I usually develop content management solutions in php, I work with designers that create the front end (html & css) and I usually develop the backend (php & mysql) of said cms. I know that the cost of the website may vary depending of the complexity of the html or the backend, but taking as reference a very basic website, what percentage of the cost should go to design and what percentage should go to development. I want to make clear that I as the developer i'm in charge of all the effects and animations of the websites using some of the javascript frameworks, not the designer. I just want to know what´s the fair share for me and for the designer.
Fair share is related to what you expect to make per hour. If you need $d/hr x h hours = cost, make sure when you give a quote to the client, your compensation is included. Regardless of what the designer will charge.
It really doesn't matter.
If the output of the designer is lets say a PSD
design of the resulting website, I would say the share should be 50% : 50%. But if its only a hand drawn pencil sketch it should be like 35% - 65%. In my view designing the website and its color schema, the fonts to be used and the overall look and feel is the most toughest job, and none the less development is no less.
It sounds like you're talking about a co-operative effort between you and another person (probably a friend?). In that case I would pay each person proportional to how much time they put in. If the web design takes no time at all but requires very complex back end work then you as the developer should be rewarded appropriately. Of course the inverse applies if the design is most of the work and the actual implementation is simple. This of course assumes you and the designer are both of equal skill levels so that time can be valued properly.
On the other hand if you're talking about things from a purely business point of view where you're going to subcontract the design to someone else then I think you're approaching the problem incorrectly. Your real question should be how much should a good designer cost.
As long as you are happy with the work the designer does and the designer is happy with how much (s)he is paid why should that have any relation to the cost your client is being charged?