We characterize the necessary and sufficient conditions of profit maximization for aggregate market behavior when participants on the supply side vary and individual firm supply is unobservable. Our approach is non-parametric. We use the conditions on market behavior to examine whether the United States cement industry could have been profit maximizing between 1993 and 1998. We find that the U.S. cement industry always rejects profit maximization when firms are required to make weakly positive profits. We also provide a measure of necessary profit loss to measure how far the industry is from profit maximization. We find errors from profit maximization that are as large as $755.1 million.