9. Consider the following model of the economy: P E = C + I + G C = 20 + 0.75(Y T ) I = 5 0.5r G = 5 T = 4 a) Derive the IS curve. b) Suppose r = 4 and P E = 110. Is the economy in equilibrium? If not, explain how it will adjust back to equilibrium. c) Suppose that, fearing a recession, households reduce consumption so that C = 15 +0.75(Y T ). Using a diagram, show how this would affect equilibrium output. d) The government would need to raise output by 20 units to return the economy back to its initial level after the decline in consumption from part (c). By how much should it change taxes to achieve this goal? Is this feasible in this model?.

1. 9. Consider the following model of the economy:
P E = C + I + G
C = 20 + 0.75(Y T )
I = 5 0.5r
G = 5
T = 4
a) Derive the IS curve.
b) Suppose r = 4 and P E = 110. Is the economy in equilibrium? If not, explain how it
will adjust back to equilibrium.
c) Suppose that, fearing a recession, households reduce consumption so that C = 15 +0.75(Y T
). Using a diagram, show how this would affect equilibrium output.
d) The government would need to raise output by 20 units to return the economy back
to its initial level after the decline in consumption from part (c). By how much should
it change taxes to achieve this goal? Is this feasible in this model?