of a new idea about income

Natural Income was born from the ideal that every citizen could afford goods and services that are fundamental in a modern society, as a guarantee of freedom and fairness. To protect these rights, the tax on individual income must be adjusted to the person's taxpayer capability.

Starting from these principles, Natural Income is designed to simplify the current italian individual income tax: obsolete, dispersive, unfair and complicated by multiple layers of laws and parameters.

The income tax must be reformed. But to make any progress we must revolutionize any system inherited from the past.

Every person shall contribute to public expenditure in accordance with their capability. The tax system shall be progressive.
— Constitution of the Italian Republic, Art. 53

An actual progressive income tax

An income tax is progressive when higher the income, higher the percentage owed to the State.

The current income tax, defined by multiple tax rate brackets, contradicts this principle by being only in part progressive, against the constitutional precepts.

  • Rich citizens are exempt from progressiveness: while low and average income people are subjected to raising tax rates, higher incomes are taxed with an almost constant rate, which make the income tax proportional for the rich.
  • Above an income level, the more you earn the less percentage you pay: subsequent laws and correctives have made the marginal tax rate not uniformly increasing; on the contrary, it grows steeply for lower incomes and decreases for higher ones.
  • To live off private income: financial and capital gain do not contribute directly to taxable income, and they benefit from separate taxation with lower rates, even though they are owned mainly by the richest citizens.

Natural Income does not require obsolete tax rate brackets, instead it uses a progressive formula which continuously increases the tax rate by the income growth. It includes all income categories, including financial and capital gain.

This way, even the rich must observe income tax progressiveness.

Fairness as people's rights guarantee

The income tax is the main instrument of wealth redistribution. Given this role, it must guarantee that all citizens can afford fundamental goods and services for their sustenance, providing for compensations of insufficient incomes.

The system currently in effect is not fair enough to balance the wealth gap, nor to oppose its continuous increment. The present disparity is mainly caused by the exponential accumulation of goods that ensures bigger incomes to people with already a large capital, a phenomenon known as Matthew effect. Over the years, governments always opted to apply correctives to support lower class people, instead of tackling the problem of wealth redistribution from its roots.

Natural Income brings to a comparable level the different income classes. Those who are more economically lucky become more involved in the public expenditure, while those who live at the edge of society have granted the opportunity to live a dignified existence and to find a chance of improvement.

A single universal income tax

Knowing your income tax should be easy as knowing how much you earn in a year.

Currently, calculating how much we owe to the State is a difficult task, subject to continuously mutating laws.

  • There are differences based on income classes, such as employees, self-employed or retirees, and on family unit.
  • Several laws, which regulates tax expenditures, are continuously added and changed over the years: you must take in to account more than a hundred cases in your individual income tax return!
  • Then you have to consider fees relative to public services, with amounts linked to the annual individual income, such as university and kindergarten fees, local tributes and many more.

Natural Income supports lower income classes and removes the necessity of the aforementioned correctives, and drastically simplifies the income tax calculation for all taxpayers.

Moreover, public services can have a fixed price relative to the kind of provided service, without requiring adaptations to the user income: it's the income tax that guarantees to everybody a fair way to afford such services.

Born to guarantee to all citizens an access to goods and services that are fundamental in a modern society
Designed to simplify an individual income tax which is obsolete, dispersive, unfair and complicated by multiple layers of laws and parameters

The perfect formula

for a natural income

The function that opposes and at the same tame brings to a comparable scale exponential phenomena, is the natural logarithm. It's the actual origin of the Natural Income name.

Contrasting exponential accumulation

Top incomes are hundreds to thousands times bigger than the lower ones. By applying the logarithm to the income with an appropriate scale factor, the gap is reduced to a few tens of times.

Limitless growth

The logarithm function does not have a maximum value, but it grows to infinity, even though more and more slowly. Applying the logarithm to an annual income does not limit how much a person can earn.

