How do you calculate the impact of each item contributing to the total discount?

Question

I have 2 items: Devices and Batteries and I am observing the revenue I get from both over 2 months: in December the Revenue for the devices was 5.1Mio in $ and Discount 292K, January (6.17Mio and 482K). The Battery Revenue was 210 and Discount amounted to 55K - yes, 99% discount (Jan: 617 and 117K). I can calculated an overall discount rate for Dec: (292K+55K)/((292K+55K)+(5.1Mio + 210))=6.4% doing the same for Jan gives me an overall 8.9% Discount Rate. I know that there was a 2.5 percentage point increase in the discount rate from Dec to Jan. How can I calculate how much the Device Discount vs Battery Discount contributed to this overall Discount Rate increase of 2.5pp?

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Answer 1

Do you mean like:

$$\frac{292K}{292K+55K} \approx 84.1\%$$

is the percentage that Devices discount contributes to the overall discount in December?

The discount rates of Devices and Batteries do not add up to the overall discount rate (the $6.4\%$ in December). In fact the overall discount rate is somewhere between the two individual discount rates, by the mediant inequality:

• Devices: $\dfrac{292K}{292K+5.1M}$
• Batteries: $\dfrac{55K}{55K+210K}$

One simpler example is that there are 10 items, each item is $5\%$ discounted. The overall discount rate is still $5\%$, not the sum of the individual discount rates.