1. Poorly defined property rights result in 'The Tragedy of the Commons', whereby community-pool resources, both renewable and non-renewable, and harvested at a rate unsustainable w/ regards to the goal of intergenerational equity. Private cost fails to consider the externalities of poor intergenerational equity, as well as the decreasing supply of a particular resource raising prices.
2. Pollutive production, i.e. the emission of CO2 by big business. The emission of CO2 harms the environment both through global warming and acid rain, amongst other things. Cost borne by society, rather than the producer, except in the case where a tax has 'internalised the externality'.