Econ | econ | penn state

The following equations characterize a country’s closed economy.

Production function: Y = A·K·N – N^2/2

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

where the initial values of A = 10 and K = 8.

The initial labor supply curve is given as: N^S = 40 + 9w.

a) (5 points) 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 = 600 – 500r

G = 100

T= 100

Initial conditions in the money market

Md/P = 78 + .5Y – 1000 (r + π^e)

where M = 2400 and π^e = 0.02 (2%)

b) (5 points) Given these initial conditions in the goods market, solve for an expression of the IS curve (r in terms of Y). 

c) (5 points) Given the initial output, as in part a), what is the goods market clearing interest rate?

d) (5 points) 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) (5 points) Please solve for an expression for the LM curve (r in terms of Y).

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 two different equilibrium points A and B) 

• The labor supply changes and is now: NS = 30 + 9w . 
• K goes up from 8 to 9

f) (5 points) 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.

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.

g) (5 points) 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 desired consumption function has changed and is now:

Cd = 1440 + .50(Y-T) – 500r

h) (5 points) What could cause such a change in the desired consumption 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) (5 points) Given this change in desired consumption, solve for a “new” expression of the IS curve.

j) (5 points) Given the change in desired consumption and the change in Y, solve for the new goods market clearing interest rate. 

k) (5 points) 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) (10 points) Using a generic two period consumption 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 consumption has changed the way it has. Be sure to label your graph completely.

m) (5 points) Is the movement from A to B more consistent with Classical economic theory or Keynesian economic theory? Explain.