I've pondered this before and this post has made me ponder it again. I like the addition of 'valuing time'. Thank you.
I think the problem is treating this like there is a single answer. There is context every time you make the 'should I pay someone to do this for me?' question that will change it quite often.
An example...Should I pay someone to clean my place? Normally the answer is 'no', because my place is small and relatively easy to clean. And perhaps more importantly, I'm not going to work more either way so how much I make for an hour of work is irrelevant. Paying someone to do something for me when it just gives me another hour of Netflix that I probably won't enjoy that much is really silly.
But maybe I have a hot date coming and, for whatever reason, I don't have time to clean my place....then it might be worth it. Or maybe I'm sick so laying like a lump has more value than the average hour of TV.
I'm not sure there is an answer to 'what is my time worth' because it is relative to the options I have at that time.
This framing easily assumes that the time is simply lost. This can make sense but it can only not make sense. An alternative formulation is how much you value you spending time for your ends rather than somebody elses ends.
Some employers will make you go throught predictable experiences, some jobs might require to unpredictably do different things. In the case of unpredictably assuming it will be maximally wasteful might make sense. However a predictable job migth have intrinsic upsides in comparison to not being concious for the time being. Programming puzzles can be intellectually simulating, your job might involve meeting or dealing with people that can be socially simulating. Granted in your free time you can focus on activities that are optimsed for the direct gains (a video game is probably more fun and stimulating than a programming job).
Theorethically your job could also be of lower value than complete waste. If you work as a hitman the moral and psychological cost could be things that compare unfavourably to not existing for the time period. Maybe being too fluent in C# alienates you from humans speaking english? In this case accounting for only the time lost is not sufficient. In a way for every working hour you also need to schedule a slot of recovery such as sleeping hours. Concievably having a longer time to unwind in entertainment from a long work day cuts out ability to maintain and improve your personal life.
The shape of the concept of paying for hours comes from the employer being able to justify your salary by comparing your work product provided to the compensation you get. The scaling effect comes from the assumtion that if a thing can be done once in a time period then in a double time period in can be done twice. However YOLO so you should probably think how the work fits in your lifes whole. What things you can or can not do if you do or do not do the work?
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Not all hours are equal. Is that an hour on a boring day, or during Less Wrong meetup?
Even with perfect flexibility of selling your time, the more you work, the more tired you get. And the less free time you have, the more you value it.
And it's usually not just about "time" but also about how much you like or dislike the work. I could outsource cooking, but I like to cook. Should I trade one hour of cooking for one hour of something I hate, only to make extra $10? I am not a money maximizer.
You are rarely literally selling your "time" anyway; it is usually a combination of time and work, isn't it? (Though there are a few jobs where most of the time you are paid for being there.)
Calculating "value of time" makes most sense when you compare two business opportunities against each other, or two ways of saving your time against each other. If one customer pays you twice as much per hour as the other one, and the work is comparable... If two gadgets cost about the same, but one of them saves you five minutes each day, and the other saves five minutes once a month...
How much is your time worth? $5/hr? $10? $30? $100? $1,000?
Whenever I ask myself that question, I notice that I am confused. Suppose you are some sort of consultant where you can sign on to some website and choose to work 1 hour and make $100 whenever you want. In that case, I can see why it'd make sense to say that your time is worth $100/hr. Instead of spending one hour cleaning your home, it would make more sense to do your consulting for one hour, make $100, hire a cleaning person to do it for $40, get your house cleaned, and have $60 left over.
But most people don't have that option. Most people don't really have any option to work more hours and make more money. And even if you are a freelancer or a consultant, gigs take time to find and are usually commitments on the order of months, not hours. So then, the above logic doesn't apply.
So maybe the question just needs to be reworded. Instead of "how much is your time worth", "how much do you choose to value your time".
Do you value your time at $1/hr? No. I think most people would pay $1 to gain one hour of extra time. Do you value it at $1,000/hr? No, I think most people would trade one hour for $1,000. So $1/hr is a lower bound and $1,000/hr is an upper bound. Continue to ask such questions and there'll be an answer. Or at least a revealed preference (hypothetically).
Then how do you decide how much to choose to value your time? I guess it depends on how much money you have. If you're tight on cash, you wouldn't want to use up your limited money to purchase more time, because you have bills to pay, for instance. But if you have a lot of disposable income, trading that money for time might be something that you want to do. Still, with that said, I don't feel like I have a good idea of how much I should value my own time, as a programmer in a normal programming job. I could see anywhere from $10/hr to $100/hr, and perhaps even outside of that range.