(The IS-LM-PC model): Suppose that the following behavioral relations characterize the goods market in period t: (1) C t = 60 + 0.5YD t (2) I t = 90...

2. (The IS-LM-PC model): Suppose that the following behavioral relations characterize the goods market in period t: 

(1) C t = 60 + 0.5YDt

(2) I t = 90 + 0.25Y t - 200(r t + x t)

(3) G t = 500; T t = 100

(4) x t = 0

(a) Derive the IS curve (as a relation between Yt and rt ).

(b) Assume the LM curve is given by r t = 0.05 (i.e. in period t, the central bank sets the real interest rate at 5 %). What is the short-run equilibrium level of output (Yt )?

(c) Suppose that L = 2950 and un = 0.20 (where L: total population, un=natural rate of unemployment). Calculate the value of potential output (Yn). How does Yn compare to the short-run equilibrium level of output (Yt )? 

(d) Calculate the natural rate of interest (rn). How does rn compare to rt? 

(e) Consider that the Phillips Curve is given by:

[π t − π t-1 = 0.05 (Yt − Yn )]

Calculate the change in inflation in period t.

(f) Draw the IS-LM-PC graph.

(g) Assume that the government intervenes in period t+1 by conducting a fiscal policy consolidation. This one-time intervention can be seen as a 5 % decrease of government spending. 

(1) Derive the new IS and calculate the new short-run equilibrium in period t+1? How does Yt+1 compare to Yn?

(2) Calculate the new natural rate of interest (rn) in period t+1. Assuming that the central bank does not change the initial real interest rate target, how would the new rn compare to rt+1? 

(h) Redraw the IS-LM-PC graph and represent the effects of this policy shift. 

(i) Given the state of this economy toward the end of period t+1, what choice would you advise to policy- makers for period t+2? (Choose among A, B, C and D). Explain why.

A. The central bank should conduct a contractionary monetary policy in period t+2, thus raising the real interest rate.

B. The central bank should conduct an expansionary monetary policy in period t+2, thus lowering the real interest rate.

C. The government should continue its program of fiscal consolidation in period t+2.

D. The government should reverse its program of fiscal consolidation in period t+2.