The percentage diff between any two levels would be kept constant if they received the same

**percentage **raise, but not if they received the same

**dollar **raise.

Generalizing, take any two arbitrary, unequal positive amounts

*a *and

*b*. If they are both increased by some percentage

*r* (expressed as a decimal), then their post-increase ratio is

; i.e. their post-increase ratio is identical to their pre-raise ratio. It's readily apparent that this would hold true for any number of periods as long as both levels received the same

*percentage *raise each period.

Wrapping this around some illustrative numbers, take 40,000 and 44,000. That is, the higher level is 10% greater than the lower. Suppose each level gets a 7% raise, putting them at 42,800 and 47,080 respectively. The ol' calculator shows that the higher level remains precisely 110% of the lower.

It's also simple to prove that for any two positive numbers

*a *and

*b* with

*a *>

*b* > 0, if you add the same positive quantity

*x *to both, then

; that is, their post-raise ratio is less than their pre-raise ratio.

Again with the same starting levels (40K and 44K), give 'em both a 3K raise. After the raise the higher level is only 9.3% greater than the lower, whereas it was 10% higher before the raise.

Hence, the

*percentage *diff between any two levels would shrink if they received the same

**dollar **raise, but would remain unchanged if they received the same

**percentage **raise.