Nova workboard

a blog from young economists at Nova SBE

RIS: moving from reality to a model

The RSI is a Portuguese measure of social protection which was created to help people “suffering from severe economic distress and at risk of social exclusion”.

What I propose to do next is to explain one of the main RIS’ specificities: any dependent worker should have a salary which 80% of its value exceeds the threshold of € 178.15; otherwise, the beneficiary will receive a subsidy equivalent to that difference.

In order to understand the implications of considering only 80% of the value of earnings, let’s assume a different rule: to get the subsidy, the sum of an individual’s monthly earnings should be less than €178.15. In that situation, the RIS can create an undesired effect: some workers would prefer not to work. This result is straightforward because some individuals will prefer to receive the subsidy instead of working and getting the corresponding disutility.

In reality, all individuals who optimize, in a situation without RSI, their trade-off between consumption (which requires money) and leisure, working a number of hours equivalent to an income below €178.15, will not work, in a situation with RSI, because they will achieve a higher utility without working.  Intuitively, the choice between working a few hours or nothing at all is easier: by working only a few hours, people will have the same amount of money (175.15€) at the end of the month as if they do not work, but while getting the disutility of working. Additionally, some people who worked before, earning an income above this limit, may prefer to stop working since, in certain situations, the loss of consumption can be offset by gains in leisure.

Besides the assumptions of positive marginal utility of consumption and negative marginal utility of working, we can make another useful assumption: the indifference curves of low skilled workers are steeper than the indifference curves of high skilled individuals. The following figure illustrates the situation of an individual who optimizes his trade-off between consumption and labor, in a situation without RSI, getting an income below €178.15 and then his optimization with the possibility of receiving RSI.


What happens here is that the implicit marginal tax rate on earnings for income below the threshold is 100% and it makes the individual be better off without working (with a subsidy equal to 178,15€). However, you should not forget that it just happens for less productive individuals.

In order to avoid that, the RIS has been designed considering the “earnings disregard policy”; by other words, the RIS scheme includes a phasing-out. There is evidence that it increases employment rates and reduces poverty levels. Can we explain this evidence with microeconomic models?


The “earnings disregard policy” changes the workers budget constraint: for the values of income below the new threshold (about 222€, because all workers receiving more than that cannot apply to the subsidy) there is a new straight line with positive slope. As you can see, the implicit marginal tax rate is no longer equal to 100% (for individuals below the threshold): if individuals work, they will see their income increase somewhat. Furthermore, there is a group of people who previously received no subsidy but now they started receiving (people with an “initial” income between 178€ and 222€).

Furthermore, individuals who still optimize at the corner solution remain at the same utility level, while individuals above 222.68€ will still maximize their utility at the same point, which is to say, getting the same utility level. In other words, nobody gets worse-off.

The theoretical analysis above was just a simple optimization of the consumer problem based on some basic assumptions, e.g., no income taxes, only dependent workers, no other sorts of income. However, such microeconomic analysis allows us to take some very interesting conclusions.

First of all, there was an expansion of the possibilities of income (for certain income levels) resulting in a rise in utility of the individuals who would be receiving the subsidy after the policy change. In other words, the welfare of those individuals is increased; regarding the total welfare effect, we cannot take any conclusion, depending on the society’s utility function and how the government would finance the subsidies.

In addition, we have another positive effect: there is an increase in labor supply. Consequently, the product of the economy would probably increase; it also has other effects since it prevents the skills’ degradation of those individuals.

Finally, we should not forget the other purposes of the RIS that are not considered in the model. The RIS try to ensure that all individuals are able to meet their basic needs, an essential right to any human.

Filipe Silvério, #617


Author: studentnovasbe

Master student in Nova Sbe

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