I suppose that would make sense if the government was solving a coordination problem?

E.g., no manufacturer will install Oliver's Optimizer, which promises a lifetime 10% savings in energy use, because it would force them to shut down operations for a month while the optimizer is installed, and put them at a disadvantage compared to other manufacturers.

By requiring the Optimizer (or equivalent) as a licensing requirement for factory operation, all manufacturers share the same burden, and thus suffer no relative disadvantage.

Is that the general idea? I'd be worried about regulatory capture in this case -- e.g., Oliver lobbying to force the market to install his Optimizer -- but that's an entirely different discussion. :)

I'd say, yes. You've correctly noticed in this subthread that government regulation is a solution to coordination problems. All kinds of situations that pattern-match to "it would be better if everyone were doing X, but X comes with some up-front costs, so whoever tries doing X first gets outcompeted by the rest" are unsolvable by the market (especially when coupled with "if everyone else is doing X, stopping doing X will save you money"); the important role of a government is then to force everyone to start doing that X at the same time and prevent them from backtracking.

To the extent you can imagine the market as a gradient descent optimization, coordination problems are where it gets stuck in a local minimum. A government intervention usually makes that local minimum stop being a minimum, thus giving the market a necessary shove to continue its gradient descent elsewhere.

> To the extent you can imagine the market as a gradient descent optimization, coordination problems are where it gets stuck in a local minimum.

I think this is a very appropriate analogy.

A thought: the cost function that the market minimizes is only a proxy for the various cost functions that we (humans) actually care about. I wonder how much (if any) “government inefficiency” is due to the mismatch between the market cost function and these other cost functions.

I don't know about inefficiency within the government, but I think most of regulating of markets happens because of it. As you've noticed, market's cost function is only an approximation of what we care about in aggregate. Regulation adds constraints and tweaks coefficients to keep the two goal functions aligned as much as possible. Which is hard, not least because we can't fully articulate what we care about, either individually or in aggregate.