Transcript I(r)

Ec 123
Section 5
THIS SECTION
IS-LM Analysis
– A simple model
– A slightly more sophisticated model
– Connection with our overlapping generations model?
Ec 123
Section 5
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Keynesian demand-side explanation for
recessions
• Lowered confidence in the future leads to low demand for goods and
services.
• Low demand leads to unemployed resources (leakages).
• Prices are sticky; i.e, it takes quite a while for prices to change enough
to absorb the unemployment.
• Note the two crucial assumptions in the story:
Demand for goods and services is volatile.
Prices are slow to adjust.
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IS-LM model
• IS-LM is a model of how the economy responds in the
short run to shocks in demand as well as changes in
economic policy.
• The model supposes that, in the short run, interest rates are
very flexible but other prices, such as wages, are sticky and
take longer to adjust.
– We are implicitly assuming prices a fixed at an artificially high
price P so that there is excess supply (insufficient demand)
(suppliers would be willing to supply more at the same price).

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IS-LM Terms
For the IS/LM model, terms such as money and income and savings and
investment have more precise meanings than they do in informal usage.
It is important to know the precise definitions.
Money = M1 = currency plus demand deposits, where demand deposits
are non-interest bearing checking accounts. By the M1 definition,
holding a bank savings account is not holding money.
Y = real income = real GDP, the total output of goods and services for the
economy. Income is a flow, meaning, it is measured over time (ex.,
quarterly or annually).
– Note: Income is the total goods and services the economy produces.
Money and income are not the same thing. Typically, a country uses the
same stock of money several times to purchase its annual income!
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IS-LM Terms
T = total taxes paid to the government.
Y - T = disposable income.
C = expenditures devoted to consumption.
G = total expenditures by government
I = private investment = total private expenditures on plant and
equipment.
S = total savings
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IS-LM Terms
It is important to recall the difference between savings and investment.
Saving is the act of deciding to put income aside. Investment is the act
of deciding what project to do with the savings.
Example: Suppose that, in order to raise the funds to build a new plant, a
firm issues bonds. The bond-holders are saving, and the bond issuer
(the firm) is investing. Alternatively, bond-holders supply savings and
bond-issuers demand savings.
– In equilibrium (without govt.) I = S
r = the interest rate paid by investors to compensate savers for funds. For
simplicity, we assume there is one interest rate.
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Relationships between variables
I(r) is the investment function and is obviously a function of
the interest rate.
• The interest rate is the price investors pay for funds, so
when r goes up, I goes down.
MD(r, Y) is money demand or the demand for liquidity.
• Money demand is a function of the interest rate and
income.
• When the interest rate rises (all other things fixed), the
opportunity cost of holding money increases, and so
money demand falls.
• When income rises (all other things fixed), agents will
want to spend more, and so money demand rises.
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Deriving the IS Curve
Suppose for the moment that all income in the economy is
devoted to consumption. How much consumption will
consumers choose? We assume that consumption is a
function of disposable income, Y - T. The following is an
example:
C = 5000 + .75(Y - T)
• The coefficient on the Ye-T term can be interpreted as the
marginal propensity to consume. Suppose the tax bill, T, is
a fixed number.
• In equilibrium expenditures (on consumption) must equal
expected income, or Yd = C, Since we are supposing C is
the only use for income, Yd = Y.
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Deriving the IS Curve
Yd=Y
Yd
Expenditures
C
equilibrium
Income (Y)
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Deriving the IS Curve
•The other elements of
the expenditure breakout
of GDP are assumed
to be autonomous, or
they do not depend
directly on
(expected) income.
equilibrium
Yd
Government
spending
Yd=Y
C+I+G
C
Investment level
is fixed given the
interest rate.
G
I(r)
•Suppose the interest
rate is fixed.
Income (Y)
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Deriving the IS Curve
•Now suppose that
the interest rate (r)
varies. When r
moves, we expect
that I will move in
the opposite
direction.
Yd
New equilibrium
Yd=Y
C+I(r1)+G
C+I(r0)+G
Interest rate
goes down
from r0 to r1
•With the change in
investment, the
goods market will
move to a new
equilibrium.
I(r1)
I(r0)
Income (Y)
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The IS curve
Yd=Y
C+I(r1)+G
C+I(r0)+G
Yd
The IS curve
gives the
combinations of
Y and r that
produce
equilibrium in
the goods
market.
Interest rate
goes down
from r0 to r1
Income (Y)
Int.
Rate
(r)
r0
r1
IS
Y0
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Y1
Output (Y)
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What determines how steep the IS curve will be?
C+I’(r1)+G
Yd
The
responsiveness
of I to interest
rates determines
the slope of the
IS curve.
(interest rate
elasticity)
C+I(r1)+G
C+I(r0)+G
Income (Y)
r
r0
More responsive
I implies a flatter
IS curve.
