Problem 4.3: Consumption tax. (40 points) Consider an economy in which there are L workers and each workers' utility is 1L(C,h) = log ((3 %}12) , where c is consumption and h. is the number of hours worked. The worker pays a consumption tax 1" for every unit of the good she purchases but no income taxes. Her budget constraint is thus (1 + T)C = wh. Firms in this economy operate with a constant returns production function that uses only labor: Y = H, where H is the total number of hours of work the firm hires and Y is the amount of output it produces. The firm's objective is to maximize its profits, given by Y wH. 1. Solve the firm's maximization problem and derive the labor demand curve in this economy. 2. Set up the Lagrangean of the worker and take the first-order conditions with respect to labor and consumption . Derive the labor supply curve in this economy. . Solve for the equilibrium wage rate (to) and employment {number of hours each individual works, 33.) in this economy. Explain what an increase in the consumption tax from 0 to 25% does to the equilibrium wage and employment. Use a demand / supply diagram to explain the intuition behind your results. In particular, would a worker who pays no labor income taxes care about what the consumption tax is in deciding how much to work? Why or why not? . Suppose the government contemplates replacing the consumption tax of T = 25% with an income tax of 7"" = 20%. Under this new income tax plan, the worker's budget constraint is c = (1 1"\")wh. What will happen to equilibrium employment under this new tax plan? Use algebra to explain your answer. Explain the economic intuition for your ndings