Compatible with a guaranteed minimum income

Providing a support for very low and null incomes does not interfere with the logarithmic formula for the income. Taxed income includes only the part exceeding the no tax area, where a guaranteed minimum income definition may be included.

The natural logarithm is the function that opposes and at the same tame brings to a comparable scale exponential phenomena
It's the actual origin of the Natural Income name


of the personal income tax

There are three fundamental parameters for calculating the income tax:

  • Gannual gross income,
    which includes all incomes in a year added together;
  • Nno tax area,
    tax deduction for subsistence incomes;
  • Sscale factor,
    that determines the income tax slope.

From the first two parameters, we can define the taxable amount T as the difference between gross and tax deduction:

T = GN

When the income is less than the subsistence threshold, no tax is applied. The tax on income exceeding the no tax area is formulated as the composition of three functions.

The first one, called area of hyperbolic sine, is a natural logarithm alternative which is more linear around the origin.

f(x)   =   arsinh (x)

Functions which have a logarithmic shape affect net income by flattening it very soon. This behaviour can be reduced by applying the function on a sub-linear scale, e.g. the square root as shown in the second function. Additional constants are needed to center the function in a way that it is 0 in the origin and it has a first derivative equal to 1.

s(x)   =  
+ x

To slow down the function growth even more for lower incomes, an additional scale is used which reduces increments around the origin.

d(x)   =  
1 + x2
  −   1

Average tax rate is then defined using a composition of the three functions above:

f( s( d(
) ) )

s ( d(
) )

This way, and unlikely from the current income tax, lower incomes lying just above the exemption threshold contribute with a reduced and sustainable portion of their amount. Higher incomes see an increasingly growing tax rate, that still never gets too close to 100%.


The scale factor S and the no tax area N shall be accurately set to keep an appropriate tax revenue and positively affect the lower income classes. They can be adjusted to keep the budget in line, lowering S when the State needs more revenue, which affects higher incomes above all.

For instance, the following parameters have been chosen

N = 10,000€ (retired)
N = 1,000€ (workers)
S = 2,950€

The first corresponds to the current absolute poverty threshold in Italy, as reported by the ISTAT (Italian National Institute of Statistics), which is equivalent to 840€/month for a single adult. The use of different thresholds for workers and retired taxpayers is required in a transitory period, before reaching a total exemption for minimal incomes.

To keep the current income tax revenue unchanged, the S parameter shall not be above 2,225€, based on income statistics in 2020 (165.1 billions Euros in tax return), the 2022 income tax cut (7 billion Euros) and social security budget (256 billions Euros in 2019). Without fine-grained data, the actual value that preserves the current tax return may slightly differ.

However, leaving tax return unchanged would increase the fiscal wedge on incomes receiving the Bonus Irpef compensation, which are still low. To avoid this undesired effect, the scale factor is increased to 2,950€. Nearly about 37 billion Euros are required yearly to sustain this change, but no enough data is available to verify the actual cost. A gradual introduction of the new income formula would allow to find the necessary resources in a sustainable way.

You can directly calculate income tax using the dedicated simulation tool.

Alternative Functions

There are multiple ways to define a progressive income tax function: Natural Income is not necessarly bound to one of those, but uniquely to the progressivity principle.

Confronta le diverse implementazioni di Reddito Naturale

Top incomes are hundreds to thousands times bigger than the lower ones: by applying the logarithm to the income, the gap is reduced to a few tens of times Even the rich must observe income tax progressiveness

Frequent questions

and answers to main doubts

No, Natural Income is a personal income tax model.

Guaranteed minimum income is a social welfare system for all citizens, which provides a fixed and unconditional monthly income. You can find an european citizens' initiative which proposes its introduction in the European Union countries.

Natural Income is perfectly compatible with a guaranteed minimum income solution, where the guaranteed amount can be excluded from the taxable amount, as it is explained in the definition.

The flat tax is with no doubt the most simple form of income tax and, at first glance, it may seem the most fair solution. It applies the same fixed tax rate to every citizen. Some political proponents have recently stated that the rate should be set between the 15% and 23% of the gross income.

