The aim of this paper is to examine the impacts of a global carbon tax on fossil fuel markets. In particular, the effect on the Norwegian, as well as the global, petroleum wealth is studied. Most empirical models of fossil fuel markets either use an exogenous price path, or model the supply side as being independent of future expectations. Hence, they are not able to test how the exhaustibility feature of fossil fuels affects the sharing of the tax burden between producers and consumers. We study a simple, dynamic model of a competitive fossil fuel market, and we first derive some general theoretical results regarding how a carbon tax may affect the producer and consumer prices. Then, simulations of the global oil market indicate that a fixed carbon tax of e.g. $10/barrel of oil may reduce the petroleum wealth of the average oil producer by 33-42%. The Norwegian petroleum wealth may decrease more than this, by 47-68%. The latter reduction may correspond to a yearly income loss of about 3% of Norwegian GDP. However, the figures should only be considered as very rough estimates, because of the simplistic nature of the model. Keywords: Carbon Taxes, Exhaustible Resources, Petroleum Wealth