To make it clear, one should also look at a signal of a specific frequency (pure tone signal). The PSD is then an infinite narrow, but infinite high peak (a delta function with the integral yielding the power of the signal). The "PSD estimate" is a smeared out function of this delta function. But as narrower the bins, as higher and narrower the peak (while keeping the area under it). On the other side, the power spectrum will always show a peak with a height corresponding to the power of the signal, independent of how narrow the bin is.  
In conclusion: In PSD, the noise levels will not change when changing the bin size as illustrated by @WMXZ, but the peak of a single tone signal will increase with decreasing bin size. In a Power Spectrum (PS), the peak of a single tone signal will not change with decreasing bin size, but the noise levels will decrease (see answer from @WMXZ). 
This is important to note when discussing Signal-to-Noise ratio by just looking at a spectrum (either PSD or PS). It often leads to confusions.