Problem 2 (Prot Maximization Short run) GMC is producing cars using machines (K) and labor (L). The technology is capital intensive; the production function is given by FlKa L) = K(3/4)L(1/2) The value of GMC physical capital (machines, real estate etc.) is equal to K =$16 billon (in calcu- lations ignore billions). We analyze rm's behavior in the short run (note K cannot be changed in the short run). Suppose the price of a car is equal to p and the wage rate is 11: (parameters). 0. ) Write down the prot as a function of L. L ) On a graph with L on the horizontal axis and $ on the vertical axis, plot two components of prot function: total revenue (pF(K, L)), and labor cost (wL) (when drawing, assume p = 1 and w = 2). On the graph, mark the prot level as the difference between the two lines (for any given L). C) Find analitically the optimal level of labor L' that maximizes the prot as a function of the real wage in / p. (we call it the rm's labor demand). Find the values of L for the following values of parameters Plot your demand for labor on the graph with the real wage (w/ p) on the vertical axis and L on the horizontal one. Using the table mark three points corresponding to the three values of (111/13). d) What is the maximal prot for each of the three (w/p) values