A coefficient to four decimals, and 6 462.72 € less

An employee on 2 200 € gross a month costs 26 400 € of annual pay. The general reduction takes 6 462.72 € off employer contributions, nearly a quarter of that salary. Before you read on: where does that quarter come from, and why not a third?

One formula, five parameters

The single degressive general reduction is not read off a scale. It is computed, employee by employee, from a coefficient applied to annual gross pay.

The formula reads: coefficient = T min + T delta × [(1/2) × (3 × minimum wage computed for a year / annual gross pay − 1)] raised to the power P.

The minimum wage computed for a year equals 1 820 times the hourly amount used. That hourly amount is frozen at 12.02 €, giving an annual reference figure of 21 876.40 €.

The coefficient is rounded to four decimals, to the nearest ten-thousandth. That precision is not cosmetic: applied to a payroll, the fourth decimal still weighs a few euros per employee.

T min, T delta and headcount

T min equals 0.0200 for every employer. It is the minimum exemption threshold, the value the coefficient converges towards as pay rises.

T delta, in contrast, depends on headcount, because it embeds the rate of the national housing aid fund contribution, which differs on either side of fifty employees.

For employers with fewer than fifty employees, liable to that contribution at 0.10 %, T delta equals 0.3781. For those with fifty employees or more, liable at 0.50 %, it equals 0.3821.

A gap of four ten-thousandths looks negligible. On the same pay of 26 400 €, it moves the coefficient from 0.2448 to 0.2472, that is some sixty euros a year per employee.

A taper that is not a straight line

The exponent P equals 1.75. It is what gives the curve its shape: the reduction does not fall linearly with pay, it drops faster at the bottom of the scale than at the top.

At the annual reference minimum wage, the bracket equals 1 and the coefficient reaches its maximum: 0.02 + 0.3781, that is 0.3981 for an employer with fewer than fifty employees.

At 26 400 €, the bracket has fallen to 0.742977; raised to the power 1.75 it weighs only 0.594, and the coefficient comes down to 0.2448. The reduction stands at 6 462.72 €.

At 40 000 €, the coefficient is no more than 0.0716 and the reduction 2 864 €. Between 26 400 € and 40 000 €, pay rose by half and the relief was divided by more than two.

The scheme's exit point sits at three times the minimum wage, that is 65 629.20 € of annual pay. Beyond that, the general reduction no longer applies.

A close reading of the formula shows that at the exit point the bracket is nil and the coefficient equals exactly T min, that is 0.0200. The scheme therefore ends on a step, not on a gradual extinction.