Quick answer,
Yes for some, no for others.
Not so quick answer,
It depends on the book, the promotion, the price, and how many others are doing the same thing.
In all honesty, if you just drop the book price and do no advertising the answer is more than likely no.
You might get a few extra sales. Though since you said it is a self help book and New Year's is typically resolution day, you might have some luck.
Do you have an advertising plan?
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