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2) Deriving the IS-LM model: Assume an economy is characterized in the short run by the
following set of equations, with the price level fixed at 1.0 (SRAS is P = 1):
C = 0.8(Y-T) T = 1000
I = 800- d r, where d=20 (M/P)d = eY – f r, where e=0.4, f=40
G = 1000 (M/P)s = 1,200
(Use the SRAS curve: P=1).
Where C is consumption, I investment, G government purchases, T taxes, P price level, and (M/P)d
real money demand.
a) Write a formula for the IS curve, expressing r as a function of Y. Graph it.
b) If firms did not care at all about the interest rate when making investment expenditure plans
(such as if d=0), how would this affect the slope of the IS curve?
c) Write a formula for the LM curve expressing r as a function of Y. Graph it.
d) If people did not care at all about their income level when deciding how much money to hold
(if e=0), what would be the slope of the LM curve?
e) What are the short-run equilibrium values for GDP, real interest rate, consumption, and
investment in the economy described by the equations in the box above?
f) Suppose that the Fed stimulates the economy by raising the money supply by 200. By how much
will Y increase in the short-run equilibrium? Illustrate this with a graph of the IS-LM curves.
What happens to investment (rise, fall, no change; explain why)? What happens to consumption?
g) Discuss how the impact on Y in part (f) depends on the value of the parameter d, which
summarizes the responsiveness of investment expenditure to the interest rate.
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