There will be four distinct categories of recipients:
("total days" represent distinct days signed in) and their welfare formulas ("x" represents distinct days of the past week signed in):

Catagory 1:
Members with fewer than 30 total days: 5 * x - 3, max is $32, a 4-day example would be $17

Catagory 2:
Members with between 30 and 180 total days: 4 * x - 2, max is $26, a 4-day example would be $14 (see additional note below)

Catagory 3:
Members with between 180 and 360 total days: 3 * x - 1, max is $20, a 4-day example would be $11

Catagory 4:
Members with greater than 360 total days: 2 * x, max is $14, a 4-day example would be $8

Additional Notes:
A. There will be a supplemental welfare bonus rolled into the welfare checks of anyone with 30 total days or more and a weekly income of less than $20. People who fall into this category will get a sliding scale of $1 to $8 extra in welfare, depending on how much they earn and how many days that week they signed in.

B. There will also be a wealth-based welfare reduction for anyone making more than $20/week. People who fall into this category will have their welfare reduced $1 for every $6 over $20 that they earn in a week.

C. Gambling winnings and icon sales don't count toward weekly income. Post awards, item series payouts, poetry awards, and job pay are examples of things that do count. NOTE: item series payouts are counted on an after-tax basis.

D. It is possible for people to receive no welfare. Under this system, the point at which that would happen would be someone earning $104 or more per week if they have 360+ total days and even if they sign in every day in the last week.

Examples, assuming all signed in every day of the last week:

Member 1 is a newbie with just 12 total days under his belt. His welfare is $32.

Member 2 has 82 total days and earned $10 in posting awards last week. Her welfare is $26 + $4 in supplemental, for a total of $30.

Member 3 also has 82 total days, but earns $33 per week in series payouts and poetry awards. His welfare is $26 - $2 for wealth adjustment, for a total of $24.

Member 4 has been here forever but has no series and makes $4/week in posting awards. His welfare is $14 + $7 in supplemental, for a total of $21.

Member 5 has been here forever and earns $80/week in series payouts. Her welfare is $14 - $10 for wealth adjustment, for a total of $4.