This thesis is based on the theory of the Green Paradox by Hans-Werner Sinn and a paper by Frederick van der Ploeg. The investigations are about a monopolistic owner of oil reserves and his response to a green backstop technology, which becomes available at some uncertain point. An isoelastic demand function and an initial exploration investment instead of variable extraction costs are assumed. The model is extended by another exploration investment at the breakthrough and variable costs of renewables. Due to the uncertain timing of the breakthrough, the depletion rates are inefficiently high and the exploration investments are reduced. An increasing tax rate or subsidization of green R&D speeds up oil depletion and lowers the exploration investments. The latter effect can reverse the Green Paradox. If the second investment is - compared to the first investment - big enough, the speed of oil depletion can be reduced. The reduced costs of renewables speeds up the oil depletion.