals, and the difficulty is to adjust the term of this mandate:

A too low rate corresponds to too long mandates. The risk is - just like what is happening today - that oldest ideas crush the youngest. Examples: the oil and nuclear industries hinder research on other energy sources; the chemical industry stifles research on organic farming; etc.

A too high rate corresponds to too short mandates. The risk is that ideas do not have time to blossom and are abandoned prematurely. Or, in the words of Silvio Gesell, money risks to be too perishable.

Here we feel intuitively that this rate should depend on life expectancy of the population. The Step 2 shows how the RTM involves life expectancy.

Note that as he had imagined, the perishable money of Silvio Gesell does not meet the RTM.

Exponential

Notes:

It takes one year to increase the money supply by 9.661%; 7 to increase it by 100% (this time is called the doubling time); 23 to multiply it by 10;

Thus, we talk about exponential growth, but contrary to what is usually found in economics, it is sustainable since it is applied to an unlimited resource.

“The greatest shortcoming of the human race is our inability to understand the exponential function.”

With this rate, the money supply is multiplied by 80 after 80 years, what we can check by going to line 80 of the table.

Explanation

The idea is the following: the generation alive in year 0 owns a money supply. We then assume that 1/80 of this generation disappears every year, and it has almost disappeared after 80 years, representing only 1/80 of the population. So the money supply in year 0 - compared to year 80 – should weigh not much, but respect the proportion of 1/80.

Formula

Just so you know, the formula for calculating the minimum rate is:

= 100 × (ev^{ 1/ev} - 1)

= 100 × (80^{ 1/80} - 1)

Clarification for those unfamiliar with this notation: “80^{ 1/80}” is the number which, when multiplied 80 times by itself, is equal to 80.

Description

Maximum rate of Universal Dividend: 9.661%

It is based on half-life expectancy.

With this rate, the money supply is multiplied by 40 after 40 years, what we can check by going to line 40 of the table.

Explanation

The idea is similar to the one outlined for the minimum rate. But this time, for the sake of symmetry, we consider two generations living in year 0: part of the money stock is owned by “1 to 40” years, the other by the “40 to 80”. We then assume that 1/40 of each generation disappears every year. They have almost disappeared after 40 years, representing at that time only 1/40 of the population. So the money supply in year 0 - compared to year 40 – should weigh not much, but respect the proportion of 1/40.

Formula

Just so you know, the formula for calculating the maximum rate is:

= 100 × ((ev/2) ^{1 / (ev/2)} - 1)

= 100 × (40^{ 1/40} - 1)

Clarification for those unfamiliar with this notation: “40^{ 1/40}” is the number which, when multiplied 40 times by itself, is equal to 40.

The first sliding cursor enables you to add rows to the table and thus to see the evolution of results over time.

Money Supply at year 0: 10 000 000

= Money Supply in early year 0 + Increase in the money supply at the end of year 0

= 10 000 000 + 563 032,715

Money Supply at year 0: 10 000 000

Amount of the increase in the money supply by year-end 0: 563 032,715

= Universal Dividend applied to the money supply in year 0

= 9,661% × 10 000 000

You can play on the second sliding cursor located in the bottom of the table; it enables to add columns and thus to see other results.

Amount of the increase in the money supply coming from each individual by year-end 0: 2 927,522

= Amount of the increase in the money supply by year-end 0 / Number of individuals

= 966 082,271 / 330

Total sum of money issued by an individual from year 0 to year 0: 2 927,522

= Amount of the increase for year 0 + Total sum of money issued in previous years

= 2 927,522 + 0

The values of this column will approach, over time, a particular value: the equal distribution of money supply (which is discussed in the next column).

This value can also be seen as the money potentially accumulated by an individual - which is possible, for example, if he lives with his parents; or if he lives and spends only what he earns otherwise; or barters; or consumes what he produces himself...

Total money issued by an individual for year 0: 0

The values of this column will approach, over time, a particular value: the equal distribution of money supply (which is discussed in the next column).

This value can also be seen as the money potentially accumulated by an individual - which is possible, for example, if he lives with his parents; or if he lives and spends only what he earns otherwise; or barters; or consumes what he produces himself...

Amount of a hypothetical equal distribution of money between individuals in year 0: 30 303,03

= Money Supply in year 0 / Number of individuals

= 10 000 000 / 330

Notes: If we calculate the amount of the equal distribution per individual in the Eurozone in 2010, the result is thirty thousand euros per citizen.

Ratio of the total emissions to the equal distribution in year 0: 0

= 2 927,522 / 33 230,552

At year 0, this value is 0; but over the years, it will approach 1; this highlights that the total emissions, done by an individual, approach the equal distribution of the money supply.

