Assume the marginal savings from emissions for an industry are given by \(M S(e)=\) \(30-e\) and that the marginal damage from emissions is given by \(M D(e)=e\). Suppose that the tax interaction effect corresponds to a welfare loss of \(\$ 10\) per ton of emissions reduced. Suppose further that the cost of collecting revenue from labor taxes is \(\$ 1.40\) for every dollar collected ( \(\$ 1\) for revenue plus \(40 \leftarrow\) deadweight loss).

a. Plot marginal damage and marginal savings from emissions for this industry. What is the efficient level of an emissions tax, ignoring the revenue recycling and tax interaction effects? Derive this result graphically.

b. Now take into account the tax interaction affect. What is the efficient number of marketable permits, if the permits are initially distributed for free? Derive this result graphically.

c. If the permits in part (b) were initially auctioned, what would be the total surplus and what would be the magnitude of the tax interaction effect, the revenue recycling effect, and the Pigovian effect.