What is the value of a coffee or haircut? How many coffees is a haircut worth?
Right now, in your situation, would you rather have a coffee or a haircut?
Would you rather have 2 coffees or 1 haircut?
And so on. There are plenty of exercises to determine how you (personally) value things, and also the shape of your utility curve. That was one of the most interesting classes I ever took: decision and utility theories.
A lot of the work was understanding the impact of different personal (or institutional) utility curves, how to determine your own and how to maximise you return not in absolute terms, but in relative terms using your utility curve.
When you take in account non-linearity of utility curves, lotteries make sense, for example, since for most people the utility of $1 is far less than 1 millionth of the utility of a million dollars.
The same with insurance. Insurance always has a negative expected value in absolute terms, but when you take in account that U(-$1) << U(-$1M)/1M, they make sense, since your utility-adjusted expected return is positive. That's also why your insurance should always have the maximum possible deductible.
Insurance works because companies and people have different utility curves.
Can you expand on that? My intuition is telling me that $1 has exactly 1 millionth the utility of a million dollars. I must not understand.
Let's say that you a running a risk of, for whatever reason, having to pay $1M in any given year with a 1 in 1M probability.
Your expected outcome is -$1 per year, which isn't much. So if someone came and offered for you to pay $1 for year for that risk to go away, you'd be indifferent.
But utility isn't linear. Losing $1 wouldn't make a difference in your life, but having to pay $1M would most likely destroy your life financially, leading to significant hardship.
So the cost, to you, of -$1 isn't the same as [1/1M]*-$1M, the latter is much higher. With that in mind, if someone offered you to pay $1 to get rid of the risk, you'd most likely accept.
In a similar way, let's look at the positive side.
Let's say you're broke, you have $0, and I offer you $10 for 1h of your time. Would you accept? Most likely, yes.
Now imagine you had $1M in the bank. Would you still accept $10 for 1h of your time? Probably not. And if you had $10M in the bank, the odds of you accepting would be even smaller.
That's because marginal utility (of pretty much anything) has diminishing returns. The value of a thing to you is different if you have zero of it, or if you have plenty of it.
The result is that even if you think that rationally the value is all the same, it isn't, and you'll actually be valuing things differently. And there's nothing irrational in that.
In aggregate across a large population, however, a bottle of water has a fairly stable price.
Haircuts and coffee are also not commodities, there are quality factors involved so variable pricing based on location, supply/demand, and the like is expected.
Like if someone gave me 3 coffees I’d be good for the day, but 10 and I’d either be too wired to cut your hair well or drink 3 and watch the other 7 get cold and stale.