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Commune math
Nov. 9th, 2009 03:19 amEvery once in a while, I have thoughts about a planned community: Something like a commune, but accommodating friends (I hope) of vastly different incomes. Just now, I thought of using a sort of hyperbolic rent/work scheme. The idea is that members contribute both work and money to the commune (thereby covering basic needs: Shelter, food, security, a reasonable amount of utilities, health care as needed and possible), and can choose to do less work if they contribute more money (or vice versa), but *not at a fixed rate of exchange*. (Work would presumably be a mixture of skilled work and rotating grunt work, though I would not attempt to draw a precise line between the two.)
My first attempt at a formula is this: (dollars/week + 50) * (hours/week + 5) = 2250
(The "2250" could be adjusted as needed to account for inflation and the financial needs of the community.)
Each week, for example, you could: Work 5 hours and pay $175; work 10 hours and pay $100; work 15 hours and pay $62.50; work 20 hours and pay $40. If you really want to, you could earn a free ticket by working 40 hours a week, or pay $400 and do no work, but the hyperbolic nature of the curve discourages either of these options. (More on this below.)
There are a couple of ways to look at this. You could see the rent as kind of a tax: Wealthier people will likely pay more and work less. But it would be a voluntary tax, as they could always opt to work as much as everyone else, and keep their money. Meanwhile, those who can't find jobs won't starve -- as long as the commune has enough income from others (or from the fruits of their labor).
Or, as I do, you could see this curve as an opportunity for each person to find a niche tailored to the monetary value of their time. If your figure your time is worth about $13/hour, you could work 8 hours and pay $123.08 per week (because working an hour less than that would cost an extra $14.42, and working an hour more would save only $12.37). If you work a minimum wage ($7.25/hour) job, you could most efficiently work 13 hours at the commune and pay $75 per week from your job earnings. If you hate that job so much that you'd gladly donate two hours at the commune to save yourself one hour of customer service hell, then work 20 hours and pay only $40 per week.
No matter where you are in the curve (except at the ends), you're surrounded by people putting more work into the community than you are (and who are saving less money per hour thereby than you are) and people who are putting more money into the community than you would comfortably be able to. And yet you gain all the benefits of both.* It's a situation made of win.
If you have any income, then you probably want to avoid the "free" 40-hour option -- that 40th hour saves you only $1.14 in rent -- unless you (laudably) enjoy volunteering your work.
The low end of the scale is very steep: The difference between working working 2 hours and not working at all is $128.57. This is to encourage people to participate in the community, even if only to a small extent, so that there's an emotional investment in it. You're less likely to litter if you've had to tidy up the grounds once or twice, for example.
Of course, there are all kinds of adjustments available: A surcharge for nicer housing. Reduced work expectation on students, the elderly and disabled. Increased value to donated work that requires an expensive education (such as medical).
(BTW, rent would be calculated by *average* weekly hours over a long period, so that you don't get shafted by a varied schedule. I'm not trying to be mean here!)
* Just to show that this "benefit" from those around you is not just rhetoric: Consider you, your yuppie friend Alice, your bohemian friend Bob and your impoverished friend Carol. Alice works 5 hours and pays $175. You work 8 hours and pay $123.08. Bob works 12 hours and pays $82.35. Carol works 17 hours and pays $52.27. Alice and Bob work an average of 8.5 hours, and pay an average of $128.68. Hence, on average they work more than you do (by half an hour) *and* pay more than you do (by $5.60). But that benefit is not just at your point on the curve: Bob gets the same benefit from you and Carol, who average half an hour more work than he does, and $5.33 more than he pays.
Why this works: Since each person can choose their point of maximum efficiency on the curve, everyone else on the curve is, from their perspective, contributing less efficiently -- that is, everyone else is contributing *more*.
(Math people: There's no particular need for it to be a hyperbolic curve. I just wanted something smooth and simple, with a negative slope, a positive second derivative, and a steep start. I'd certainly be open to other ideas, if you care to make a case for them.)
(Gratuitous link: Sinbad comic. It starts out okay, and becomes hilarious.)
My first attempt at a formula is this: (dollars/week + 50) * (hours/week + 5) = 2250
(The "2250" could be adjusted as needed to account for inflation and the financial needs of the community.)
Each week, for example, you could: Work 5 hours and pay $175; work 10 hours and pay $100; work 15 hours and pay $62.50; work 20 hours and pay $40. If you really want to, you could earn a free ticket by working 40 hours a week, or pay $400 and do no work, but the hyperbolic nature of the curve discourages either of these options. (More on this below.)
There are a couple of ways to look at this. You could see the rent as kind of a tax: Wealthier people will likely pay more and work less. But it would be a voluntary tax, as they could always opt to work as much as everyone else, and keep their money. Meanwhile, those who can't find jobs won't starve -- as long as the commune has enough income from others (or from the fruits of their labor).
Or, as I do, you could see this curve as an opportunity for each person to find a niche tailored to the monetary value of their time. If your figure your time is worth about $13/hour, you could work 8 hours and pay $123.08 per week (because working an hour less than that would cost an extra $14.42, and working an hour more would save only $12.37). If you work a minimum wage ($7.25/hour) job, you could most efficiently work 13 hours at the commune and pay $75 per week from your job earnings. If you hate that job so much that you'd gladly donate two hours at the commune to save yourself one hour of customer service hell, then work 20 hours and pay only $40 per week.
No matter where you are in the curve (except at the ends), you're surrounded by people putting more work into the community than you are (and who are saving less money per hour thereby than you are) and people who are putting more money into the community than you would comfortably be able to. And yet you gain all the benefits of both.* It's a situation made of win.
If you have any income, then you probably want to avoid the "free" 40-hour option -- that 40th hour saves you only $1.14 in rent -- unless you (laudably) enjoy volunteering your work.
The low end of the scale is very steep: The difference between working working 2 hours and not working at all is $128.57. This is to encourage people to participate in the community, even if only to a small extent, so that there's an emotional investment in it. You're less likely to litter if you've had to tidy up the grounds once or twice, for example.
Of course, there are all kinds of adjustments available: A surcharge for nicer housing. Reduced work expectation on students, the elderly and disabled. Increased value to donated work that requires an expensive education (such as medical).
(BTW, rent would be calculated by *average* weekly hours over a long period, so that you don't get shafted by a varied schedule. I'm not trying to be mean here!)
* Just to show that this "benefit" from those around you is not just rhetoric: Consider you, your yuppie friend Alice, your bohemian friend Bob and your impoverished friend Carol. Alice works 5 hours and pays $175. You work 8 hours and pay $123.08. Bob works 12 hours and pays $82.35. Carol works 17 hours and pays $52.27. Alice and Bob work an average of 8.5 hours, and pay an average of $128.68. Hence, on average they work more than you do (by half an hour) *and* pay more than you do (by $5.60). But that benefit is not just at your point on the curve: Bob gets the same benefit from you and Carol, who average half an hour more work than he does, and $5.33 more than he pays.
Why this works: Since each person can choose their point of maximum efficiency on the curve, everyone else on the curve is, from their perspective, contributing less efficiently -- that is, everyone else is contributing *more*.
(Math people: There's no particular need for it to be a hyperbolic curve. I just wanted something smooth and simple, with a negative slope, a positive second derivative, and a steep start. I'd certainly be open to other ideas, if you care to make a case for them.)
(Gratuitous link: Sinbad comic. It starts out okay, and becomes hilarious.)
