Dynamic Macroeconomics

15.1.2 The IS-LM Model

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A more general form of the basic Keynesian model considers that aggregate
investment depends on the real interest rate and introduces the equilibrium
condition in the market for money to analyze the simultaneous determination
of real output and the interest rate. This form is analyzed in chapters 10–18
of Keynes [1936], and was codified as the IS-LM model, in an important
paper by Hicks [1937].
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The main difference from the previous model of the Keynesian cross is
that investment ceases to be treated as exogenous, and is considered to
depend negatively on the real interest rate. Assuming that inflationary
expectations are given, investment will depend negatively on the current
nominal interest rate. Consequently, the equilibrium condition in the goods
and services market takes the form
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where i is the nominal interest rate. The effect of the nominal interest rate on
investment is assumed to be negative:
Equation 
(15.6)
describes the combinations of real output and the nominal
interest rate that ensure equilibrium in the market for goods and services. It is
depicted as the downward-sloping investment-savings (IS) curve in 
figure
15.2
.

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Figure 15.2
Aggregate output and the nominal interest rate: the IS-LM model.
When a new endogenous variable (the nominal interest rate) is introduced,
one should analyze how it is determined. This is done through introducing the
equilibrium condition in the money market. This condition states that the
demand for money (which is assumed to be a positive function of aggregate
output and a negative function of the nominal interest rate) is equal to the
money supply (as defined by the policy of the central bank). The equilibrium
condition in the money market takes the form
where M is the nominal money supply, P the price level (which is considered
as given in this version of the model), and m the demand function for real
money balances (liquidity preference, in the terminology of Keynes).
The properties of the money demand function are described by

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Equation 
(15.7)
describes the combinations of real output and the nominal
interest rate that are consistent with equilibrium in the money market, in the
sense that money demand is equal to the exogenous money supply for the
given price level. It is depicted as the upward-sloping LM (liquidity-money)
curve in 
figure 15.2
.
Real output and the nominal interest rate are determined at the point where
both the market for goods and services and the market for money are in
equilibrium. At the point of intersection of the IS curve (which describes
equilibrium in the market for goods and services) and the LM curve (which
describes equilibrium in the money market), the economy is thus in short-run
equilibrium. Because the price level is assumed to be fixed, this equilibrium
can occur at less than full employment. In fact, this is the assumption usually
made in Keynesian models.
It is simple to deduce that an increase in government expenditure or a tax
cut shifts the IS curve to the right and causes an increase in real output and
the nominal interest rate. It is also simple to deduce that an increase in the
money supply shifts the LM curve to the right and causes an increase in real
output and a reduction in the nominal interest rate. Both fiscal and monetary
policies can thus lead to an increase in aggregate demand and an increase in
real output and employment. This is the mechanism through which aggregate
demand policies affect output and employment in Keynesian models.
The advantage of the IS-LM model over the Keynesian cross is that the IS-
LM model can be used to analyze the impact of monetary policy in addition
to fiscal policy. An increase in the money supply increases aggregate demand
in the short run by reducing interest rates and thus causing an increase in
investment. This of course requires that nominal interest rates can in fact be
reduced through monetary policy.
If expectations about the future are such that people hoard cash and the
demand for money demand becomes infinitely elastic at the current interest
rate (or if interest rates are close to zero, and zero is the lower bound), then
monetary policy loses its ability to increase aggregate demand through
increases in the money supply. Such a situation, which was mentioned in
chapters 13 and 15 of the General Theory, came to be known as a liquidity
trap. We shall return to an analysis of such a case when we discuss the role
of monetary policy in chapter 20.
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