Question

THIS IS THE GENERAL EQUILIBRIUM PROBLEM THAT I PROMISED. YOU FIRST SOLVE FOR THE INITIAL EQUILIBRIUM AS POINT A. WE CONSIDER TWO DIFFERENT AND SEPARATE SHOCKS (I CALL THEM SCENARIOS). THE FIRST SHOCK IS TO THE IS CURVE, THE SECOND SHOCK IS A ‘LM’ SHOCK. AGAIN, WE CONSIDER THESE SHOCKS SEPARATELY SO THAT AFTER YOU COMPLETE SCENARIO 1 (THE IS SHOCK), WE GO BACK TO THE ORIGINAL CONDITIONS AND CONSIDER THE SECOND SCENARIO WHICH IS THE ‘LM’ SHOCK.

Consider the following model of the economy

Production function: Y = A·K·N – N²/2
Marginal product of labor: MPN = A·K – N.

where the initial values of A = 6 and K = 10.

The initial labor supply curve is given as: N^S = 30 + 4w

Initial conditions in the goods market

C^d = 120 + .50(Y-T) – 500r
I^d = 800 – 500r
G = 100
T = 100

M^d/P = 218 + 0.5Y- 1000(r + π^e)
   
Nominal Money supply   M = 3000
   
Expected inflation is equal to 3% (π^e = 0.03)

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 (S^d = I^d ), 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 diagram…each diagram will have three different equilibriums points A, B, and C)

SCENARIO #1 – AN IS SHOCK!

Suppose that the consumption function has changed and is now

C^d = 140 + .50(Y-T) – 500r

S1 a) (4 points) Name and support two reasons why the consumption function would change like this.

S1 b) (6 points) What is the new, short run (fixed price level) expression for the IS 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 to your four diagrams as point B. Be sure to label diagrams completely with the inclusion of all the relevant shift variables like we did numerous times in the video lectures.

S1 d) (4 points) Find the real interest rate associated with the long run general equilibrium.

S1 e) (4 points) Find the new price level associated with the long run general equilibrium.

Please label these long run conditions to your four diagrams as point C. Be sure to label diagrams completely with the inclusion of all the relevant shift variables like we did numerous times in the video lectures.

S1 f) (5 points) Now we know that one of the Fed's mandates is price stability. What would the Fed have to do, in terms of open market operations, so that the price level remains at its initial value? Assume the money multiplier is 0.8. Please show your work.

SCENARIO #2 – AN LM SHOCK!

Let’s return to our original conditions: Please write down the expressions for your ORIGINAL IS curve and LM curves (so the grader can follow your starting points).

IS: r = ___________________________

LM: r = __________________________

Now draw four separate diagrams: (40 points total) Top left: a desired savings equals desired investment (S^d = I^d ), 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 diagram…each diagram will have three different equilibriums points A, B, and C)

SCENARIO #2– AN LM SHOCK!

S2 a) (4 points) Now suppose that there is a shock to real money demand so that the new real money demand function is:

M^d/P = 248 + 0.5Y- 1000(r + π^e)

Name and support two reasons why the nominal money stock might change like this - please do your best to relate your answer to real world events.

S2 b) (6 points) What is the new, short run (fixed price level) expression for the LM curve? Please show all work.

S2 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 to your four diagrams as point B. Be sure to label diagrams completely with the inclusion of all the relevant shift variables like we did numerous times in the video lectures.

S2 d) (4 points) Find the new price level associated with the long run general equilibrium.

Please label these long run conditions to your four diagrams as point C. Be sure to label diagrams completely with the inclusion of all the relevant shift variables like we did numerous times in the video lectures.

S2 e) (4 points) Let us focus on the movement from point A to B (the short -run) in your money market diagram. Explain why (and in what direction) the real interest rate had to change to 'clear' the money market. Be as specific as possible as we talked about this a great deal in the video lectures!

S2 f) (5 points) Now we know that one of the Fed's mandates is price stability. What would the Fed have to do, in terms of open market operations, so that the price level remains at its initial value? Assume the money multiplier is 0.8. Please show your work.

S2 g) (5 points) What else could the Fed do, besides conducting open market operations, in order to for the price level to remain at its initial value?

Answer 1