For problems like global climate change that may involve global extinction, we must not just focus, as most economic analysts do, on the trading-off of current consumption (current mitigation investment reduces consumption) against future consumption (less need for future investment), but also consider the effects of mitigation investment in reducing the extinction probabilities. Future utility/welfare values should only be discounted at the uncertainty of their realization, making these values even in the far future important as this discount rate should be very low (0.01 per cent per annum or less). Immediate and strong actions of environmental protection including greenhouse gas reduction may thus be justified despite high consumption discount rates (about 5 per cent). Unexpectedly, an increase in the extinction probabilities may increase or decrease our willingness to reduce them; precise conditions are given. The related intuition that, the higher the probability of destruction of your house by fire, the less willing you will be in investing on things like interior decoration that does not change the probability of destruction, but the higher your willingness to pave a fire clearance that does reduce the probability of destruction, is examined.