Suppose individuals get utility from consumption and disutility from working according to the following utility function: (c) = -1 where c and I denote consumption and hours of work, respectively, and o> 0 is a parameter. Moreover, assume that the hourly wage is given by w in terms of the consumption goods. (a) Set up the maximization problem of the individuals and solve for the optimal choices of consumption and labor (c", 1"). (10 points) (b) Now, suppose that labor income is taxed at rate 7. Solve for the new optimal choices of labor and consumption (c,,4). (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? Briefly 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? Briefly explain. (5 points) (e) Discuss which effect dominates. Hint: It depends on the parameter a. (5 points) (f) Solve for the tax rate that maximizes government's tax revenues for o. Explain why the revenue-maximizing tax rate is strictly less than 100%. (5 points)