Ok I found a savegame from a quick speed game that I did a few weeks ago, so I can show you guys what the situation is.
^^^ Here is my Babylonian Empire at year 1986 AD. I have only 8 cities. I'm about to start teching electronics and at my current tech rate it will take 3 turns. As you can see, the empire is earning 758
per turn currently, and the cost of the tech is 1742
. Assuming my tech rate stays constant (which is close enough) for 3 turns, that means I waste 3*758-1742=532
over the course of 3 turns. So effectively I would make use of only 77% of the beakers that I
actually generate from my cities.
It looks like we might be able to manage to get the tech in 2 turns if we put some scientists to work. It's easy to work out that to get the tech in 2 turns one would need 871
per turn. Can we get that extra 113
necessary? Yes we can - it takes 13 scientists employed across 3 cities, as pictured in the next 3 screenshots.
(not really necessary to look at but included in case you're curious)
Here is the final beaker rate: 871
per turn and Electronics now takes 2 turns.
So what have we achieved? Let's work it out. If we run those 13 scientists for 3 turns, we will get the tech in two turns and then put 871
towards the
next tech. Effectively we earn 871*3=2613
over 3 turns. If we had not employed the scientists, we'd have gotten 1742
over 3 turns (and gotten the tech one turn slower as well, which may or may not be important).
The difference between those two amounts is 871
. So effectively, employing 13 scientists earnt us that many beakers over 3 turns, or 871/3 = 290
per turn. (Note there is an opportunity cost because those 13 citizens could have been doing something else, but we will see that this is more than worth the cost)
Compare this with the raw extra beakers that those 13 scientists contributed, which was 113
.
How much did we increase our overall beaker production by employing these 13 scientists?
In raw figures, as you saw, we went from 758 to 871
which is a 15% increase. This is the amount you should
expect your tech rate to improve by.
However taking into account the saved beakers, we went from 1742 to 2613
which is a 50% increase in beaker production. That is just enormous. To be clear, the effect of doing careful micro was the 35%, while the raw effect of the extra scientists was only 15%. You can see that the potential gain from such micro can be massive compared to the ordinary gameplay mechanisms for increasing your science rate (hiring more scientists).
This example is fairly typical in a quick speed game and when you have a decent tech rate. The silly thing is that the higher the tech rate the more this can be abused, because the larger the effect is of shaving a turn off the time to the next tech.
and perhaps a small amount less 
for a few turns, but you will instead waste (4*501-2000) = 4 
) solution. If you carry over only half the overflow beakers then people will still try to minimise the overflow to minimise wastage and basically end up in exactly the same routine they are in now. Let beakers carry over one for one and there is no longer any problem, except possibly some rebalancing of tech costs.
