The Ryan - interesting. You’re suggesting (for those who may be bewildered by the language) that even if we’re at a equilibrium point of marginal costs = marginal benefits, there may be an even higher equilibrium further along the scale, if only we increase or decrease regulation enough.
You are of course correct, from an entirely function-theoretic point of view. However for the global maximum to not be the equilibrium point we would require at some point on the graph either:
[list=1]
[li]increased costs of regulation to result directly in an increase in utility; or[/li][li]increased benefits of regulation to directly decrease utility.[/li][/list=1]
This is arguably a contradiction, by definition of ‘benefits’ and ‘costs’. I find it hard to envisage a cost curve which is not a decreasing function of utility; similarly surely a benefit curve must be an increasing function of utility. In this case there can be only one equilibrium point.
However, since I hadn’t really considered this argument before I’m waiting for suggestions that I am wrong.
As for continuity - if the two curves are strictly decreasing and increasing respectively, I think that there can still only be one optimum regulation point, though there would not be a unique answer for how much utility it provides.
Hmm, although my degree was in mathematics, I’ve been a actuary (read economic statistician) for a few years and as such my theory on this is a little rusty. The above seems to make sense. Do you disagree?