Anyway, it would be a fair tax if:

  • the cost of living for each person were null;
  • capital were not generating exponential profits.

The flat tax, with its single rate, would not affect the income erosion caused by the cost of living, neither the exponential capital accumulation. Moreover, it's a proportional income tax, which means it would be unconstitutional: to overcome this, flat tax proposals introduce a minimum income that can be deducted. Even if removing the tax burden from lower incomes, the flat tax moves it onto the average incomes, causing their impoverishment. Paradoxically, it would push lower incomes down, and wolul allow higher ones to grow limitless. The gap between the rich and the poor would become more extreme.

Natural Income tackles these effects, bringing both lower and higher incomes to a central range, reducing a gap that is continuously growing.

At last, the low tax rate of a flat tax would cause a great revenue loss, which must be compensated by more deficit while hoping that a possible economical growth will repay it. With Natural Income the tax revenue would stay steady, just with a more fair distribution.

The natural logarithm isn't easy as sums and products used when calculating the income tax with tax brackets. The actual complexity affecting the current income tax is the unbearable amount of clauses, surtaxes and tax exemptions, which make tax calculation a maze of continuously changing laws.

Anyway, you can find the logarithm and the square root functions in any smartphone calculator. Moreover, with specific automated tools, you need only to enter all your incomes to calculate the owed tax.

The problem of the discrepancy between income and net worth affects also the current income tax with tax brackets. Whatever system is into effect, it should come with a broader concept of income, including a percentage of the net worth in the total income calculation.

For instance, if we state that the 2% of net worth is considered income, largest capitals would be taxed more, like in the following example:

  • a citizen with a 30,000€ income and a house worth 100,000€ would have a total income of 32,000€, which implicates an income tax of 3,784€;
  • a citizen with a null income but a capital of 10,000,000€ would have a total income of 200,000€, with an income tax equal to 137,571€.

The second case may seem an excessive taxation, but it is equivalent to a property tax with a 1,35% rate.

With the 2% net worth rate and a no tax area up to 10,000€, an individual with a 500,000€ net worth and without any other form of income would not be taxed.

The rising fiscal pressure would certainly move abroad the private capitals of wealthy citizens. That's why it is necessary to tax the voluntary change of the fiscal residence.

A possible option could be to tax a percentage of the net worth produced in the Country. Who made large wealth in Italy owes its fortune mostly to the italian society, including of labourers, companies, and services granted by the State, made possible by all taxpayers. Leaving Italy from the fiscal point of view should require that a part of the net worth stays in the Country.

The considered income is the individual one, ignoring the person's marital state. This may encourage both spouses to work, as in single-salary families the role of the worker is taken statistically more often by the man.

Anyway, in single-salary families with low income, the spouse and the children are supported by social security checks. The checks may be replaced by a guaranteed minimum income, leaving intact the social support for families. Considering average family incomes, the two different situations are quite similar in terms of total income.

Natural Income is meant for the individual income taxation, not for legal entities like companies. It would affect wages and shares of profits only, not the company gain.

It would actually be a deterrent for excessive manager wages amd large shares of profits, leaving more money for internal investments and contributing to the company progress, with advantages not limited to the business environment.

Not necessarily: there are various factors that make the cost of living different, which shouldn't be ignored. Ideally, the State should level such divergences, but they can't be easily solved.

The Natural Income parameterization may be used to assimilate the cost of living differences on individual, family or local base, slightly changing the income tax parameters.

By using the same principle, the regional and town surtaxes may be implemented with such variations, while preserving the progressive property of the income tax.

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Natural Income is far from becoming an actual usable tool. In fact, there are still many aspects that must be considered and examined.

But the founding idea stays solid: being a tool useful to cut down disparity and inequality in a society that is evolving toward the wrong way. And to make progress, this idea needs to be accepted and shared among people who believes in its principles.

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