Monday, August 31, 2009

Any problem can be solved by the proper application of algebra..

Fun with numbers..... 

So it's clearly a Pittsburgh scene to have the city and county fighting over G20 costs, both real, and potential. It's hard to tell from the reporting, but they seem to be fighting over whether the costs are being paid 50/50 between them.

Hmm.  Is 50/50 the goal?  If there is a per person equity then you have to start by realizing the county is 4 times as big as the city.  Should the ratio of cost sharing be 25:75??

Maybe not.  Someone living in the city is also part of the county and so paying their share of the county's bill as well.  So it's not that simple. What is the most equitable ratio of cost sharing if the goal is to equate the cost borne by city and non-city residents in Allegheny County.

Let R = the proportion of total costs borne by the city, (1-R)= the proportion of costs borne by the county.. 

Assume the ratio of county to city population is exactly 1 to 4 which is pretty close to current estimates.  Let's call the total cost of  G20 on somebody as T.   The population of the city as P, and the population of the county as 4P. 

What is R when the costs on a city resident equal the cost on a county resident not living in the city?  realize that a city resident is paying both city and county taxes. So

Cost to City Resident  = Cost to County Resident

or  RT/P + (1-R)T/4P = (1-R)T/4P

Wait..  If there is any cost at all (i.e. if T>0) then R can only = zero. Funny that.

Yeah, the algebra was unnecesssary, but there is an uber uber geeky pun in all of this.  Anyone?


Blogger Vannevar said...

The only way to make sure that county-not-city residents pay the same as county-and-city residents is to have the county pay the whole thing, and the city pay for nothing.

But I'm sorry, I can't find the UUGP (uber uber geeky pun). Cheers, V.

Monday, August 31, 2009 11:28:00 PM  
Blogger Ms. Monongahela, Ms. Chief Editor said...

I see a big problem with your algebra. :-)

Tuesday, September 01, 2009 7:50:00 AM  
Anonymous MH said...

Were you going to explain the pun?

Thursday, September 03, 2009 4:24:00 PM  

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