First, not all placebos are inert - for example, "active placebos" contain substances which cause side effects. In some drug trials, active placebos are chosen intentionally for their effects, because drug effects can unblind the test. Active placebos tend to be more effective than inert placebos.
Second, placebos work even if the patient is told it's just a placebo - the placebo effect occurs even if the patient knows "nothing is being done".
The placebo effect is NOT "the subject believing something is being done."
The term "placebo" is from Latin, it means "to please", and the "placebo effect" was given that name because the patient seems to be unconsciously responding to the doctors expectations "to please" the doctor.
This works both ways - if the patient is given negative expectations, the patients condition may worsen in response - this is sometimes called the nocebo effect, although it is still a placebo effect.
It's a real effect, and even affects people who don't believe it such as yourself.