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Consider an economy populated by a large number of workers with utility function U = xα[1 – ]1-α , where x is disposable income, l is the fraction of time worked (0 ≤ ≤ 1), and a is a preference parameter (with 0 , where t (0; 1) is the marginal tax rate and B > 0 is the unconditional benefit payment.
a. Find the optimal labor supply for someone with ability w. Will the high-skill person work more than the low-skill person? Will the high-skill person have higher disposable income than the low-skill person? Show that the condition for job market participation
b. If tax proceeds are only used to finance the benefit B, what is the government’s budget constraint?
c. Suppose that the mean skill in the population is and that the lowest skill is a fraction g
d. Find the optimal tax rate if the government seeks to maximize the disposable income of the lowest skill worker subject to everyone working.