Consider the partial model of Chapter 3 with an aggregate abatement cost function C(E satisfying the usual properties. The regulator charges an emission tax. Assume there exists a marginal cost of public funds denoted by λ, and that the regulator’s objective function is SC(E)=C(E)+D(E) −λτE, where τ is the tax rate.

(a) Determine the optimal tax rate and show that it can be smaller or larger than the marginal damage, depending on the elasticity of the marginal abatement cost function. Draw two figures to illustrate the different cases.

(b) Interpret the optimality formula for the tax rate. How can you decompose it using the concepts studied in this chapter? Which effect is missing?