Consider the model as in exercise 10.4, but assume the polluting firm has monopoly power on the output market. For this we assume the monopolist faces a downward sloping inverse demand function P(x), resulting in a concave revenue function. Show that the monopolist chooses a sub-optimal level of care.

Data from exercise 10.4

Consider a competitive firm engaging in risky activity, where damage is a function of output level x. The cost of production is C(x), which is increasing and convex in x. The damage function is D(x) and the cost of care is simply a, as before.