Labor Income Tax. {35 points] Suppose individuals get utility from consumption and disutiiit}r from working according to the following utility function: L31 o shit}: 10 I where c and f denote consumption and hours of work, respectively. and o 3' is a parameter. Moreover, assume that the hourly wage is given by w in terms of the consumption goods. {a} Set up die maximization problem of the individuals and solve for the optimal choices of con sumption and labor [ch 1\" 1|. (5 points} {b} Now, suppose that labor income is taxed at rate T. Solve for the nevir optimal d1oices of labor and consumption (or, if}. (5 points} {c} Does the introduction of the tax induce an increase or a decrease in the individual's labor supply through the substitution effect? Briey explain. {5 points} {d} Does the introduction of the tax induce an increase or a decrease in the individual's labor supply through the income effect? Briey explain. {5 points} {e} Discuss whidi effect dominates. Hint: it depends on the parameter o'. 1'5 points) {f} Solve for the tax rate that maximizes government's tax revenues for o = %. Explain why the revenuemaximizing tax rate is stricyr less than lD'EPEI. (It? points}