Learning Objectives
• Understand the relationship between the
aggregate expenditure function to
graphically derive the IS curve.
• Learn how to shift the IS curve
• Understand how government spending, and
taxes shift the IS curve.
The IS Schedule
• The IS schedule plots every income interest
rate (Y, r) combination that results in
equilibrium in the real goods market.
– The IS schedule is an equilibrium schedule.
• At every point on an IS schedule, aggregate
expenditures are just equal to aggregate supply.
The IS Schedule: Derivation
AE
AE(r1)
E2
AE(r2)
E1
0
r
r2
Y1
Y
E1
E2
r1
0
Y2
Y
Y
IS
Y
At E1, where the interest rate is r2,
aggregate expenditures equal aggregate
supply, and the the equilibrium level
of income is Y1.
At E2, where the interest rate is r1,
aggregate expenditures equal aggregate
supply, and the equilibrium level of
income is Y2.
The points E1 and E2 are two points on an
IS schedule. Each point represents an
income/interest rate combination that
yields equilibrium in the real goods market.
The IS Schedule: Derivation
• At the equilibrium point E1, where the interest
rate is assumed to be r2, aggregate
expenditures just equal aggregate supply.
• Let the interest rate fall to r1, causing interest
sensitive spending to rise.
• Equilibrium now occurs at E2, where aggregate
expenditures, AE(r1), are just equal to
aggregate supply.
The IS Schedule: Derivation
• The points E1 and E2 can be transferred from the
top graph to the bottom graph.
– To transfer E1, we find the point Y1, r2 in the bottom
graph.
– To transfer E2, we find the point Y2, r1 in the bottom
graph.
• The points E1 and E2 are two points on an IS
schedule.
– Each point represents an income/interest rate
combination that yields equilibrium in the real goods
market.
The IS Schedule:Shifts
AE
AE(r1)
E2
AE(r1)
A shift in the IS schedule occurs
when there has been a change in
spending that is not caused by a
change in the rate of interest.
E1
0
r
r1
0
Y1
Y2
E1
Y
Increases in spending shift the IS
curve to the right; decreases in
spending shift the IS curve to the
left.
E2
IS1
IS2
Y
The IS Schedule: Shifts
• At point E1, the equilibrium level of income is
Y1 and the interest rate is r1.
– Let spending increase with no change in the rate of
interest.
• The aggregate expenditure curve shifts up to AE(r1),
and income increases to Y2.
– The interest rate is still r1.
• The new equilibrium occurs at the point E2.
• When we transfer the points E1 and E2 to the IS
graph, E1 represents a point on IS1 and E2 a
point on IS2.
IS: The Algebra
• IS
Y = C + I + G + NX where C = a + b(Y – tY), I = e – dr
and NX = X – nr – (M + mY)
Y = a + b(Y – tY) + I – dr + G + X – nr – M
Y – bY + btY + mY = a + I – dr + G + X – nr – M
1
Y=
1– b(1 – t) + m a + I – dr + G + X – nr – M
IS: The Algebra
• IS
Y=
1
1– b(1 – t) + m a + I – dr + G + X – nr – M
• Note:
– The inverse relationship between Y and r
– The coefficient of t is negative.
• Increases in t rotate the IS to the left; decreases rotate it right
– The coefficients of G, I and X are positive
• Increases (decreases) in G, I and X shift the IS right (left).
– The coefficients M and m are negative
• Increases (decreases) in M and m shift (rotate) IS right (left).
Net Exports and the IS
• Net exports are assumed to be determined by
domestic interest rates and domestic GDP.
– Exports: X = X – nr
• As interest rates rise, the dollar rises, and exports fall
by n times the change in r.
– Imports: M = M + mY
• As GDP rises, imports rise by m times the change in Y.
– Net Exports: X – M = X – nr – ( M + mY) =
NX = X – nr – M – mY
Explaining Exchange Rates with
Interest Rate Parity
• Interest rate parity says that the higher
domestic real rates of interest are relative to
foreign real interest rates, the higher will be
the value of the domestic currency, other
things remaining the same.
Learning Objectives
• Understand how people choose how much money to
demand.
• Learn how money demand changes when interest
rates and income change.
• Understand how money supply and money demand
interact to determine the equilibrium rate of interest.
