part 1

1. (35 points total) We discussed the idea of crowding out and why it occurs. In this problem we are considering two scenarios: Scenario 1: G rises and the Fed does not accommodate the shock to money demand. Scenario 2: G rises and the Fed accommodates the shock to money demand, as they would if they were committed to the zero bound.

(10 points for each correct and completely labeled diagram). Draw three diagrams side by side. On the left, draw a consumption function, in the middle, draw a money market diagram, and on the right, draw an investment demand function.  Locate the initial equilibrium as point A, labeling the relevant values using subscript A as in the level of consumption at point A as CA, the level of interest rates as iA, etc. Scenario 1: G rises, no accommodation by the Fed, locate the new equilibrium as point B on all three diagrams, being sure to label your diagrams completely. Show and explain the crowding out that Barro discusses in the “Government Spending is no Free Lunch” article.  In particular, we are assuming total crowding so that Y does not change, along with the assumption of a closed economy. Be sure to explicitly identify the crowding out on the consumption function and investment demand functions that you drew above. Scenario 2: G rises, the fed completely accommodates the shock to money demand so that interest rates remain unchanged (identical to the Romer assumption). Show this development as point C on all three diagrams.(5 points) In the Romer paper, the multipliers that they use assume that the Fed will keep interest rates constant for the foreseeable future. Referring to your diagrams, does this assumption increase/decrease/ or have no effect on the estimated spending multiplier? Explain.

2. (25 points total) Consider the following model

i) C = 1500 + mpc (Y – tY)

ii) I = 800

iii) G = 500

iv) X – M = 500 – mpi (Y)

where:

t = the (flat) tax rate

mpc = the marginal propensity to consume

mpi = the marginal propensity to import

suppose mpc = .80, t = .25, mpi = .2

a.    

(5 points) solve for the equilibrium output

b.     (5 points)  Solve for the (government) spending multiplier.

c.     (10 points) When we discussed the multiplier we discussed the impact effect.  For example, suppose that G increases by 100 to 600 and we assume, as we often do, that firms match the increase in demand by increasing Y by 100.  In round two, this is an increase in income of 100 to consumers. Trace out exactly where this 100 increase in income goes in the second round and compare to our simpler treatment with a closed economy and lump sum taxes. Hint, there are three leakages to address(again, please be very specific as to where the 100 increase income ‘goes’ in this second round).

d.     (5 points) What would happen to the multiplier if the mpi rises to .25.  Please explain the intuition.