macro econ

Assume that the aggregate production function is represented by the following: Y = K\"(AN)'3L1'\""6 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 )3 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 or = ,6 = %, K = 125, L = 64, and A = 8. Find the labour demand equation, i.e. an expression for the demand for labour (Nd). c) Now assume that labour supply is given by the following function: N' = 4[(1 01.9%] where t is the tax rate on labour income. Find the equilibrium levels of the real wage, employment and the level of full employment output when t = D. d) Suppose labour efciency increases to A = 27, and again t = 0. What happens to the equilibrium levels of the real wage rate, employment and the total output (Y) compared to part (c). e) Suppose now that the tax rate on labour income is 25%, Le. t = 0.25, and againA = 8. \\Vhat are the new equilibrium levels of the real wage, employment and the level of full employment output? Compare the results to part c)