2. [EQUILIBRIUM IN THE LABOR MARKET] (25 marks) Suppose that the production function is Y=9K0.5L0.5 The capital stock is K=25 The labor supply curve is LS=100[(1t)w]2 where w is the real wage rate, t is the tax rate on labor income, and hence (1t)w is the after-tax real wage rate. (a) (5 marks) Derive the marginal product of labor (MPL). (b) (5 marks) Assume that the tax rate on labor income, t equals zero. Find the equation of the labor demand curve. Calculate the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after-tax wage income of workers. (c) (5 marks) Repeat part (a) under that the assumption that the tax rate on labor income t=0.6. (d) (5 marks) Suppose that a minimum wage of w=2 is imposed. If the tax rate on labor income, t=0, what are the resulting values of employment and the real wage? (e) (5 marks) Does the introduction of the minimum wage increase the total income of workers, as a group