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. 

a. 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.

b. 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. 

(a) Solve for the equilibrium output 

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

c. 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).