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Solving for Equilibrium Levels in a Closed Economy Model

Part a: Finding Equilibrium Levels

The following equations characterize a country’s closed economy.

Production function: Y = A?K?N – N2/2

Marginal product of labor: MPN = A?K – N.

where the initial values of A = 9 and K = 9.

The initial labor supply curve is given as: NS = 31 + 9w.

a) Find the equilibrium levels of the real wage, employment and output (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 these initial equilibrium points as point A.

Initial conditions in the goods market

Cd = 1000 + .50(Y-T) – 500r

Id = 610 – 500r

G = 100

T= 100

Initial conditions in the money market

Md/P = 212 + .5Y - 1000 (r + πe)

where M = 2400 and πe = 0.02 (2%)

b)Given these initial conditions in the goods market, solve for an expression of the IS curve (r in terms of Y).  

c) Given the initial output, as in part a), what is the goods market clearing interest rate?

d) Given the initial output as in part a) and the goods market clearing interest rate as in part c), what is the general equilibrium price level?

e) Please solve for an expression for the LM curve (r in terms of Y).

We now have numerous changes to our economic conditions (all is not constant). Think of all these changes happening together, that is, we go from one state of economic affairs to a different state of economic affairs.  Below are the changes.

•    The labor supply changes and is now: NS = 10 + 9w . 

•    K goes up from 9 to 10

f) What could cause such a change in labor supply?  Please give two specific and well supported reasons. Be sure to explicitly identify/choose one of your (two) reasons to use as a "relevant" shift variable in your graph.

g) Given the change in NS and K, repeat part a) (i.e., find the equilibrium levels of the real wage, employment and output).  Add these results to your labor market and production function diagrams respectively and label as point(s) B. Be sure to label the diagram completely with the relevant shift variables in parentheses next to the function.

Given the change in labor market conditions / production function we have one other change and that is the investment function has changed and is now:

•    The desired investment function is now Id = 1020 – 500r

h)What could cause such a change in the desired investment function? Please give two specific and well supported reasons. Be sure to explicitly identify/choose one of your (two) reasons to use as a "relevant" shift variable in your graphs.

i) Given this change in desired investment, solve for a "new" expression of the IS curve.

j)Given the change in desired investment and the change in Y, solve for the new goods market clearing interest rate. 

k)Given the change in Y and r, solve for the new (if applicable) general equilibrium price level (we assume that prices adjust immediately to their general equilibrium value)

Please locate this new general equilibrium as point B on all your diagrams.

l) Using a generic user cost / desired capital stock diagram,  show the movement from point A to point B.  Please be sure to be consistent and use the same reason that you chose in part h). Explain exactly why the desired capital stock has changed the way it has. Be sure to label diagram completely.

m)Is the movement from A to B more consistent with Classical economic theory or Keynesian economic theory?  Explain.

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