Consider the basic model shown in section 3.1 , but assume the social damage function is linear such that D(E)=d×E for d>0.

(a) Show that for an efficient amount of pollution, both individual firm and total emissions decrease with an increase in d.

(b) Derive the comparative static relationships between d and the following potential policy variables: emission tax rate, total amount of issued permits, subsidy rate.
Suppose now we have a convex damage function D(E,d) where D_E(•)>0, D_EE(•)>0, D_d(•)>0, and D_Ed(•)>0. That is, both total damage and marginal damage increase as d increases.

(c) Derive the relationship between d and the variables listed in part (b).

Data from section 3.1

Consider an area where a number of polluting firms and affected households are located. For concreteness, suppose the firms are coal- burning electrical plants emitting sulfur dioxide that impacts people living in the area. The firms are output price takers, selling electricity on the national market. People living in the area buy electricity on the national market and therefore do not rely exclusively on the local firms for electricity production. Each of J firms produces a level of emissions ej, and