Economics
coachC = 3000 + 0.8 (Y – T) – 12,000r
I = 1000 – 25,000r
G = 2000
NX = –100
T = 1200
Suppose further that the following table describes the monetary policy rule of the Central Bank of Inflatoria:
Rate of inflation (π)  Real interest rate (r)  Shortrun equilibrium output Column C  Shortrun equilibrium output Column D 
0.01  0.02 


0.02  0.03 


0.03  0.04 


0.04  0.05 


a. [2 points] Find the equation for planned aggregate expenditure as a function of output and the real interest rate.
b. [4 points] Calculate the level of shortrun equilibrium output at each inflation rate. Show your work and complete column C in the table above.
c. [2 points] By hand, draw and label a diagram that shows the relationship between inflation and shortrun equilibrium output, i.e., the aggregate demand curve.
d. [2 points] Based on the aggregate demand curve you constructed for (c), suppose that when the inflation rate is 4%, the Inflatoria economy is at both a shortrun and a longrun equilibrium. What is the level of potential output? Add the inflation adjustment and longrun aggregate supply curves to your diagram.
e. [4 points] Suppose that a financial crisis causes autonomous consumption to fall by 400 and autonomous investment to fall by 300, so that the new functions are C= 2600 + 0.8(Y  T) – 12,000r and I = 700 – 25,000r. Now, what is the equation for planned aggregate expenditure as a function of output and the real interest rate? Calculate the new level of shortrun equilibrium output at each inflation rate; show your work and complete column D in the table above. Sketch a new diagram showing the relative positions of the old and new aggregate demand curves. In the short run, what is the new level of equilibrium output? What is the output gap?
f. [2 points] In response to the change in output in (e), suppose that the government declares that it will increase government purchases in order to raise GDP. Calculate the multiplier. Using the multiplier, determine by how much government purchases would need to be changed in order to raise GDP back to potential. Show your work.
g. [2 points] Instead of using government purchases as in (f), suppose that the government wants to reduce taxes in order to spur spending and raise GDP. By how much would taxes need to be reduced in order to raise GDP back to potential? Show your work. Is this change in taxes realistic?
h. [2 points] Instead of using government purchases or taxes, suppose that the Central Bank of Inflatoria plans to use monetary policy to raise GDP by changing the monetary policy rule. At the existing inflation rate, would the Central Bank need to raise, or lower, the real interest rate? To achieve potential output, what real interest rate should be set by the Central Bank? (Round to one decimal place.) Show your work.
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