Well that's what I'm trying to figure out; I'm a newbie and it's my first road bike so its a bit challenging but heres what happened

I accidentally stripped the bolt on my Tiagra 10 speed 4601 derailleur the shop replaced it with what I thought was a Tiagra 10 speed 4601 but it turned out to be a Tiagra 9 sped 4500. I find my low end and high end gearing is very weak and I have to switch into the big cog more often to get into gears that I was comfortable in at the small cog which is effecting my ride and performance.

The specs on the 9 speed 4500 are as follows;

Wide link design
• Total capacity: SS 31T, GS 37T

Specifications:
• Series TIAGRA
• Model No. RD-4500
• Pulley Cage: SS/GS
• Speeds: 9
• Max Front Difference 16T (SS)/22T(GS)
• Total Capacity 31T (SS)/37T(GS)
• Max Rear Sprocket: 27T
• Min. Rear Sprocket: 11T

What I'm wondering is if the above derailleur specs are even compatible with;

Crankset Shimano Tiagra
Chainrings 50/34
Front Derailleur Shimano Tiagra
Rear Derailleur Shimano Tiagra
Rear Cogs Shimano Tiagra, 10-speed: 12-30
Shifter: Shiamno Tiagra

If anyone could help me out with that I would greatly appreciate it because I'm just a noobie and I really want my bike working in tip top shape again.

Thanks in advance!