1. Suppose a worker's utility function is u(c, l) = a In C + (1 a!) lni where: a. C is consumption b. l is leisure hours c. (1 l) is labor hours (so total hours available are normalized to l) d. a is an exogenous parameter The government also imposes a tax on wages (w) equal to 1' (Greek letter tau) such that the after- tax rate is (1 I). The worker earns no other income other than wage income. a. Write the worker's budget constraint as c =... b. Write the lagrangian lnction and the rst order conditions (FOC) for C and I. c. Solve the model for C * and l * {that is, solve for C and l in terms of the wage, tax rate, and parameters