California exemptions because withholding increased 10%

Continuing the thread from "Federal District Court Judge Tosses Key Parts of DoMA", CA increased withholding 10% because of the emergency. So we can claim more exemptions to negate the increase. Here is my formula:

If you make between $3,862 and $83,334 a month, and are single or married and both of you work, which describes a lot of the people I know in the Bay Area, then:

Let N be the number of exemptions under the new rules. The tax withheld is:

T = (Wages - N*83 - 303)*0.10505 + 197.66 - N*8.98 = (W-303)*0.10505+197.66 - N*(83*0.10505+8.98)

Under the old rules, the the tax withheld is probably,

t = (Wages - N*83 - 303)*0.0955 + 197.66 - N*8.98 = (W-303)*0.0955+197.66 - n*(83*0.0955+8.98)

T = t (W-303)*0.10505+197.66 - N*(83*0.10505+8.98) = (W-303)*0.0955+197.66 - n*(83*0.0955+8.98) (W-303)*0.10505+197.66 - (W-303)*0.0955-197.66 + n*(83*0.0955+8.98) N*(83*0.10505+8.98) (W-303)*(0.10505-0.0955) + 197.66*(1-1) + n*(83*0.0955+8.98) N*(83*0.10505+8.98) (W-303)*(0.10505-0.0955) + n*(83*0.0955+8.98) = N*(83*0.10505+8.98) N = ((W-303)*(0.10505-0.0955) + n*(83*0.0955+8.98)) / (83*0.10505+8.98)

If you make W000 a month, and were claiming n=1 exemption, then

N = ((10000-303)*(0.10505-0.0955) + 1*(83*0.0955+8.98)) / (83*0.10505+8.98) = 6.187

Since we're in the middle of the year, you should maybe set N 6.187+5.187 = 11.374