Goods and Financial Markets: The IS-LM Model
• In this chapter we will look at the;
1. Goods market and derive the IS relation.
2. Financial markets and derive the LM relation.
3. We will learn how output and the interest rate are
determined in IS-LM framework in the short run.
The Goods Market and the IS Relation
• Equilibrium in the goods market exists when production, Y,
is equal to the demand for goods, Z. We took I, G and T as
given (exogenous).
• And the equilibrium condition was given by:
Y = C(Y − T) + I + G
• In the simple model developed in chapter 3, the interest
rate did not affect the demand for goods. In the chapter 5
we will abandon this simplification and introduce the
interest rate through the investment function in our model
of equilibrium in the goods market.
•
Investment, Sales, the Interest Rate and Output
• In this chapter, we capture the effects of two factors affecting
investment:
• The level of sales (+) The interest rate (-)
I = I (Y , i )
• Taking into account the investment relation above, the
equilibrium condition in the goods market becomes:
•
Y = C(Y − T) + I(Y , i) + G
An Example of an Investment Function
• For simplicity, let us again (as for consumption) assume that
investment has a linear relationship with income. We also
incorporate an effect of interest rates on investment:
I  b0  b1Y  b2i
• This function corresponds to our assumptions about the
derivatives of I(Y, i) with respect to Y and i.
I  I (Y , i )
 
Equilibrium in the Goods Market
To determine equilibrium, use
C  c0  c1 (Y  T )
I  b0  b1Y  b2i
Then solve for equilibrium using
Y=Z:
Z  c0  b0  b2i  G  c1T
 c1  b1 Y
Y
1
c0  b0  b2i  G  c1T 
1  c1  b1
0  c0  b0  b2i  G  c1T
0  c1  b1  1
• The demand for goods is an increasing function of output.
Equilibrium requires that the demand for goods be equal to output.
• An increase in the interest rate
decreases the demand for
goods through the investment
at any level of output.
• An improvement in the
investors expectation for
the future, increases the demand
for goods through the investment
at any level of output.
The Effects of an Increase in the Interest Rate on Output
1
c0  b0  b2i  G  c1T 
Y 
1  c1  b1
dY
b2

di
1  c1  b1
Deriving the IS Curve
• Equilibrium in the goods market implies that
an increase in the interest rate leads to a decrease
in output. The IS curve is downward sloping.
• If in equilibrium:
1
c0  b0  b2i  G  c1T 
Y
1  c1  b1
• then can solve for i:
c0  b0  G  c1T
i
b2
(1  c1  b1 )Y

b2
Shifts of the IS Curve
1
c0  b0  b2i  G  c1T 
Y
1  c1  b1
•
•
•
•
•
An increase in taxes (T) shifts the IS curve to
the left.
A decrease in government spending (G) shifts
the IS curve to the left.
A decrease in consumer confidence (co )
shifts the IS curve to the left.
A deterioration in investors expectation for
the future (bo ) shifts the IS curve to the left.
An increase in the sensitivity of investments
to the interest rate (b2 ) shifts the IS curve to
the left.
Financial Markets and the LM Relation
• The interest rate is determined by the equality of the supply of
and the demand for money:
M  €YL i 

M = nominal money stock
€YL(i) = demand for money
€Y = nominal income
i = nominal interest rate
Equilibrium in the Financial/Money Market
The LM relation: In equilibrium, the real money supply is equal
to the real money demand, which depends on real income, Y,
and the interest rate, i:
• Nominal money supply is equal to
the nominal money demand
M  €YL i
• Real money supply is equal to the
real money demand
M
 YLi 
P
The Effects of an Increase in Income on the Interest Rate
An increase in income leads, at
a given interest rate, to an
increase in the demand for
money. Given the money
supply, this leads to an increase
in the equilibrium interest rate.
Notice that now the increase is
in real income (Y), not nominal
income (€Y).
Deriving the LM Curve
Equilibrium in financial markets implies that an increase in
income leads to an increase in the interest rate. The LM curve
is upward-sloping.
 Y level real income
corresponds with i
rate of interest
 Y’ level real income
corresponds with i’
rate of interest.
Shifts of the LM Curve
An increase in the money supply leads the LM curve to shift down.
Putting the IS and the LM Relations Together
(The IS-LM Model)
• Equilibrium in the goods
market implies that an
increase in the interest rate
leads to a decrease in output.
Equilibrium in financial
markets implies that an
increase in output leads to an
increase in the interest rate.
When the IS curve intersects
the LM curve, both goods
and financial markets are in
equilibrium.
IS relation: Y  C(Y  T )  I (Y , i )  G
LM relation:
M
 YL(i )
P
Fiscal Policy, Activity, and the Interest Rate
• Fiscal policy affects the IS curve, not the LM curve.
• Recall from the chapter 3. T - G gives us the budget balance.
If T > G there is a budget surplus
If T < G there is a budget deficit
If T = G there is a balanced budget
• Fiscal contraction, or fiscal consolidation, refers to fiscal
policy that reduces the budget deficit /or increases the budget
surplus.
• An increase in the deficit /or decrease in the surplus is called a
fiscal expansion.
The Effects of a Contractionary Fiscal Policy
A fiscal contraction
(increase in taxes or
decrease in government
spending) shifts the IS
curve to the left, and
leads to a decrease in the
equilibrium level of
output and the
equilibrium interest rate.
Monetary Policy, Activity, and the Interest Rate
• Monetary contraction, or monetary
tightening, refers to a decrease in
the money supply.
• An increase in the money supply is
called monetary expansion.
• Monetary policy does not affect the
IS curve, only the LM curve. For
example, an increase in the money
supply shifts the LM curve down.
• Monetary expansion leads to higher
output and a lower interest rate.