Problem III. Labor Income Tax (20 points) Assume that individuals are identical and have the following utility function: u(c,l) = log(c) + log(T-1), where c represents consumption, l represents hours of work, and 6 is a parameter. Labor income is the only source of income and wage is given by w. 1. Set up the maximization problem of this individual and solve for the optimal choices of labor and consumption (c*,l*). (5 pts) 2. Now, suppose that labor income is taxed at rate T. Solve for the new optimal choices of labor and consumption (c",1"). (5 pts) 3. Suppose T = 45, 0 = 0.5, and T = 10%. Plot the labor supply curve in the presence and in the absence of the labor income tax. (5 pts) 4. For the individual's choice of labor, explain intuitively the direction of the substitution and income effect of the introduction of the tax. Does the income effect or substitution effect dominate? (5 pts)