Question

Question 3: Productivity, Output, and Employment (20 marks) Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a and B are parameters whose values are between O and I a) Derive an analytical expression for the marginal product of capital (MPK), marginal product of labour (MPN), and marginal product of land (MPL). Show analytically that the MPK, MPN and MPL exhibit diminishing marginal returns by examining the second derivative of the production function b) Assume that α= β K-125. 1-64and A-8. Find the expression for the labour demand (Nd). Now assume that the labour supply is given by the following: where w is the real wage rate c) What are the equilibrium levels of the real wage rate, employment and the total output d) Suppose labour efficiency declines to A 1, what happens to the equilibrium levels of the real wage rate, employment and the total output (Y) compared to part (c)

Answer 1