This remarkable property can also be observed in the “Graphs” tab.

About this column

Monthly amount of money issued by each individual for year 0: 243,96

= Amount of emission in year 0 / 12

= 2 927,522 / 12

For example, when data used are those of the Eurozone in 2010, this column shows that the amount of universal dividend may seem low (243,96 euros per month during year 0).

It is certainly modest in the current monetary system - which favors losses in speculative bubbles, in a blind competition, an obstinacy to keep alive outdated industries, a fear of the future, etc. – but it is difficult to assert that the same would be true for a system combining “100 % money” and Universal Dividend.

“It’s as if someone were out there making up pointless jobs just for the sake of keeping us all working.”

in year 0, an individual borrows 20 492.64 euros (= 7 × 2927.52, equivalent to 7 times the UD at year 0);

repayment is scheduled on 7 years, at the rate of one UD per month;

after 7 years, he has repaid 27 486,15 euros, the total sum of annual UD over last 7 years.

About these graphs

Both of these graphs show over time:

money issued and potentially accumulated by an individual;

money corresponding to an equal distribution of the money supply between individuals of the community.

On the left, the values are quantitative, expressed in conventional monetary unit (eg, in number of euros); on the right, the values are relative, expressed in number of UD.

Money at birth

The money owned by the individual in year 0 (at birth, for example) is 0; that is, 0 time the amount of the equal distribution.

Thanks to the second sliding cursor, this value can be adjusted between 0 and 2 times the amount of the equal distribution.

between 0 and 1, the individual at birth possesses less than the equal distribution; over time, the capacity of its capital increases and converges toward the equal distribution;

between 1 and 2, the individual at birth possesses more than the equal distribution; over time, the capacity of its capital decreases and converges toward the equal distribution.

This sliding cursor goes only from 0 to 2, it is an illustrative choice that is not related to the RTM.

Selected year

At year 0:

money issued by each individual: UD = 2927.52

money issued and potentially accumulated by the individual
= money at birth + Total sum of money issued by an individual from year 0 to year 0
= 0 + 2 927,522
= 0 (that is to say 0UD)

money corresponding to an equal distribution
= 30 303,03 (that is to say 12.5UD)

ratio between these two quantities
= 0 / 30 303,03
= 0,088 (it approachs 1 over the years)

Conclusion

From a quantitative point of view, the money will certainly be gradually devalued as there are money creations. But we must consider a point of view which is relative to the equal distribution.

About Pie Chart

The two sectors of the diagram enable to compare:

the amount of money issued and potentially accumulated over the years by an individual which owns all the money at year 0 (eg, at birth);

the amount of money issued and potentially accumulated over the years by the rest of the individuals – who therefore has no money at year 0.

At year 0, only the first sector is visible, but over the years, it ends up being erased by the second sector.

Selected year

At year0:

money supply = 10 000 000

money for the individual “all money at year 0”

= Money supply at year 0 + Total sum of money issued by an individual since year 0

= 10 000 000 + 2 927,522

= 10 000 000
that is to say 100% of money supply

money for the others

= money supply - money for the individual “all money at year 0”

= 10 000 000 - 10 000 000

= 0
that is to say 0% of money supply

Step 1 – to set the 3 core values

%

Step 2 – to use specific Universal Dividend rates (related to life expectancy)

Step 3 – to view results in different forms (table, graph or pie chart)

## Comments

## About the RTM

Where does money come from?

Who are the privileged individuals - past and present - that emit money? Do they not distort the ability of each one to say "this has value, and this has none"? Is this not

alienating? Is this notundemocratic?Should we not - wherever we live, and whatever our time - receive an equal freedom to assign value through the emission of money?

The

Relative Theory of Money(RTM) leads to a simple solution to this problem: regular increase in the money supply following a rate established by the RTM, the new money being uniformly emitted by each individual of the community. This corresponds to a system providing anUniversal Dividendthroughmoney creation.These emissions could be managed by a central bank, or better, by a

decentralized electronic cashsystem, such asDuniterorOpenUDC.## About this application

This web application deals with the Relative Theory of Money (RTM) designed by Stéphane Laborde, hoping not to misrepresent its spirit.

All the results presented here can be easily reproduced in a spreadsheet program such as LibreOffice Calc.

Suggestions:

you can skip to Step 3 and play, for example, on the first sliding cursor located at the bottom; in this way, you can add lines and see the evolution of results over time;

you can also click the table and, thanks to the arrow keys on the keyboard, move from one cell to another; this comments area will then be updated to describe the selected cell.

