The establishment of an asking, or ceiling, price from which reductions can be bargained is a common selling practice. For a monopolist seller of a single object, this article characterizes the best such ceiling price and shows that its use is optimal among all incentive-compatible mechanisms in a class of situations characterized by customers (1) who arrive one at a time and so do not compete with other directly and (2) who learn their idiosyncratic willingnesses to pay only by incurring idiosyncratic inspection costs.
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Chen et al. (1996) studied this question.