Does the ratio of Laplace transforms of powers of a function identify the function?

Abstract We study the following question: if f is a nonzero measurable function on [ 0 , ∞ ) and m and n distinct nonnegative integers, does the ratio f n ˆ / f m ˆ of the Laplace transforms of the powers f n and f m of f uniquely determine f? The answer is yes if one of m , n is zero, by the inverse Laplace transform. Under some assumptions on the smoothness of f we show that the answer in the general case is also affirmative. The question arose from a problem in economics, specifically in auction theory where f is the cumulative distribution function of a certain random variable. This is also discussed in the paper.