IS’
r1
Q0
Ec 123
Section 5
IS
Q1
Q’1
Output (Y)
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The Money Market
Interest
Rate
r
The LM curve is
determined by
equilibrium in the money
market.
• Assume that the supply of
money MS is fixed (or
inelastic) in the short run.
• Then the equilibrium will be
the interest rate (the price of
money) where MD = MS.
MS
r1
If income increases (Y1 >
YO), demand for money will
increase (shift). If the Fed
does not increase the
money supply, interest
rates will increase (to r1).
r0
MD(Y1)
MD(Y0)
Money
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Deriving the LM curve
Int.
Rate
r
MS
Interest
Rate
r
r1
r1
r0
r0
The LM curve gives
the combinations of
Y and r that produce
equilibrium in the
money market.
LM
MD(Y1)
MD(Y0)
Money
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Y0
Y1 Output (Y)
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What determines how steep the LM curve will be?
r’1
MS
LM’
Interest
Rate
r
r1
LM
r1
MD(Y1)
r0
Money demand is less
sensitive to changes
in the interest rate.
(less elastic)
r0
New LM curve is
steeper if money
demand is less
sensitive to changes
in interest rates.
M’D(Y1)
MD(Y0)
M’D(Y0)
Money
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Y0
Y1 Output (Y)
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Putting the IS and LM curves together
Int.
Rate
r
Interest
Rate
r
Describes all
possible equilibria in
the goods market.
LM
Describes all
possible equilibria in
the money market.
IS
Output (Y)
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Output (Y)
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Putting the IS and LM curves together
Int.
Rate
r
LM
Only combination of
Y and r that is an
equilibrium in both
the goods and
money market.
r
IS
Y0
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Output (Y)
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IS-LM and policy analysis
IS-LM analysis is good for understanding the qualitative
effects of various policy changes or short term shocks to
the system.
• Changes in fiscal policy (i.e., changes in G and T) will
shift the IS curve.
• Changes in monetary policy will shift the LM curve.
• Shocks (exogenous events) may also shift either curve.
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The 2008 Stimulus Package
Yd=Y
C+I(r0)+G’
C+I(r0)+G
Yd
Govt. spending shifts
from G to G’.
•Expansionary
fiscal policies shift
the IS curve to the
right.
•Contractionary
fiscal policies shift
the IS curve to the
left.
Income (Y)
Int.
Rate
(r)
r0
IS’
IS
Y0
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Y1
Output (Y)
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The 2008 Stimulus Checks (150 billion)
Int.
Rate
r
LM
Output goes up (Y’ > Y) but
so does interest rates (r’ >
r).
r’
r
IS’
IS
Y Y’
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Output (Y)
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What determines the size of the shift?
d
Y =Y
C’+I(r0)+G’
Yd
C’+I(r0)+G
C+I(r0)+G’
C+I(r0)+G
•The slope of the
consumption line
determines the size
of the shift.
•C’ has a higher
marginal propensity
to consume than C
so fiscal policy
results in more
growth.
Expansionary
Fiscal Policy:
G’>G
Income (Y)
Int.
Rate
(r)
r0
Y0
Ec 123 Section 5
IS’IS’
IS
Y1 Y’1
Output (Y)
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The Fed announces a lower interest rate target
Int.
Rate
r
MS
M’S
Interest
Rate
r
r
r
r’
r’
LM
LM’
MD(Y0)
To achieve the
lower target (r’) the
Fed must increase
the money supply.
Money
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Y0 Output (Y)
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The Fed announces a lower interest rate target.
Int.
Rate
r
•Expansionary
monetary policies
shift the LM curve
to the right.
•Contractionary
monetary policies
shift the LM curve
to the left.
LM
LM’
Output goes up (Y’ > Y) but
interest rates do not go
down as much as targeted.
r
r”
r’
IS
Y Y’
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Output (Y)
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Relative slope of IS and LM curves determines the
effectiveness of fiscal v. monetary policy
Int.
Rate
r
LM
Good for monetary
policy:
Big growth with
little change in
interest rates.
LM’
Int.
Rate
r
Good for fiscal
policy:
Big growth with
little crowding out.
LM
r’
r
r
r’
IS
IS’
IS
Y0
Y’
Output (Y)
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Y0
Y’
Output (Y)
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Summary
The IS curve:
• Gives the combinations of Y and r that produce equilibrium in the goods
market.
• Slopes down.
• Shifts to the right when there is an increase in government spending and shifts
to the left when there is a decrease in government spending.
• Shifts to the left when taxes increase. Shifts to the right when taxes decrease.
• Is relatively flat in the interest elasticity of investment is relatively high. Is
relatively steep if the interest elasticity of investment is relatively low.
The LM curve:
• Gives the combination of Y and r that produce equilibrium in the money
market.
• Slopes upward.
• Shifts downward with an increase in the money supply and shifts upward with
a decrease in the money supply.
• Is relatively steep if the interest elasticity of money demand is relatively low.
Is relatively flat if the interest elasticity of money demand is relatively high.
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