Unsustainability of the socialist welfare

Thinking about the unsustainability of the socialist welfare, demonstrated by the economic crisis in Eurozone, led me to come up with this simple equation (see the figure). I am pretty sure that there are more developed economic models (that I am ignorant of), describing the same thing. I post this however for the benefit of those who still think that the existing opposition to overtaxing the rich and growing inequality gaps is the issue of morality rather than something based on logical approach to reality.

The model in the photo describes a progressive tax system, which has only two tax rates - the one applied to the richest group of the population (say, the richest 1%) and the one for everybody else (99%). I first show that a meaningful welfare system cannot exist without a progressive tax system - indeed, if the two tax rates are taken equal, the amount of the welfare benefits per person is given simply by the fraction of the average income taken by the taxation. This means that a person earning average income does not really need welfare system - one can simply get the same benefits by saving a fraction of the one's income. (And I ignore the expenses on the government bureaucrats, who take care of tax collecting and welfare distribution.)

To be fair, this would still work in a society without middle class - the society where the number of the individuals with the income around average is very small, compared to the number of those, whose income is much lower than the average. We know, however, that this is not the case in the Western democracies.

The conclusion: middle class wants a welfare system which gives us more than we pay in taxes! And this is exactly the welfare system that exists in most of the developed countries (Europe, Israel and likely even US.) In short, most of welfare that we enjoy in terms of pensions, healthcare benefits, unemployment payments etc. is already paid for by "the rich"!

I further re-write my very first equation in a slightly different form, in order to show that the increase in the  welfare (the demand of the Occupy movement and other western social protest movements) can be achieved only through increasing the part of revenue coming from the rich - either by increasing the tax rates or by increasing the income of this group of people.

Pay attention that the increase in the welfare includes not only the increase in the size of the monthly/yearly payments per individual - it should also account for the increase in the population, receiving the welfare. Depending on how you count, the increasing longevity after the retirement should be included either as an increase of the individual welfare or the increase of the population (eligible for the certain pension and health benefits).

It seems that increasing the tax rates is what the popular demand is. This demand is however unsustainable, given that the tax rate cannot exceed 100%. In fact, regardless of whether one subscribes to the "supply-side economy" or not, one probably agrees that raising the tax rates will destroy the insensitive for high earners well before they reach 100%.

The other solution is allowing the share of the income of the highest earners to grow... but this means growing inequality gap! Thus, the social protest's simultaneous demands for reducing the inequality gap and greater state-provided benefits are incompatible! We really have to choose one of these! 


In fact, the sad conclusion is that the growth of the demand for the benefits, due to the population increase and higher longevity, means that the welfare states will be eventually forced to reduce the amount of the benefits per person - either by the reducing the nominal size of the benefits, or by raising the retirement age and other benefit eligibility requirements.