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Problem Set # 9
Solutions
Chapter 12
a. The invention of the new high-speed chip increases investment demand, which shifts the IS
curve out. That is, at every interest rate, firms want to invest more. The increase in the demand
for investment goods shifts the IS curve out, raising income and employment.
The increase in income from the higher investment demand also raises interest rates. This
happens because the higher income raises demand for money; since the supply of money does not
change, the interest rate must rise in order to restore equilibrium in the money market. The rise in
interest rates partially offsets the increase in investment demand, so that output does not rise by
the full amount of the rightward shift in the IS curve.
Overall, income, interest rates, consumption, and investment all rise.
b. The increased demand for cash shifts the LM curve up. This happens because at any given
level of income and money supply, the interest rate necessary to equilibrate the money market is
higher.
r (^2)
r (^1)
A
B
IS 1
Y
r
IS 2
LM
Y 1 Y 2
r (^2)
r (^1)
A
B
IS
Y
r LM 1
Y 2 Y 1
LM 2
The upward shift in the LM curve lowers income and raises the interest rate. Consumption falls
because income falls, and investment falls because the interest rate rises.
c. At any given level of income, consumers now wish to save more and consume less. Because of
this downward shift in the consumption function, the IS curve shifts inward.
Income, interest rates, and consumption all fall, whil einvestment rises. Income falls because at
every level of the interest rate, planned expenditure falls. The interest rate falls, because the fall in
income reduces demand for money; since the supply of money is unchanged, the interest rate
must fall to restore money-market equilibrium. Consumption falls both because of the shift in the
consumption function and because income falls. Investment rises because of the lower interest
rates and partially offsets the effect of the fall in consumption.
d. Expected inflation rises, so if the nominal interest rate remains the same, the real interest rate
has fallen. (Ordinarily we think of both inflation and expected inflation (and indeed often prices)
as fixed in the short run.) If the central bank maintains the same nominal interest rate, the real
interest rate fall shows up as the LM curve shifts down and to the right (it drops by the increment
to expected inflation); this provides the equivalent of a monetary stimulus, raising output through
the usual channels … until inflation rises as the short run ends and we enter the long run.
r (^1)
r (^2)
B
A
IS 2
Y
r
IS 1
LM
Y 2 Y 1
f. The LM curve gives the combinations of income and the interest rate at which the supply and demand for real balances are equal, so that the money market is in equilibrium. The general form of the LM equation is M/P = L(r, Y). Suppose income Y increases by $1. How much must the interest rate change to keep the money market in equilibrium? The increase in Y increases money demand. If money demand is extremely sensitive to the interest rate, then it takes a very small increase in the interest rate to reduce money demand and restore equilibrium in the money market. Hence, the LM curve is (nearly) horizontal, as shown in Figure 11–19.
An example may make this clearer. Consider a linear version of the LM equation:
M/P = eY – f r.
Note that as f gets larger, money demand becomes increasingly sensitive to the interest rate. Rearranging this equation to solve for r, we find
r = (e/ f) Y – (1/f)( M/ P).
We want to focus on how changes in each of the variables are related to changes in the other variables. Hence, it is convenient to write this equation in terms of changes:
r = (e/ f) Y – (1/f) (M/ P).
The slope of the LM equation tells us how much r changes when Y changes, holding M fixed. If (M/ P) = 0, then the slope is r/ Y = (e/ f). As f gets very large, this slope gets closer and closer to zero. If money demand is very sensitive to the interest rate, then fiscal policy is very effective: with a horizontal LM curve, output increases by the full amount that the IS curve shifts. Monetary policy is now completely ineffective: an increase in the money supply does not shift the LM curve at all. We see this in our example by considering what happens if M increases. For any given Y (so that we set Y = 0), r/ (M/ P) = ( – 1/f); this tells us how much the LM curve shifts down. As f gets larger, this shift gets smaller and approaches zero. (This is in contrast to the horizontal LM curve in part (c), which does shift down.)
Chapter 12
To raise investment while keeping output constant, the government should adopt a loose monetary policy and a tight fiscal policy, as shown in Figure 11–20. In the new equilibrium at point B, the interest rate is lower, so that investment is higher. The tight fiscal policy—reducing government purchases, for example—offsets the effect of this increase in investment on output.
The policy mix in the early 1980s did exactly the opposite. Fiscal policy was expansionary, while monetary policy was contractionary. Such a policy mix shifts the IS curve to the right and the LM curve to the left, as in Figure 11–21. The real interest rate rises and investment falls.
Chapter 12
The figure to the left shows what the IS-LM model looks like for the case in which the Fed holds
the money supply constant. The figure to the right shows what the model looks like if the Fed
adjusts the money supply to hold the interest rate constant; this policy makes the effective LM
curve horizontal.
Holding the Money Supply Constant Holding the Interest Rate Constant
a. If all shocks to the economy arise from the exogenous changes in the demand for goods and
services, this means that all shocks are to the IS curve. Suppose a shock causes the IS curve to
shift from IS 1 to IS 2. The figures below show what effect this has on output under the two
policies. It is clear that output fluctuates less if the Fed follows a policy of keeping the money
Y
r (^) LM
IS
Y
r
LM
IS
