Suppose that there are three types of programs and taxes that apply to individuals with relatively low

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Question:

Suppose that there are three types of programs and taxes that apply to individuals with relatively low earnings:
1. Welfare transfer of $3000 paid to those with earnings below $6000 that's then (linearly) eliminated between earnings of $6000 and $12,000 so that people with earnings above $12,000 receive nothing.
2. An EITC-like program that is intended to encourage work. It pays nothing to those with no earnings and then linearly increases to reach $4,000 for those earnings $8,000. Individuals with earnings between $8,000 and $14,000 continue to receive the transfer of $4000 which is then (linearly) eliminated between earnings of $14,000 and $24,000.
3. Earnings greater than $15,000 are subject to a 30% income tax.

(a) What are the marginal tax rates that combine the effect of all three programs that apply at each of the following earnings levels: $3,000, $7,000, $10,000, $13,000, $14,500, $20,000 and $25,000?
(b) Consider a person with preferences given by ln(C)+10ln(L) where C is consumption and L is leisure. The maximum amount of leisure is normalized to 1 so that 1-L is labor supply and the total annual earnings if person selects L units of leisure are given by w(1-L). For what values of w will the person choose to work (i.e. set L<1) given programs described in part (a)?
(c) Suppose that in the presence of all these programs, a rational consumer maximizing utility over consumption and leisure ends up with earnings of $13,000. Would her labor supply be smaller or higher if there were no programs at all?
(d) Suppose that the primary earner in the family makes $20,000 and will continue to work the same amount regardless. The other spouse considers working. Does the presence of all these programs encourage or discourage work? What does it tell you about work incentives of EITC?