View Question
 ```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. Vodka.```
 ```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```