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Edgeworth's taxation paradox states that a unit tax can decrease the market price of a good. This paper presents a new version of the paradox in which a tax reduces price--and increases industry output--because it attracts additional entry into the market. It is particularly striking that the demand conditions under which cost pass-through exceeds 100% for a fixed number of firms are also those for which pass-through can turn negative with endogenous entry. A novel application to the environment shows that a Pigouvian emissions tax can lead to an increase in industry emissions. A basic principle of environmental policy therefore fails under the conditions of the paradox. Copyright 2014 Oxford University Press 2013 All rights reserved, Oxford University Press.