The minimum wage miracle

With the new Constitution of 1988, it was granted to every worker, the right to earn at least an amount called "minimum wage". In the second chapter, sixth article, it defines this minimum wage as the amount capable of attending the basic vital necessities of a worker and his family with home, food, education, health, leisure, clothing, hygiene, transportation and social security. It is also establish, that this minimum wage should undergoes periodic readjustments to overcome inflationary degradation of the worker's purchasing power. Although the Constitution does not specifies how often those readjustments should happen and what amount should be given, we observe in the history of readjustments that there is a regularity. There is almost one readjustment every year and the readjusting factor kept following the rule: CPI (consumer price index, which is used as a measure of inflation) + percent GDP growth. The rule of readjustment followed by the government in the last years to define the readjustment factor is: the CPI of the year that has just passed plus the percent GDP growth experienced in the year before. That means: readjustment_factor[n] = CPI[n-1]*GDP[n-2]. This might be observed in the figure right bellow, where the actual minimum wage value is plotted in blue and the predicted readjustment (using the rule) in red:



It is clear now that the readjustment try to follow this rule.

The interesting point about this readjustment rule is that it promotes the distribution of wealth. As the country keeps growing, the minimum wage also keeps increasing, at a larger step. Not everyone wage keeps increasing at the minimum wage's rate. It might clearly be apprised in the figure bellow. The cyan curve shows the average wage of Brazilians. If it were to be readjusted using the same rule the minimum wage uses, it would gives us the green curve. Looking at the graphic, we see that the average wage is always bellow the green curve, what shows that, on average, the wages don't follow the minimum wage increase.



The consequence of this is better viewed when we normalized all curves by the actual minimum wage value, what is presented in the next figure.



In 1995, the average Brazilian wage was around 8 times greater than the minimum wage. In the last year, in 2009, it reached a ratio 3:1. This means distribution of wealth. Observing the curve, it seems like the curve is going to saturate at a ratio between 3:1 and 2:1, what would leave Brazil in a similar position to developed countries. Here is some ratios of average wage to minimum wage in some countries: USA 3.28:1, Spain 2.55:1, Netherlands 2.22:1, Portugal 2.02:1, France 2.00:1, UK 1.88:1 (data from: source 1 and source 2).