  We study the following question: if $f$ is a nonzero measurable function on
$[0,\infty)$ and $m$ and $n$ distinct nonnegative integers, does the ratio
$\widehat{f^n}/\widehat{f^m}$ 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.
