I calculated myself in excel. Even when I'm not so good at making formulas as Caliban, I tried, and here are the results. I took into account decimals too, so the values changed a bit from what he said.
And here is the formula I used, if anyone wants to correct me: =(uncut value* %Improvement)-uncut value
I found out that some cut are simply not worth their cost, and marked them in red. It is better to just use the one above them, wich is cheaper and gives a better profit for the same rocks. We will be still using emerald cut and low value gems to unlock the others, and the break even value I got was the same as the ones Caliban found, so I did not add them.
I hope this helps a little to make better profits for the greedy sims out there.
Type_________Gem Value Cut*
Emerald________ <$40
Oval__________$42-$60
Pear Plumbbob______$61-$83
Marquis Crystal Ball____$84-$166
Brilliant_______$167-$500
Heart-Shaped__$501+