This paper aims to test Sutton's "lower bounds" approach on the analysis of market concentration in a small open economy, Taiwan. Exporting, the important feature of a small open economy is also considered to investigate the role of foreign competition on market structure. Estimated by a stochastic frontier approach, the findings are in accordance with Sutton's predictions, whereby the lower bounds for high advertising and/or R&D-intensive industries are higher than those for low advertising and/or R&D-intensive industries in Taiwan. While, the lower bounds of concentrations for exporting intensive industries do not significantly from that of non-intensive industries. In addition, deviations from the lower bound are explained by industry characteristics.