Question

why is lump sum compensation for an externailty nondistortionary?

Answer 1

It doesn't have anything to do with externalities. I would like to say that you can use the same argument as with taxes. Taxes that are percentages of your wage (income tax) will be distortionary because they will change your incentives/decision to work, whereas a lump sum tax won't change your labour supply (hours worked) because you will pay it regardless of the number of hours worked. Put differently, they do not change your marginal decision to work an extra hour or not. Similarly, a lump sum transfer/compensation that does not change your decision between working that last marginal hour or not will not be distortionary. In more technical terms it only has an income effect, but no substitution effect as it doesn't make working relatively more expensive in terms of its opportunity cost of leisure. Hence it only makes you richer/poorer (income effect) but doesn't change the relative price of goods. You can apply the same logic to production. The lump-sum compensation does not alter a MR=MC production condition. Hope that helps