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Multiplying deltas

If your price increase by 10% and quantity sold increases by 20%, is there a way to quickly calculate new revenues without figuring out what the new price is or qty is after the increase? Say old price was 5, quantity was 6. Keeping the numbers simple here as an example but the real ones are much larger

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Top answer
on Aug 16, 2021
#1 Coach for Sessions (4.500+) | 1.500+ 5-Star Reviews | Proven Success: ➡ interviewoffers.com | Ex BCG | 10Y+ Coaching

Hi there,

Yes, you don’t need to calculate the new price or quantity.

Basically you have:

p*q*1,2*1,1=p*q*1,32

So you can say that revenues will increase by 1/3 after the change (or by 32% if you want to be very precise).

Best,

Francesco

Anonymous A
on Aug 16, 2021
Thanks, is there a quick way to find the incremental revenue without calculating the new revenue or new price / quantity?
on Aug 17, 2021
#1 Coach for Sessions (4.500+) | 1.500+ 5-Star Reviews | Proven Success: ➡ interviewoffers.com | Ex BCG | 10Y+ Coaching
Hi there, you don’t need to calculate the new revenues/price/quantity with the formula above, you will automatically know revenues will increase by 32%. Hope this helps
Ian
Coach
on Aug 15, 2021
Top US BCG / MBB Coach - 5,000 sessions |Tech, Platinion, Big 4 | 9/9 personal interviews passed | 95% candidate success

Hi there,

I see what you're trying to do here, but I think in this case a shortcut will add more complexity/difficulty than anything.

I'd do .5 (10% of 5) times 1.2 (20% of 6) to understand the difference.

Anonymous A
on Aug 15, 2021
Thanks, so +0.5 x +1.2 would be +0.6, so does this mean Revenue increases by +0.6? Because if I multiple (5x6) and subtract from the new revenues from (5.5x7.2), I don’t get the delta that I would get if I just multiply the delta price x delta quantity.
Clara
Coach
on Aug 17, 2021
McKinsey | Awarded professor at Master in Management @ IE | MBA at MIT |+180 students coached | Integrated FIT Guide aut

Hello!

I don’t think that there are any tricks here! Actually, it’s a pretty straight forward math: 

Price x quantity x 1.1 x 1.2

5 x 6 x 1.1 x 1.2 = 30 x 1.1 x 1.2 = 33 x 1.2 = ~40

Hope it helps!

Cheers, 

Clara

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