Assume that the strict liability rule holds and a potentially polluting firm is risk averse. Define ŷ implicitly by ŷ= a^sl _s (ŷ) + D, where a^sl _s (ŷ) is the solution to the solvent firm’s problem and ŷ divides wealth into (privately) optimal solvent and insolvent regimes. Characterize the optimal choice for care as a function of wealth. More precisely, show that there exist wealth levels y0, y1, and y2 with y0

(a) the firm engages in no care so that a^sl(y)=0 for y≤y⁰, for some y⁰≥0.
More precisely, if ρ(0)=1, then a^sl(0)=0 and a^sl(y)>0 for y>0. If ρ(0)<1, then y≤y⁰;

(b) a^sl(y) is increasing in y for y⁰2 and:

(i) a^sl(y)* for y1 (ii) a^sl(y)=a^* for y=y¹, and if the firm is risk neutral, also for y>y².  If the firm owner is risk averse, then for y>y2 the solution a^sl_s(y) can be smaller or larger than the social optimum

(iii) a^sl(y)>a^* for y¹2;

(c) the cutoff level of wealth ŷ= a^sl _s (ŷ) + D dividing private solvency and insolvency can be larger or smaller than the socially optimal division.