Christina Romer and Jared Bernstein in "The Job Impact of the American Recovery and Reinvestment Plan" calibrated the impact of the proposed

Christina Romer and Jared Bernstein in "The Job Impact of the American Recovery and Reinvestment Plan" calibrated the impact of the proposed expansionary fiscal policy (we know it as an increase in G and/or a lower T) on jobs and GDP growth (Click Here for paper). In order to do so, they make assumptions about the size of Government spending and tax multipliers.  One important assumption is contained in the paragraph below about the level of the federal funds rate:

" For the output effects of the recovery package, we started by averaging the multipliers for increases in government spending and tax cuts from a leading private forecasting firm and the Federal

Reserve’s FRB/US model. The two sets of multipliers are similar and are broadly in line with other estimates. We considered multipliers for the case where the federal funds rate remains constant, rather than the usual case where the Federal Reserve raises the funds rate in response to fiscal expansion, on the grounds that the funds rate is likely to be at or near its lower bound of zero for the foreseeable future."

So in this question, we are going to employ some of the tools that we have acquired throughout the semester to understand how this assumption, "that the funds rate is likely to be at or near its lower bound of zero for the foreseeable future," effects the government spending and tax multipliers.

a) (30 POINTS) In this question, we are going to compare the size of the Government spending multiplier under two different assumptions: i) the Fed sits on their hands so that when G rises, r rises with it (the standard case), and ii) the Fed accommodates the (real) shock to money demand so that real interest rates remain constant.

In the space below, draw 4 diagrams (label them 1 through 4) with 1) a closed economy desired saving; desired investment diagram, followed by 2) an IS – LM diagram followed by 3) a money market diagram followed by 4) an aggregate supply ; aggregate demand diagram. 

We begin at our initial point A which is at an output well below potential GDP (i.e., there is a significant 'output' gap). We let G rise and with the assumption that the Fed sits on their hands (assumption i) above) we move to point B, which corresponds to an output closer to potential GDP, but still not quite there.  We then assume assumption ii) above so that the Fed accommodates the real shock to money demand to keep real interest rates constant.  This assumption takes us to point C, which is at potential GDP (i.e., the output gap is gone!).

Start at an initial equilibrium and label as point A in all diagrams, with all the associated market clearing variables denoted by subscript A.  For example, in your IS – LM diagram, the interest rate that clears the goods and money market is labeled as rA with the associated output at YA. Note importantly that we are assuming fixed prices throughout this exercise. Now let G rise to G' and show how all your graphs are affected.  In particular, locate point B in all graphs making sure you refer to each graph separately explaining the intuition of the movement from point A to point B.  Note, we are assuming assumption i), the Fed sits on their hands and does not accommodate the shock to real money demand.

b) (20 points for explanation) We now apply assumption ii), the one Romer and Bernstein use "that the funds rate is likely to be at or near its lower bound of zero for the foreseeable future." In terms of our analysis, the Fed is going to make sure that real rates remain at their initial level (i.e., they totally accommodate the real shock to money demand). Show this accommodation as point C on all of your diagrams. Recall that we are at full employment/potential GDP at point(s) C.  Again, make sure you refer to each graph separately explaining the intuition of the movement from point B to point C.  

c) (20 points) Now compare the government spending multiplier under assumption i) no Fed accommodation and ii) the Fed accommodates the real shock to money demand.  Be specific with regard to the multiplier as well as the intuition. To support your intuition, draw two diagrams: the user cost = MPKf and the two period consumption model clearly locating points A, B, and C.  Referring to your 2 graphs, explain the intuition as to why we move from point A to point B as well as why we move from points B to C. Be sure to label your graphs completely or points will be taken off.  Make sure you relate your discussion of your two graphs to the difference in the multiplier depending on what the Fed does or doesn't do.