Abstract: We study the following problem. Let m, n be two distinct nonnegative integers and f a nonzero measurable function on [0,∞) of at most exponential order. Let H_(n,m):=L(f^n)/L(f^m) be the ratio of the Laplace transforms of f^n and f^m. Does knowledge of the function H_(n,m) uniquely specify the function f? This is a generalization of Lerch's theorem (Laplace transform specifies the function). Under some rather strong assumptions on f we show that the answer is affirmative. This problem finds applications in auction theory where one is interested in identifying the distribution of bids based on the distribution of the highest ones. This is a joint work with Takis Konstantopoulos.