This is more of a bio-psychology question, and I'll admit off the bat I'm a bit rusty. So be patient with me.
Dreaming only happens during REM-sleep (Rapid Eye Movement). This is where the brain tries to 'reboot' the mind, to help you feel 'rested'. The thing about dreams in and of themselves, they are... strange. They are basically (or at least typically) fractions of your day (week, month) scattered across the canvas of your semiconscious mind (here I mean the 'aware' part of your brain). So you 'relive' parts of it in various ways as a means of helping you 'digest' those memories.
This typically works out in strange ways (hence my calling them strange). So if you're having an erotic dream, a sensation (a touch, a glance, a look in someone's eyes) could be superimposed onto someone or something else. For example, someone at work/bar/library is flirting with you, that gets superimposed on your sibling/mother/whoever during your dream, because you were already 'thinking' about them in that segment of the dream.
Now, the reason I describe all that is to show the clear difference between 'dreams' and REM sleep. You would need to figure out if this 'cost' is the REM sleep (which is biologically needed to feel rested) and 'dreaming' (which is an psychological process of 'processing your day'). The difference (as I understand it) would be one means you're going to be cranky and tired for life (REM) and the other means you won't process your day quite the same way and could become mentally unresponsive to certain (or all) stimuli (dependent on other factors and/or how extreme you want the price to be).
I'd advise you research the psychological studies done on sleeping and dreaming, and there've been quite a few. A good starting place, if ever there was one.
