-Why children will save more
children gets $Y+X allowance, children spends $X. children saves $Y
economy improves because of the multiplier process.
parents get increment, children get more money.
children gets $Y + X + (5%*increment), children spends $X, saves $Y+ (5%*increment)

-Why parents will benefit
assuming parents get $A monthly, and $(X+Y) is 5% of $A,
if the economy improves, and if parents get increment of $B,
amount of money parents have left after giving allowance, after increment (95% * [A+B]) > amount of money parents have left after giving allowance, before increment (95% * A)

-Exceptions
children gets $Y+X+constant before parent's pay is increased. where constant>increment and constant increases with salary increment following a linear equation(ie. y=mx+c) where constant increases with increment.

For you.

_____________________