Question 4 Suppose that the equation of Y rea_l GDP is given by: Y = AK"(NH)'6 where A, K and N measure, respectively, total factor productivity, the amount of capital, the number of hours of work employed, and the average level of education attained by domestic workers. :1) Compute the marginal product of labor. b) Divide both sides of the production function by N to derive an expression for the equation of the average product of labor lnction, real output per hour of work. Average labor productivity is also known as \"labor productivity". c) Explain in words why the two productivity measures differ. d) Is the marginal product of labor smaller or greater than the average product of labor for any level of N? Prove your answer mathematically. e) Is the average product of labor an increasing or decreasing function of A, K, N or H? Support your answer by conducting a growth accounting exercise on the determinants of APN and explain the intuition of your answer. f) Decompose the average product of labor into 1. total factor productivity, 2. Physical capital deepening (KIN) and 3. Human capital