• Understand the relationship between money demand
and money supply can be used to derive the LM
curve
• Learn how to shift the LM curve.
The Money Market
• Interest rates are determined in the money
market through the interaction of money
supply and money demand.
Money Supply
• The supply of real money balances is defined as
the ratio of nominal money balances and the
price level, M/P.
– where M is the nominal money supply and P is the
price level.
• The money supply is assumed to be an exogenous
variable determined by the central bank.
• The price level is also assumed to be exogenous as
well as fixed in the short run.
• As a result, the real money supply is assumed to be
fixed in supply and invariant with respect to the
interest rate.
Money Demand and Interest Rates
• Money demand is assumed to be determined
by both the level of income and interest rates.
• Md = L(r, Y).
• The interest rate is the cost of holding money.
• As r rises, the opportunity cost of holding
money rises and people hold less.
• As r falls, the opportunity cost of holding
money falls and people hold more.
Money Demand and Income
• Money demand is assumed to be determined
by both the level of income and interest rates.
• Md = L(r, Y).
• People hold money to make transactions.
• Higher levels on Y are associated with more
transactions. Money demand increases.
• Lower levels of Y are associated with fewer
transactions. Money demand decreases.
The Money Market
The equilibrium rate of interest is
determined by the intersection of
money demand and money supply.
r
Money supply is vertical because M/P
does not vary with the interest rate.
re
Md=L(r, Y)
0
M/P
Money
Money demand slopes down because
the opportunity cost of holding money
rises and falls with r.
The Money Market: Money Demand
Shifts
Increases in Y shift money demand
to the right.
r
Higher levels of income increase the
transactions demand for money
Decreases in Y shift money demand
to the left.
0
Md=L(r, Y3)
Md=L(r, Y2)
Md=L(r, Y1)
M/P
Money
Lower levels of income decrease the
transactions demand for money.
The Money Market: Monetary
Policy
r
M/P1 M/P2 M/P3
Contractionary monetary policy shifts
M/P to the left, increasing the
equilibrium interest rate.
r2
Expansionary monetary policy shifts
M/P to the right, decreasing the
equilibrium interest rate.
re
r1
Md=L(r, Y)
0
M/P1 M/P2 M/P3
Money
The LM Schedule: Derivation
r
r2
r1
LM
r
E2
E2
E1
E1
Md=L(r, Y2)
Md=L(r, Y1)
0
M/P
Money
0
Y1 Y2
Y
The LM Schedule: Derivation
• At point E1, money demand equals money
supply
– The equilibrium interest rate and level of income are
r1 and Y1. This combination is one point on the LM
schedule.
• Let Y rise to Y2.
• At the point E2, money demand equals money
supply
– The equilibrium interest rate and level of income
now are r2 and Y2. This combination is another
point on the LM schedule.
The LM Schedule: A Decrease in the
Money Supply
r
r2
r1
LM2 LM
r
E2
1
E2
E1
E1
Md=L(r, Y1)
0
M2/P M1/P
Money
0
Y1
Y
A Decrease in the Money Supply
• At the point E1, money demand equals money
supply.
– The equilibrium interest rate and level of
income are r1 and Y1 respectively.
• Let the money supply decrease, causing the
interest rate to rise to r2. Income is still Y1.
• Equilibrium now occurs at the point e2.
• The point E2 lies on LM2 because it represents
equilibrium in the money market when Y = Y1
and r = r2.
The LM Schedule: An Increase in
the Money Demand
LM2
r
r
r2
E2
r1
E1
0
M1/P
LM1
E2
Md2=L(r, Y1)
Md1=L(r, Y1)
Money
E1
0
Y1
Y
An Increase in Money Demand
• At the point E1, there is equilibrium in the
money market.
– The equilibrium interest rate and level of income
are r1 and Y1 respectively.
• Let money demand increase. Y is still Y1.
• Equilibrium now occurs at E2, where r is r2 and
Y is Y1.
• The point E2 lies on LM2 because it represents
equilibrium in the money market when Y is Y1
and r is r2.
LM: The Algebra
• LM
– M/P = L(r,Y)
• L(r,Y) = eY – fr where e and f >0
– M/P = eY – fr
– r = (e/f)Y – (1/f) M/P
• Note:
– The positive relationship between r and Y
– The coefficient of M/P is negative
• Decreases (increases) in M/P shift the LM left (right).
