Well, you may think that there could be one happy ending to a clogged bath tub story: An unclogged tub.
You are half right:
I finally decided to call a plumber. just as I was making out my mind as to who call, I got in the mail a renewal notice from a company. It said "Dear Policyholder, your one year home warranty plan is due to expire."
I forgot all about this policy that the previous owner bought for me!
I call them up and told them that my bathtub is clogged. "No problem. Will send a plumber over there. Just give him $25."
For $25, a plummer came and took care of the matter.
It turned out that I did not have a drum trap. His hand-held snake, forcefully plunged and rotated, did the trick.
Downside of the story: no more daily visits to the gym to take showers. Before taking a shower, I was of course exercising. With the bathtub working now, I will probably not go to the gym as often!
Once again, thanks for all of you who took the time to write and advise me on the problem.