Money Supply at year 0: 10 000 000

The field is prefilled with the value 10 000 000, it is the number of millions of euros in the Eurozone in 2010.

Number of Individuals: 330

The field is prefilled with the value 330, it is the number of millions of citizens of the Eurozone in 2010.

For simplicity, we assume that the population is constant over time.

Life expectancy (in years) of individuals in the community: 80

In the Relative Theory of Money, life expectancy is used to determine the minimum and maximum rate of the Universal Dividend.

## Description

Rate of Universal Dividend: 9.661%

This rate is set by the community and represents the increase in the money supply which occurs every year. No other form of creation is provided by this monetary system. In particular, to use the terminology of Irving Fisher, it is a “100 % money” system (to sum up, money can not be lent more than once, and a debt can not pretend to be real money).

## How to assign its value

The money can be seen as a

ballot paperwhich gives amandateto a whole generation of individuals, and the difficulty is to adjust the term of this mandate:A too low rate corresponds to too long mandates. The risk is - just like what is happening today - that oldest ideas crush the youngest. Examples: the oil and nuclear industries hinder research on other energy sources; the chemical industry stifles research on organic farming; etc.

A too high rate corresponds to too short mandates. The risk is that ideas do not have time to blossom and are abandoned prematurely. Or, in the words of Silvio Gesell, money risks to be too perishable.

Here we feel intuitively that this rate should depend on life expectancy of the population. The Step 2 shows how the RTM involves life expectancy.

Note that as he had imagined, the perishable money of Silvio Gesell does not meet the RTM.

## Exponential

Notes:

It takes one year to increase the money supply by 9.661%; 7 to increase it by 100% (this time is called the doubling time); 23 to multiply it by 10;

Thus, we talk about exponential growth, but contrary to what is usually found in economics, it is sustainable since it is applied to an unlimited resource.

## Description

Minimum rate of Universal Dividend: 5.63%

It is based on life expectancy.

With this rate, the money supply is multiplied by 80 after 80 years, what we can check by going to line 80 of the table.

## Explanation

The idea is the following: the generation alive in year 0 owns a money supply. We then assume that 1/80 of this generation disappears every year, and it has almost disappeared after 80 years, representing only 1/80 of the population. So the money supply in year 0 - compared to year 80 – should weigh not much, but respect the proportion of 1/80.

## Formula

Just so you know, the formula for calculating the minimum rate is:

= 100 × (ev

^{ 1/ev}- 1)= 100 × (80

^{ 1/80}- 1)Clarification for those unfamiliar with this notation: “80

^{ 1/80}” is the number which, when multiplied 80 times by itself, is equal to 80.## Description

Maximum rate of Universal Dividend: 9.661%

It is based on half-life expectancy.

With this rate, the money supply is multiplied by 40 after 40 years, what we can check by going to line 40 of the table.

## Explanation

The idea is similar to the one outlined for the minimum rate. But this time, for the sake of symmetry, we consider two generations living in year 0: part of the money stock is owned by “1 to 40” years, the other by the “40 to 80”. We then assume that 1/40 of each generation disappears every year. They have almost disappeared after 40 years, representing at that time only 1/40 of the population. So the money supply in year 0 - compared to year 40 – should weigh not much, but respect the proportion of 1/40.

## Formula

Just so you know, the formula for calculating the maximum rate is:

= 100 × ((ev/2)

^{1 / (ev/2)}- 1)= 100 × (40

^{ 1/40}- 1)Clarification for those unfamiliar with this notation: “40

^{ 1/40}” is the number which, when multiplied 40 times by itself, is equal to 40.The first sliding cursor enables you to add rows to the table and thus to see the evolution of results over time.

Money Supply at year 0: 10 000 000

= Money Supply in early year 0 + Increase in the money supply at the end of year 0

= 10 000 000 + 563 032,715

Money Supply at year 0: 10 000 000

Amount of the increase in the money supply by year-end 0: 563 032,715

= Universal Dividend applied to the money supply in year 0

= 9,661% × 10 000 000

You can play on the second sliding cursor located in the bottom of the table; it enables to add columns and thus to see other results.

Amount of the increase in the money supply coming from each individual by year-end 0: 2 927,522

= Amount of the increase in the money supply by year-end 0 / Number of individuals

= 966 082,271 / 330

Total sum of money issued by an individual from year 0 to year 0: 2 927,522

= Amount of the increase for year 0 + Total sum of money issued in previous years

= 2 927,522 + 0

The values of this column will approach, over time, a particular value: the equal distribution of money supply (which is discussed in the next column).

