Why is my half resolution render taking a quarter of the time of the full one? I render an animation at 200 samples; $1920$ x $1080$, using Cycles.

A still takes about 2min44s to be rendered.  Tiles are $480$ x $360$.

I noticed that when doing half resolution renders, the same still would take only 43s, which means only 26 % of the full resolution time.

Is it a normal behaviour ?
That is simple math, area doesn't scale linearly, it has a quadratic relation to the dimensions of the shape, if you double the size you quadruple the area hence a four times the render time.

If the area of a $4 \times 4 = 16$ and you halve it then $2 \times 2 = 4$ which is one fourth

Hence you get a quarter of the area and consequently one fourth of pixels to calculate; that's about four times less computation power required leading to roughly one fourth of render time, give or take, for the same scene and settings.