General Equilibrium Problem 1 Part 1 Introduction Consider the following model of the economy Production function Y A K N N2 2 Marginal product of labor MPN 2A K N where the initial values of A 5 and K 6 The initial labor supply curve is given as NS 20 3w Cd 85 50 Y T 500r Id 50 500r G 50 T 100 Md P 85 0 5Y 1000r Nominal Money supply M 400 We assume that expected inflation is zero e 0 so that money demand depends directly on the real interest rate since i r 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 Part 2 IS Curve In the space below 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 Derive desired saving function set equal to desired investment express r iin term of Y to in 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 Part 3 LM Curve e 3 points Find the expression for the LM curve r in terms of Y Please show all work Now draw three separate diagrams 30 points total a FE IS LM diagram a desired savings equals desired investment Sd Id and a money market diagram locating this initial equilibrium point as point A BE SURE to LABEL all diagrams completely 10 points for each correctly drawn and labeled diagram each diagram will have three different equilibriums points A B and C Part 4 Portfolio Shock SCENARIO 1 AN LM SHOCK Now suppose that the real demand for money has changed and is now Md P 105 0 5Y 1000r S1 a 6 points What would cause such a development Explain using the relevant characteristics of asset demand S1 b 4 points What is the new short run fixed price level expression for the LM curve Please show all work S1 c 4 points What is the short run Keynesian fixed price level of equilibrium output and real interest rate Please show all work Please label these new short run conditions on your FE IS LM diagrams as point B Be sure to label diagram completely with the inclusion of all the relevant shift variables like we did numerous times in class Part 5 Long Run Adjustment S1 d 3 points If the Fed did nothing explain how exactly the economy will return to full employment S1 e 4 points Assuming that the Fed did nothing find the new price level associated with the long run general equilibrium Please label this long run equilibrium on your FE IS LM diagrams as point C Be sure to label diagram completely with the inclusion of all the relevant shift variables like we did numerous times in class S1 f 5 points Is this result desirable That is with perfect information would the Fed allow this long run adjustment to take place Why or why not Explain in as much detail as possible using a real world event hint it s a central banking nightmare S1 g 5 points Suppose otherwise and that the Fed wanted to keep prices constant at their original level at points A and B What would the Fed have to do exactly as in open market operations Assume that the money multiplier is 1 Be specific and show work Finally draw an aggregate demand and aggregate supply curve locating points A B and C Please label everything completely Be sure to add the SRAS curves and the LRAS curve to your two AD curves A completely drawn and labeled diagram is worth 10 points