Assume there is a single firm producing the output with a general cost function C(x,e,). (a) Set

Assume there is a single firm producing the output with a general cost function C(x,e,κ).

(a) Set up some reasonable assumptions on C(x,e,κ).

(b) Determine the socially optimal allocation, given a convex (linear) damage function.

(c) What instrument(s) does the regulator need to induce the firstbest allocation?

(d) Derive a rule for the second-best optimal tax when the regulator only has an emission tax as her instrument.

(e) Now assume C(x,e,κ)=(ax−be−κ)²/2b+cx²/2, and repeat (a)
through

(d) for the specific functional form.