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Q: Formula ( Answered,   0 Comments )
Subject: Formula
Category: Science > Math
Asked by: vodka-ga
List Price: $50.00
Posted: 29 Oct 2003 11:22 PST
Expires: 28 Nov 2003 11:22 PST
Question ID: 270829
Country     Aids Pop    Purchasing power  Population   Price
---------   ---------   ----------------  -----------  ---------
Swaziland   170,000 	$4,400             1,161,219   $  800,000
Mozambique  1,100,000   $1,000            17,479,266   $1,000,000
Botswana      330,000   $9,500             1,573,267   $2,000,000
Angola        350,000   $1,600            10,766,471   $__________?
Namabia       230,000   $6,900             1,927,447   $__________?
Congo (DRC) 1,300,000   $  610            56,625,039   $__________?

Based on all the information given for the first three countries, i
need a formula to work out the purchase price for the last three
countries. I need to apply that formula to the rest of the countries
of the world.

Request for Question Clarification by mathtalk-ga on 04 Nov 2003 18:03 PST
Hi, vodka-ga:

It sounds like you'd want to have very round numbers for the purchase
prices, possibly because these figures are to be used in a kind of
board game.

Is a rough formula, to which rounding is applied, sufficient for your needs?

regards, mathtalk-ga

Clarification of Question by vodka-ga on 05 Nov 2003 11:59 PST
Hi Mathtalk,

I think that will be fine, as long as it is pretty accurate taking
into consideration the differences between the populations and their
relative purchasing power.

Subject: Re: Formula
Answered By: mathtalk-ga on 05 Nov 2003 18:34 PST
Hi, vodka-ga:

Here's the formula I came up with:

Let C be the cost of a country in dollars, with:

A = AIDs population
D = purchasing power in dollars
P = total population

C = 0.000722 * ( D*(P - 2.62*A) - $12,000*A )

Note that as the units of D are dollars/person and other inputs A,P
are "pure" numbers or population counts, the units of the right hand
side expression are consistent.

For the three countries that you have cost "data" for, the results are
in good agreement with the given dollar amounts:

Country      Price (given)    Price (formula)
==========   ==============   ===============
Swaziland      $  800,000       $ 801,133.80
Mozambique     $1,000,000      $1,008,826.05
Botswana       $2,000,000      $2,001,626.95

The three parameters in my formula were rounded a bit, for simplicity
and to avoid a pretense of greater accuracy than the data allows.  Of
course I could exactly match the three results (using three
parameters), but this would not have much predictive value for other
countries, so I made the answer simpler to keep this in perspective.

regards, mathtalk-ga

Clarification of Answer by mathtalk-ga on 05 Nov 2003 19:00 PST
For the second set of three countries that you ask about, the formula
predicts these amounts:

Country      Price (formula) 
==========   =============== 
Angola        $8,345,708.90
Namabia       $4,607,402.78
Congo (DRC)  $12,175,529.16

Naturally you might want to round these to the nearest half million or so.

The form of the model I chose has a kind of interpretation that may be
of interest to you.  If the AIDS population were zero in a country,
the formula simplifies to a cost proportional to the total purchasing
power of the country's population.  This cost basis is then offset by
the AIDS population parameter in two ways, one which depends on the
(individual) purchasing power in the country and one which is fixed
(per capita of the AIDS population) independently of the country. 
These offsets might be interpreted as 1) loss of a certain number of
individual's purchasing power (e.g. due to care-giving
responsibilities assumed by the general population) and 2) costs of
medicine and other expenses that are not country specific.

regards, mathtalk-ga
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