Yes, placebos work because the power is in the expectation or belief in the suggestion and the power of the mind. Doctors use them more often than people think. The body is a self healer in lots of cases. The placebo helps the person have faith until the healing is complete.
Sri T, thanks for answering. Yes, you are absolutely right. I'm very surprised that placebos actually work (in some conditions). Apparently we have a healer built in our brain (or body) and we aren't even aware of it.
When I worked in the pharmacy we serviced a nursing home. We dispensed many placebos. Corn starch was added to an empty capsule, and dispensed one to two times a day. Yes it helped the woman, because she believed it would. That is why many healers recommend a good mind set, it will help in any condition. "all things are possible, if you only believe". A negative mindset will only delay healing.