IS/LM: Equilibrium
r
LM
The intersection of the IS curve
and the LM curve shows the
interest rate and income level
that satisfy equilibrium in the
real goods market and
equilibrium in the money market.
r
IS
0
Y*
Y
Fiscal Policy
• Fiscal Policy: A tool of macroeconomic
policy that seeks to influence the level of
economic activity through control of
government expenditure and taxation.
– Expansionary Fiscal Policy
• Decreases in taxes and/or increases in spending that
tend to increase economic activity.
– Contractionary Fiscal Policy
• Increases in taxes and/or decreases in spending that
tend to dampen economic activity.
Fiscal Policy: Demand Side
Transmission Mechanism
Investment
Spending Rises
Government
Spending
Falls
Deficit
Decreases
Aggregate
Spending
Decreases
Taxes
Increase
Contractionary Fiscal Policy
Interest Rates
Fall
Export
Spending Rises
IS/LM: Contractionary Fiscal Policy
r
A decrease in G or an increase in T
shifts the IS curve to the left.
LM
If r does not change, Y falls by the
amount Y1Y3 = E1B. But at point B,
Y1<Y3 so Md < MS, causing interest
rates to fall.
r1
B
E2
r2
0
E1
IS1
Y1
Y2
Y3
IS2
Y
As r falls, interest sensitive spending
rises. Equilibrium is reached at
Y2 and r2.
Government Spending
• Transmission Mechanism
– The decrease in government spending causes
aggregate spending and the IS curve to shift left.
– As GDP falls, the transactions demand for money
falls.
– If the supply of money does not change, interest
rates fall.
– As interest rates fall, some interest sensitive
spending rises.
– Equilibrium occurs at Y2 and r2.
Taxes and the IS Curve
• Transmission Mechanism
– An increase in taxes decreases disposable
income and consumption, causing the IS curve
to rotate to left.
– As GDP falls, the transactions demand for
money falls. If the supply of money does not
change, the interest rate falls.
– As the interest rate falls, some interest sensitive
spending rises.
– Equilibrium occurs at Y2 and r2.
Monetary Policy
• A tool of macroeconomic policy under the
control of the Federal Reserve that seeks to
attain stable prices and economic growth
through changes in the rate of growth of the
money supply.
Monetary Policy
• Expansionary Monetary Policy
– An increase in the money supply designed to
decrease interest rates and thus increase interest
sensitive spending
• Contractionary Monetary Policy
– A decrease in the money supply designed to
increase interest rates and thus decrease interest
sensitive spending.
Interest Rate Channel
Change in
Money Supply
Change in
Interest Rates
Change in
GDP
Change in
Exchange
Rates
Monetary Policy
• Transmission Mechanism
– The increase in the money supply increases
liquidity in the portfolios of individuals.
• Money supply is now greater than money demand at
the current rate of interest.
– People rebalance their portfolios by using the
excess liquidity to buy other assets such as
bonds.
– As the price of bonds rises, interest rates fall.
Monetary Policy
• Transmission Mechanism
– The increase in the money supply decreases
interest rates and the value of the dollar.
– As the value of the dollar falls, exports increase
and imports decrease.
Interest Rate Parity: Example
• Assume that U.S. real interest rates are
higher than those in other countries.
– The high rates of return on U.S. assets will
attract foreign buyers, but in order to buy
U.S. financial assets, foreigners must first
buy dollars.
Interest Rate Parity: Example
• The demand for dollars increases in the
global marketplace, causing the dollar to
appreciate.
• The supply of the other currency increases
in the global marketplace, causing it to
depreciate.
IS/LM: Expansionary Monetary
Policy
LM1
LM2
r
An increase in the money supply,
other things remaining the same,
means that at r1 and Y1, money
demand is less than money supply.
The excess supply puts downward
pressure on interest rates, and as
r falls, interest sensitive spending
and Y rise.
r1
r2
IS
0
Y1 Y2
Y
IS/LM: Interaction of Fiscal and
Monetary Policy
r
LM
What happens when fiscal policy
is expansionary and monetary
policy is contractionary?
r
IS
0
Y*
Y
IS/LM: Interaction of Fiscal and
Monetary Policy
r
LM
What happens when both fiscal and
monetary policy are expansionary?
r
IS
0
Y*
Y