Yikes, those recommendations. Pay these people to do your chores for you because they charge less per hour than we claim you value your time. Talk about presenting a false dichotomy. Those aren't the only choices. Where's the comparison of cost to just doing your chores, investing your hard earned pay, and making returns without work in the future?
Regardless of the common mantra on MMM, the suggested approach is the rational one with one caveat: that a marginal hour worked at your current job produces more income. For salaried employees, this is not necessarily true (though it's hard to know since the "overtime" bonus of harder work might come in the form of eventual raises).
If you state that you value saving an hour of time working around the house at $30 and you make $40/hour at work, it's better to work an extra 45 minutes and hire someone to do the house chore with the extra $30 you make. There is no impact to net savings as a result and "doing your chores" is 33% less efficient than doing more of your day-job and hiring someone to do the chores. If your answers do not come out reasonably like this maybe you had low consistency.
You misunderstand my protests. Simply work more and buy time now or don't work more is a false dichotomy. If you look at it as a single choice like they present it, sure, your example is rational. But there are really two decisions in play in the single choice they present. Should you work extra hours? Should you pay somebody to free up hours used by chores now?
Let's just go with yes to working more, since your example presents at least one thing where there is more value to working extra than not.
Having worked an extra hour, there are many things you can do with that money beyond paying somebody to do your chores. So let's answer the second question. If you can get more value out of something other than paying somebody to do your chores right now, it isn't rational to pay somebody to do your chores right now.
You have the option to invest that money. At the $40 and $30 values of work and chores in your example and fairly standard assumptions about investments, a fund to cover chores forever can be built in about 13 years by doing one extra hour of work each week and investing it, rather than spending it to free up chore time. As long as you're far enough from dying, don't discount future time too heavily, and aren't super risk averse, this is a better means to acquire time than the option presented.
Allowing that, then no, it isn't rational to hire somebody now. Suppose you're a 30 year old living to the average 79, you work 13*52*2 = 1352 hours to get your chores done for the rest of your life while investing versus 49*52*.75 = 1911 hours to get your chores done for life just working extra. Assuming average life expectancy, you'd have to be at least 45 for it not to be better.
And investing has other upsides. You aren't working extra or doing chores in your older years. There's probably going to be something left over to pass on. You can use that capital for other things if an even better generator of value presents itself.
But you can work that extra hour to have more to invest regardless of if you work
another 45 minutes to save an hour's worth of chores at home; here are some of the options assuming a baseline 40 hour work week, $40/hr wage, $30/hr to hire someone to do housework on your behalf (recall the underlying assumption that each type of work is equivalently pleasant to you):
(1) work 40 hours at your job + work 1 hour on a chore at home = 41 hours worked, $0 extra invested
(2) work 40.75 hours at your job + work 0 hours on a chore at home (hire someone) = 40.75 hours worked, $0 extra invested
(3) work 41 hours at your job + work 1 hour on a chore at home = 42 hours worked, $40 extra invested
(4) work 41.75 hours at your job + work 0 hours on a chore at home (hire someone) = 41.75 hours worked, $40 extra invested
Comparing (1) and (2) is what I initially suggested: you are getting the same thing but for 15 minutes less of your time. But if you want to invest more, it makes sense to work an extra hour in
both (3) and (4). In (4) you still get 15 minute saved to complete the chore
and still can invest $40 extra. This shouldn't be surprising since it is the reason why division of labor and specialization create considerable economic gains.
Naturally, this logic fails if working a marginal extra 45 minutes at your job is qualitatively much worse than spending an hour at home on a chore (but if a marginal 45 minutes at your job is so bad, it might be rational to
reduce the hours worked from 40 and spend more time optimizing household spend).