Reminder: This is simplified for clarity.
To start off, the value of a dollar can be represented by these equations.
5d = 1p,
if d < p, d = 0,
The cheapest item on the market (p) costs five dollars (d). Since the value of d is based on the price of p, if you cannot afford p your money has no value and is worth 0.
For example, your monthly cost of living is $3000 and you have been paid $2640 ($15/h, 40 hours a week, 22 days). This includes all taxes and surprise expenses. Lets redefine the variables above to W and C (wage and cost of living).
c = $3000,
w = $2640,
if w < c, w = 0,
Because your wage is lower than your cost of living for the month, it is worth nothing.