Question 3: The Aggregate Production Function and Employment [40 marks] Assume that the aggregate production function is represented by the following: Y = K\"(AN)I3 + LY Y stands for output, K stands for the capital stock, N stands for the number of people employed, L stands for the quantity of land used in production, andA stands for a measure of labour efciency. a, , and y are parameters whose values are between 0 and 1. a) Derive an analytical expression for the marginal product of capital (MPK), marginal product of labour (MPN), and marginal product of land (MPL). Then verify that the MPK, MPN, and MPL exhibit diminishing returns by examining the second derivative of the production function. b) Suppose the real wage paid to labour is w. Also, assume that a = = y = 0.5, K = 64, and A = L = 16. Find the labour demand equation, i.e. (Nd). c) Now assume that labour supply is given by the following function: NS = 4[(1 t)w] where t is the tax rate on labour income. Therefore, the after-tax real wage rate is (1 t)w. Find the equilibrium levels of the real wage, employment and the level of full employment output when t = 0. d) What happens to the level of employment and real wage if labour becomes more pro- ductive, for example if A = 64? e) Suppose now that the tax rate on labour income, 1', equals 0.25 and again A = 16. What are the new equilibrium levels of the real wage, employment and the level of full employment output? Compare the results to part (c). f) Suppose again that t = 0, and that the government has imposed a minimum wage of 6. What is the new level of employment? What is the level of unemployment? Does the introduction of minimum wage increase the total income of workers (taken as a group) compared to part (c) above