This question focuses on labour productivity, labour demand, and generally on the production function. Assume that the Aggregate Production Function is represented by the following equation: Y = K (AN BN) + CL 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, A and B stand for measures of labour efficiency, and C for a measure of land efficiency. a is a parameter whose value is between 0 and 1, 3 and y are parameters whose values are > 1. (a) Derive the formulas for: - the marginal product of labor (MPN). - the marginal product of capital (MPK). - the marginal product of land (MPL). (b) Using calculus derive a formula for the aggregate labour demand (ND). Express aggregate labour demand as a function of the real wage w (and all other variables and parameters). (c) The aggregate quantity of labor supplied is NS = 50 + (1 + s)w, where s is a wage subsidy paid by the government. Assume that s = 1, A = 100, B = 1/4, K = 1, = 2: solve for the equilibrium real wage (w*), full-employment level (N*). Assume that L = 10, C = 1 and y = 2: find the full-employment level of output (Y*). (d) The government's goal is to achieve the employment level N** = 100: what is the value of the subsidy s** that is needed in order to reach this target? What are the implied wage w** and output Y**? Comment on your findings.