This value can also be seen as the money potentially accumulated by an individual - which is possible, for example, if he lives with his parents; or if he lives and spends only what he earns otherwise; or barters; or consumes what he produces himself...

Total money issued by an individual for year 0: 0

The values of this column will approach, over time, a particular value: the equal distribution of money supply (which is discussed in the next column).

This value can also be seen as the money potentially accumulated by an individual - which is possible, for example, if he lives with his parents; or if he lives and spends only what he earns otherwise; or barters; or consumes what he produces himself...

Amount of a hypothetical equal distribution of money between individuals in year 0: 30 303,03

= Money Supply in year 0 / Number of individuals

= 10 000 000 / 330

Notes: If we calculate the amount of the equal distribution per individual in the Eurozone in 2010, the result is thirty thousand euros per citizen.

Ratio of the total emissions to the equal distribution in year 0: 0

= 2 927,522 / 33 230,552

At year 0, this value is 0; but over the years, it will approach 1; this highlights that the total emissions, done by an individual, approach the equal distribution of the money supply.

This remarkable property can also be observed in the “Graphs” tab.

## About this column

Monthly amount of money issued by each individual for year 0: 243,96

= Amount of emission in year 0 / 12

= 2 927,522 / 12

For example, when data used are those of the Eurozone in 2010, this column shows that the amount of universal dividend may seem low (243,96 euros per month during year 0).

It is certainly modest in the current monetary system - which favors losses in speculative bubbles, in a blind competition, an obstinacy to keep alive outdated industries, a fear of the future, etc. – but it is difficult to assert that the same would be true for a system combining “100 % money” and Universal Dividend.

## Wage labor

For example, let's considerer a wage labor (but would it survive the introduction of Universal Dividend?):

in year 0, a employee receives 243,96 euros per month - the equivalent of one monthly UD at year 0;

7 years later, his salary quantitatively has increased to 465,24 euros per month - in fact it has stagnated since it is always equivalent to one DU.

## Debt

It is the same with the credit:

in year 0, an individual borrows 20 492.64 euros (= 7 × 2927.52, equivalent to 7 times the UD at year 0);

repayment is scheduled on 7 years, at the rate of one UD per month;

after 7 years, he has repaid 27 486,15 euros, the total sum of annual UD over last 7 years.

## About these graphs

Both of these graphs show over time:

money issued and potentially accumulated by an individual;

money corresponding to an equal distribution of the money supply between individuals of the community.

On the left, the values are quantitative, expressed in conventional monetary unit (eg, in number of euros); on the right, the values are relative, expressed in number of UD.

## Money at birth

The money owned by the individual in year 0 (at birth, for example) is 0; that is, 0 time the amount of the equal distribution.

Thanks to the second sliding cursor, this value can be adjusted between 0 and 2 times the amount of the equal distribution.

between 0 and 1, the individual at birth possesses less than the equal distribution; over time, the capacity of its capital increases and converges toward the equal distribution;

between 1 and 2, the individual at birth possesses more than the equal distribution; over time, the capacity of its capital decreases and converges toward the equal distribution.

This sliding cursor goes only from 0 to 2, it is an illustrative choice that is not related to the RTM.

## Selected year

At year 0:

money issued by each individual: UD = 2927.52

money issued and potentially accumulated by the individual

= money at birth + Total sum of money issued by an individual from year 0 to year 0

= 0 + 2 927,522

= 0 (that is to say 0 UD)

money corresponding to an equal distribution

= 30 303,03 (that is to say 12.5 UD)

ratio between these two quantities

= 0 / 30 303,03

= 0,088 (it approachs 1 over the years)

## Conclusion

From a quantitative point of view, the money will certainly be gradually devalued as there are money creations. But we must consider a point of view which is relative to the equal distribution.

## About Pie Chart

The two sectors of the diagram enable to compare:

the amount of money issued and potentially accumulated over the years by an individual which owns all the money at year 0 (eg, at birth);

the amount of money issued and potentially accumulated over the years by the rest of the individuals – who therefore has no money at year 0.

At year 0, only the first sector is visible, but over the years, it ends up being erased by the second sector.

## Selected year

At year 0:

money supply = 10 000 000

money for the individual “all money at year 0”

= Money supply at year 0 + Total sum of money issued by an individual since year 0

= 10 000 000 + 2 927,522

= 10 000 000

that is to say 100% of money supply

money for the others

= money supply - money for the individual “all money at year 0”

= 10 000 000 - 10 000 000

= 0

that is to say 0% of money supply