Allocation of Price and Volume changes to a change in Rate
Assume you have three or more products {A, B, C, ...} and each has a price (P) and volume (V). There's a set of prices and volumes in period 1 that results in an average price across all products (AvgP1). Then the product prices and volumes move independently in period 2. This results in a change in the average price (AvgP2).
I want to allocate the price and volume movements for each product so that the sum of all the allocations add up to the total change. Preferably, I'd like to do this without "normalizing" an initial set of answers. I also want to be able to calculate the Price and Volume impact for each product with only knowing that product's Price and Volume and the total portfolio average Price and total Volume  in other words, I don't want to have to iterate through all products to determine to impact from a single product.
Note that this is different from the typical Price/Volume impact analysis since it's broken into the components of Price and NOT Revenue. Also, if a low price product decreases in volume, we would expect it to have a positive Volume Impact on the Avg Price, and vice versa. If any product decreases in Price, the Price Impact of that product would be negative, and vice versa.
Example data:
Product  Period 1 Price  Period 1 Volume  Period 2 Price  Period 2 Volume  Product Price Impact  Product Volume Impact 
A  $2.00  2000  $2.50  3000  Pa  Va 
B  $1.00  1000  $0.90  2000  Pb  Vb 
C  $0.50  3000  $0.60  500  Pc  Vc 
Avg/Total  AvgP1: $1.083  6000  AvgP2: $1.745  5500  Pttl  Vttl 
Solve for Pa through Vc. In the example above:
 Pa+Va+Pb+Vb+Pc+Vc = Pttl + Vttl = (1.745  1.083) = $0.662
 Pa is positive, Pb is negative, Pc is positive, Va is positive, Vb is negative, Vc is positive
 AvgP1 + Pa + Va + Pb + Vb + Pc + Vc = AvgP2
Answer
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Appears to work exactly as expected. Great solution. Thank you!
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