3. The IS-LM Model
Consider an economy characterized by the following equations for consumption (C), investment (I), government spending (G), taxes (T), aggregate demand (Z), output (Y), and the interest rate (i):
C = 54 + 0.3*(Y – T)
I = 16 + 0.1*Y – 300*i
G = 35
T = 30
Z = C + I + G
i = ?
Suppose the central bank has set the interest rate equal to 2% (this is, ? = 0.02).
a) Find the equation for the IS relation. Find the equilibrium levels of output (Y*), consumption (C*), and investment (I*), and check that C*, I*, and G add up to Y*.
Suppose the government increases its spending by 6 to G’ = 41.
b) Find the equation for the new IS relation. Find the new equilibrium level of output (Y**). What is the value of the multiplier in this economy?
c) Find the new equilibrium levels of consumption (C**) and investment (I**). Explain intuitively why, despite the fact that public saving (T–G) went down, investment (if you did the math right) has actually gone up.
Suppose now that government spending remains at its original level of G = 35. Consider a drop-in consumer and business confidence that changes the consumption and investment equations to:
C = 44 + 0.3*(Y – T)
I = 8 + 0.1*Y – 300*i
d) Find the new equilibrium level of output (Y***).
e) Can the government reverse the effects of this decline in consumer and business confidence and restore the original output level Y* using fiscal policy alone (i.e., with no change in monetary policy)? If so, how much of a change in G (call it ?G) would it take? Explain.
As an alternative to raising G by ?G, could the government accomplish its goal (restoring Y*) by lowering taxes T by this same amount (?G) instead? Why or why not? Explain.
f) Can the central bank reverse the effects of this drop-in consumer and business confidence and restore the original output level Y* using monetary policy alone (i.e., with no change in fiscal policy)? If so, how much of a change in the interest rate ? would be necessary? Explain.
g) Propose a fiscal-monetary policy mix (i.e.: a simultaneous change in G and/or T and in ?) that accomplishes the goal of returning the economy to its original output level Y*.
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