Two plants are emitting a uniformly mixed pollutant called gunk into the beautiful sky over Tourist Town. The city government decides it can tolerate total emission of no more than 100 kg of gunk per day. At a level of 25 the plant G has marginal reduction costs of 100 - 4x and is currently polluting while plant K has marginal reduction costs of 150 - y and currently pollutes at a level of 150.
Q: Assume the authorities are considering either a tradable emission permit system, in which they give half the permits to each firm, or a tax system. If both systems work perfectly, discuss how much will the firms have to pay, in total, for pollution reduction under the two schemes? Could this explain why Tourist Town would be more likely to adopt a permit giveaway system?