rincewind - not sure I understand your point.
"If everybody had to study for 10 years to bake a cake, cakes would become more expensive"
This is not exactly true unless the demand for cakes is perfectly inelastic, but I will admit that if the cost of becoming a cake supplier increases, total supply should decrease (all else equal), the result will be a higher equilibrium price. The point I was trying to make with the cake metaphor is simply that the price of x is not determined by the cost of the inputs, but by the value of the output.
The part of your comment that I don't understand is the bit about the government support. I don't really see how that relates to the cake metaphor. Am I missing something?
Also, you're describing a situation that can logically only arise in the context of market failure (this is interesting because I alluded to this in my first comment).
If people aren't willing to pay the higher cost of the cake because the benefit doesn't justify the cost, why would it make sense for the government to use tax money to intervene?
Short answer: it doesn't.
This only makes sense if the total benefit of cake > the cost of the cake, but there was some market inefficiency in the way.
You could certainly argue that this is the case with scientific research. In fact I personally would agree with this argument. But it has nothing to do with how long the scientist spent in school and what they "deserve" to earn based on that education.
I really want some cake now.