A local government is considering whether to impose a tax on a factory that emits pollution. The factory's marginal private cost of production is $50 per unit, while the marginal social cost, considering the pollution, is $70 per unit. The factory produces 100 units per day. If the government seeks to achieve social optimality, what is the key principle they must apply in their decision-making process regarding this tax?

The key principle the government must apply in deciding on the tax is that the tax should equal the difference between the marginal social cost and the marginal private cost. In this case, the marginal social cost of $70 includes the harmful effects of pollution, while the factory only considers its private cost of $50. This means the government should impose a tax of $20 per unit, which is the gap between these two costs. By doing this, the factory would be incentivized to reduce its output or find cleaner production methods, aligning its production with the social cost of pollution. For example, if the factory produces fewer units due to the tax, it helps lower overall pollution, achieving a better outcome for society.