How much has price and quantity increased from year 1 to year 2?

We sell two products.

Product A:

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price y1 = 10

quantity y1 = 2

sales y1 = 20 (price*quantity)

price y2 = 10

quantity y2 = 1

sales y2 = 10 (price*quantity)

Product B:

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(p) price y1 = 5

(q) quantity y1 = 2

(s) sales y1 = 10

(p) price y2 = 1

(q) quantity y2 = 2

(s) sales y2 = 2

Analysis:

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I want to know by how much our prices and quantities have increased for all products in total (or maybe rather on average) from year 1 to year 2.

Let's use capital letters for the total profit, quantity and sales per year: S, P, Q.

I know that S = P * Q.

I want to measure the price and quantity change. So let's set the capital letters to ratios of year 1 values: S1=1, P1=1 and Q1=1. I know that S2 = 12/30.

What are P2 and Q2?

Re: How much has price and quantity increased from year 1 to year 2?

Hi there, I'm not following this too well, but i'll give it a shot.

Consider quantity alone. The sum of products in the 1st year was 2+2=4 and in the second 1+2=3.

The change therefore in volume of product is -1 and in percentage is a decrease by 25%, as (4-3)/4 = 0.25

How is that?

Re: How much has price and quantity increased from year 1 to year 2?

That's good. But I'd like the % change to be volume weighted. So that decreases in quantity influence the change in quantity level more from year 1 to year 2 when the quantity decreases for a high priced product than when it decreases for a low priced product.

If the quantity of product A (price y1 = 10) increases that should have a more significant impact on sales (S=P*Q) than if the quantity of product B (price y1 = 5) increases with the same amount.

I tried to solve it like this:

Price level Article A Year 1 = 10/10 = 1

Price level Article B Year 1 = 5/5 = 1

Price level Article A Year 2 = 10/10 = 1

Price level Article B Year 2 = 1/5 = 0.2

Sales Article A Year 1 = 20

Sales Article B Year 1 = 10

Sales Article A Year 2 = 10

Sales Article B Year 2 = 2

I then calculated the volume weighted price level for year 2 for all articles combined as:

P2 = (1*20+0.2*10)/(20+10) = 0.7333323 [(relative price level article A * sales article A + relative price level article B * sales article A)/(sum sales)]

I calculated the volume weighted quantity level for year 2 for all articles combined the same way:

P2 = (0,5*20+1*10)/(20+10) = 0,6666667

S2 = 12/30 = 0.4

Now I expect P2*Q2=S2,

but S2 = 0.4 and P2*Q2=0.4888889

So if the price decreases of a product I want it to affect the "price level" more if that product is sold in high quantities. If the quantity decreases of a product I want it to affect the "quantity level" more if that product is sold at high prices.

Is this doable?