Normally I am a lurker (on a lot of forums) but I have gotten a lot of info here expecially from 2 many projects and I wanted to pay a little back to this forum.
I believe you are correct and need more airflow. Others have commented that you have to allow air to enter the room in order for the air to be exhuasted from the room. But not stated, is that your installation maybe restricting air flow on the discharge side too.
Most of the inexpensive residential bathroom exhaust fans are not made to discharge much air in the first place, and then it is through 3" to 4" plastic piping. If the contractor put too many elbows in the pipe you may not be able to overcome the friction loses and the result is reduced air flow. Three to four inch dia. pipe will not allow much airflow at the ESP (external static pressure) supplied by most cheap fans. Additionally something could be lodged in the discharge pipe, or at the discharge fitting.
If you have an attic over your bathroom then you could install your own exhasut air system with a ceiling grille, duct and fan supported from rafters. This will reduce noise (done right you won't even hear the fan) and you can size a fan to provide the flow you require.
If you don't have an attic search around for a more expensive replacement and get one with a high static (ESP) capacity. I agree 200 CFM would be a minium. As stated above 200 CFM is a lot to push through a 4" plastic pipe. If it is possible you might replace the 4" pipe with a 6" or 8" duct.
Do not discharge the fan exhaust into your attic. Make certain the discharge is not directly under an eave or rake or second story deck. If you use a discharge wall fiting with a backdraft damper be certain that it operates freely.
The suggestion of additional insullation is an interesting one but the best you could hope for with this is to slow down the rate condensation. You wouldn't be doing anything about removing it. This might help a little with an underperforming fan, say give the fan more time to exhaust the air. I would spend the money on a more powerful fan.
If you cool your house in the summer you can save money by removing the humidty through an exhaust fan rather than pay for the AC make condensate.
You might also research an electrical delay to the fan motor. When you shut off the bathroom fan, likely in concert with the bathroom light, set the delay device for an extra period of run time. Or put the fan on it's own switch and leave it on for a long time, like 1 hour or more.
David
