THE EFFECT OF market size on the concentration of output has long been of interest to students of industrial organization. It is generally thought that increases in the size of market reduce concentration. Unfortunately, the supporting evidence for this view is limited and hardly persuasive. On the one hand cross-sectional studies often show the combined market share of output of the four leading firms to be smaller in industries within the larger markets.2 Whether this inverse relation can be explained on economic or statistical grounds has not been discussed. Larger markets typically have a large number of firms. (The appropriate definition of market is discussed below.) The inverse relation between concentration and the number of firms in an industry could arise if random samples were selected from a common size distribution of firms. The larger the sample size, the lower the concentration ratio. The presence of an inverse relation may constitute verification of a hypothesis of economic theory or may be consistent with random sampling hypothesis.3 The explanatory value of the random sampling hypothesis is evaluated in Section 3 of the paper. Studies of changes in concentration over time often fail to show an inverse relationship between changes in concentration and changes in the size of market.4 The stability of U.S. concentration ratios over time has been noted