Consider the following model of the economy Production function: Y = AKN N2/2 Marginal product of labor: MPN = AK N. where the initial values of A = 6 and K = 10. The initial labor supply curve is given as: NS = 20 + 9w Initial conditions in the goods market Cd = 100 + .50(Y-T) 500r Id = 800 500r G = 100 T = 100 Md/P = 78 + 0.5Y- 1000(r + e) Nominal Money supply M = 1800 Expected inflation is equal to 2% (e = 0.02) 1 a) (6 points) Solve for the labor market clearing real wage (w*), the profit maximizing level of labor input (N*), and the full employment level of output (Y*). Please show work. Draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph. Be sure to label everything including this initial equilibrium point as point A. (10 points for completely labeled and correct diagrams) b) (4 points) Derive an expression for the IS curve (r in terms of Y). Please show all work c) (3 points) Find the real interest rate that clears the goods market. Please show all work d) (3 points) Find the price level needed to clear the money market. Please show all work e) (4 points) Find the expression for the LM curve (r in terms of Y). Please show all work Now draw four separate diagrams: (40 points total) Top left: a desired savings equals desired investment (Sd = Id ), Top right: a FE - IS LM diagram, Bottom left: a money market diagram, Bottom right: An AD - AS diagram, locating this initial equilibrium point as point A. BE SURE to LABEL all diagrams completely (10 points for each correctly drawn and labeled diagrameach diagram will have three different equilibriums points A, B, and C)