The biggest external cost with machine washing is the hot water, but most detergents now are optimised for cold / room temperature wash.
The biggest actual cost for hand washing is the time consumed - you may call it opportunity cost. Historically the societal benefits of the shift from having someone (typically 'the woman' of the household) spending 10-20 hours a week attending to laundry, to requiring perhaps a half hour of someone's time, have been better studied.
Yes, I'm aware top loaders are still popular in the US, which may change the economics markedly.
It's cheaper in regard to what alternatives are sacrificed for each unit of clothing cleaned.
And of course there might be some sort of marginal environmental or other cost between the two as well.
I'm finding it amusing that so many people are focusing on the time portion and somehow managing to downplay it.
Even the energy costs are lower, considering how ridiculously little energy modern washing machines take.
I may be the only one in the thread who has washed clothes by hand (Granny made me acquire the skill), so let me say doing it correctly is a real upper body workout. A family load of laundry would take many hours and an athlete to do it in a day. Each piece must be done individually. Hanging it all up to dry requires a lot of space too.
> these appliances ... free up an entire person to go work
And they help free up the other eight or nine hours that you don't spend working or sleeping during a day as well. They also help to free up many hours on the weekend.
The time savings and improvement to quality of life is immense. And we're just beginning. We're only fully 50-60 years into the appliance revolution.
I think the introduction of running water, especially hot water, into homes, and washing machines around the same time, made a substantial improvement in terms of availability of ~half the potential working population.
> Rosling, however, believes washing machines foster education and democracy. He doesn't think the "haves" should tell the "have-nots" how to spend their days either.
http://www.businessinsider.com/hans-rosling-washing-machine-...
I see where you're coming from, though, and realize that's not what you meant. For places where kids can go to school and a parent is not spending tons of time washing clothes instead of spending it with the children, the argument runs differently.
But even not counting for how much time it actually costs. The energy costs are lower for a washing machine. The detergent necessary is tiny. The health risks are minimized. (Let that one sink in. Touching dirty laundry is a great way to get sick. Especially if you are scrubbing it to wash away the soiled parts.)
So no, it is more than just a great theoretical argument. And the idea that folks are being wasteful by having a laundry machine is... well, astonishing to me.