Hi TPat, this is more a general economic theory and mathematics question than pure accounting but let's try it:
I assume that Gross profit = Sales - CoGS.
Now, if P is price of the product and V is volume and C is cost per unit, then:
Gross profit = P*V - C*V
if you then decrease your price by N% and this leads to 15% increase of V, then the equation is (ceteris paribus):
Gross profit = P*(100% - N%)*V*(100%+15%) - C*V*(100%+15%)
This is general equation based on the iformation you provided. Let's make two examples of it. A few assumptions first:
P=100;V=100;C=50
N1=10%
N2=20%
Now, for both examples, the original gross profit = 100*100 - 50*100 = 10,000 - 5,000 = 5,000
Example 1:
Gross profit = 100*(100%-10%)*100*(100%+15%) - 50*100*(100%+15%) = 100*90%*100*115% - 50*100*115% = =10,350 - 5,750 = 4,600
There is actually 8% decrease of goss profit.
Example 2:
Gross profit = 100*(100%-20%)*100*(100%+15%) - 50*100*(100%+15%) = 100*80%*100*115% - 50*100*115% = =9,200 - 5,750 = 3,450
There is even bigger, 31% decrease of goss profit.
What this shows is that it everything depends on what economic theory calls elasticity of demand curve, or the sensitivity of the volume on product price. In other words, you'd have to say how big the price decrease was, if it was 10% or 0.001% price reduction that made the volume rise up 15% and then just calculate it manually, no general answer can be provided, unless we know the mathematical expression of the demand curve of this product.
Hope this helps a bit.
Regards
Radek
