In my opinion its thrust damage should be significantly higher. (even at a cost of slashing damage)
Lets compare a rapier with a good cavalry wallon broadsword.
Broadsword does 6 more slashing damage and 1 more thrust damage, which counts as piercing, so has a bonus against armors. It is only 5 units(cm?) shorter and 3 points slower. It is also 66 gold cheaper. It is 0.3 units(kg?) heavier, but it doesn't change much.
Balance-wise it doesn't add up if you ask me.
In my opinion you could keep the price but make it stronger.