Often the problem will appear to be a pressure issue when it comes to volume or flow issue. A restriction in a line or just having a long line or under sized line could be the problem. There are many considerations; do you have enough pressure at your mains? Do you have an old furred up pipe work, perhaps lead or galv? Is your main stop open fully?
If you install a pressure gauge, you can check pressure. It should be above about 35 PSI. 35 PSI would be on the low side, but should be ok. Look at the
http://www.milwaukeeplumbers123.com then look at it when the water is on full in the bathtub. If the pressure is ok until you turn on the water than it is a flow problem.