[EQAB-list] quick & dirty cost:benefit analysis

[Robert G Kennedy III, PE]

I don't think your brain is at all addled!

"velocity": When money comes into a system, it doesn't just get spent  
once and then sit there under a mattress. The party who got dollars in  
exchange for a good or a service turns around and buys other goods or  
services with those dollars. Depending on which sector of the economy  
the dollar happens to be sitting in, this "turnover" can happen quite  
a few times in a year. The rate at which dollars turn over is  
sometimes called "the velocity of money". In governmental and  
industrial sectors, the velocity tends to be low, just a few turnovers  
per year. Say 1-3. In commercial/retail the velocity tends to be  
higher -- economists often use 7 turnovers as a rule of thumb. Dollars  
spent on food and essentials can have a very high velocity. (Recall  
the nationwide debate early this year about how the economic stimulus  
package would be best applied.)

So I used 5 as an average.

Furthermore, I asssumed that only half those dollars get spent within  
city limits the first time. Depending on which businesses the Recycle  
Bank manages to recruit for partners, this proportion could be a lot  
higher or a lot lower. 50% seemed reasonable for a first cut.

"Leakage": Moreover, I assumed that a proportion of those dollars  
"leak" out of the local system each time they're spent. Imagine trying  
to do a bucket brigade with cupped hands instead of buckets - most of  
the water will end up on the ground by the end of the line at the  
fire. The bigger and more well-rounded the local system is in terms of  
satisfying economic needs, the more likely those dollars will stay  
inside. You can also call the process "extinction". A tiny system  
can't hold onto its dollars, in much the same way that a tiny raindrop  
or a tiny black hole evaporates a lot faster than a big one. The  
fraction 1/e shows up everywhere in nature, and in complex living  
systems, so I used that. (My mistake: I meant to write [1-(1/e)]^(n-1)  
in my first draft.) So the fraction of 1 dollar which remains behind  
in the system after 1 year (5 turnovers) is:
1-[1-(1/e)^(5-1)] = 1-[1-(0.37)^4] = 1-[1-0.16] = 0.16

Unless it's a black market or FedGov biz, the City collects its 2.75%  
share of sales tax (out of 9.75% total tax) on every transaction.

So the total dollar flow subject to sales tax in 1 year is the sum of  
the series:
[1-(1/e)]^0 + [1-(1/e)]^1 + [1-(1/e)]^2 + [1-(1/e)]^3 + [1-(1/e)]^4 =
1 + 0.63 + 0.40 + 0.25 + 0.16 =
2.44

So the recomputed marginal value to the city in terms of increased  
sales tax value is:
11,645 x $198.00 x 50% x 2.44 x 2.75% = $77356

I will recompute the rest of my back-o'-the-envelope analysis later  
this w/e, using the updated figures and assumptions Ellen gave me.

-- 
Robert G Kennedy III, PE
www.ultimax.com


Quoting Pat Imperato <psimperato at aol.com>:
> Thanks Robert.? This is good info.? However, I lost you on the  
> "velocity of money and leakage".? Can you provide my addled brain  
> with a little more explanation.? Thanks.