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This paper evaluates the relevance of market structure on the short-run effectiveness of carbon taxation by utilizing the introduction of Australia's carbon tax in 2012, its removal in 2014, and between these dates a change in market structure in Western Australia where the dominant generator became vertically integrated with the market retailer. The market power of the dominant firm decreased with the introduction of the carbon tax, reducing its profit incentive to lower its coal based generation in some demand conditions and increasing equilibrium carbon emissions. However, when vertically integrated, the dominant firm behaved more competitively and the carbon tax reduced equilibrium carbon emissions. The results indicate that the immediate short-run impacts from carbon taxation can be small and perhaps even induce emissions in imperfect markets. However, these short-run results have limited long-run implications because it is expected that a carbon price would result in incentives for electricity generators to invest in a less emissions-intensive capital stock. Rather, these short-run findings highlight the importance for an emissions tax to cover a broad base of industries and be long lasting in order to achieve substantive reductions in carbon emissions.