The reality of practically anything will be more nebulous than the math.
The question is whether a precise language has the potential to describe some slice of the situation accurately. That is the case here.
I didn’t write my own first post in regular hyu-mon language (because that’s literally what the title requests), but every statement was fully in keeping with both the letter and spirit of the thread.
But the OP saw the term “positive externality” and concluded that there would be nothing of relevance in what followed. That’s an understandable mistake when the terminology might as well be written in Martian. It’s the natural result of pragmatic non-familiarity with an esoteric subject.
But this shit is solid, yo.
In this case – if we take what’s written in the OP seriously – then there is a clear possibility for the couple to arrange their household in a way that makes both of them happier.
This “theorem”, aha, actually holds quite generally. Comparative advantage is highly relevant even at the household level… especially if each person trusts the other.
This part is hardly nebulous at all.
If you had the opportunity to put another 10 hours a week in order to afford a place you’d prefer to live in, and were excited about the opportunity to make the transfer – and the other person was not at all opposed – then that is a clear improvement in situation. There is gain and no harm. The positive externality is a twist that makes it easier in a healthy household for the other party to reciprocate, and result in an even more desirable outcome for both members of the household.
That’s as clear as these things ever get.
You can always add complications. Maybe the promotion at work is more stressful than expected. Maybe the new house has annoying quirks in the living that were not apparent in the seeing. Maybe trust in the relationship itself breaks down. Maybe one person gets hit by a bus. There aren’t any certainties in life.
Nevertheless.
It remains generally solid that the person who wants something more should be the one who puts in most of the effort to get it. Or in the case of costs, it makes sense for the person for the lower cost to do the task. When our boy was born, who was the one who woke up every night (for more than a year!) to feed him? It was, quite naturally, the one who found it much easier to fall back asleep after the disruption.
Burdens like these are balanced in other ways. Each partner pulls the weight they can carry more easily, for the general benefit of both.
In most cases, I wouldn’t expect to see exactly equal hours on any single task from a happy and trusting couple.
Quite the opposite.
Hours worked is more observable than personal preference. If two people are carefully balancing observable effort to precisely match, then that’s often (not always, but often) because there are deeper questions of underlying motivation, and the balance in observable effort is how suspicion is allayed. That’s the sort of behavior you’d expect from college roommates, not life partners.
(There is mathematics for this, too.)
Efforts will tend to be asymmetrical in high-trust environments because talents and preferences are asymmetrical. In a relationship that is working, this will be because the other person is picking up slack along different dimensions… and both people feel that the burden carried in one place is fairly matched with the burden somewhere else.
But that’s not even what the OP (as plausibly interpreted) is about. The OP is straight win-win with asymmetrical efforts,