Download The LM Curve - Imperial College London

Economic
Environment
Lecture 5
Joint Honours 2003/4
Professor Stephen Hall
The Business School
Imperial College London
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Revision
• Money demand is:
• positively related to income; the more income people
have, the more money they want to hold.
• negatively related to the interest rate; because the
higher is the interest rate, the more people would
prefer to save rather than hold money.
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Money Supply & Demand
• For a given level of income, there is an interest rate, which
will induce households and businesses to demand exactly
the amount of money, which the government has chosen to
supply. We will call this the “money market equilibrium”,
and depict it as follows:
Money supply
i
ie
Money demand
M
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money
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The LM Curve
• The previous diagram shows the equilibrium
interest rate for a given level of income “Y”.
(Note the functional notation on the money
demand curve).
• But we do not yet know what Y is! Remember,
Ye is what we are trying to find.
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The LM Curve
• According to our first assumption, money demand will
increase (i.e. visually shift rightward) as income
increases. As this happens, the equilibrium interest
rate “ie “ will also increase
Money supply
i
i2
i1
Md(Y2)
i0
Md(y0}
M
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Md(Y1)
money
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The LM Curve
• Therefore, all we really have is a set of interest
rate/income combinations that will serve to clear the
money market. If we plot the i, Y combinations
explicitly, we have what is known as the LM-Curve.
i
LM-curve
i2
i1
i0
Y0
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Y1
Y2
Y
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The LM Curve
r
r
LM
r1
r1
r0
LL1
r0
LL0
L0
Real money
balances
Y0
Y1
Income
At income Y0, money demand is at LL0 and equilibrium
in the money market requires an interest rate of r0.
At Y1, money demand is at LL1,and equilibrium is at r1.
The LM schedule traces out the combinations of real income
and interest rate in which the money market is in equilibrium.
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This Week
• The LM curve shows combinations of Y
and i which give equilibrium in the money
market
• The IS curve shows combinations of Y and
i which give equilibrium in the goods
market
• This week we put the two together.
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IS-LM Equilibrium
• We looked first at the commodities market, and then at the money
market. Once the interest rate was introduced as a variable, we
were unable to solve for the exact equilibrium output level (or
equilibrium interest rate) for either market. Instead, we obtained
the following two relationships:
The IS-curve:
• Shows combinations of interest rate and output that put the
commodities market in equilibrium.
The LM-curve:
• Shows combinations of interest rate and output that put the money
market in equilibrium.
• When viewed as mathematical equalities, the IS-LM curves are
simply two equations in two unknowns (ie and Ye). Therefore, they
can be solved simultaneously.
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IS-LM Equilibrium
Putting the two curves together:
LM-curve
Interest
Rate
ie
IS-curve
Ye
Output
Clearly, the unique equilibrium values for Y and i are found at the
intersection of the two curves. (And, once these equilibrium values
are known, the values for all other variables like C, I, T, etc. can be
found as well!). This is best illustrated by example.
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Shifting IS and LM schedules
• The position of the IS schedule depends
upon:
– anything (other than interest rates) that shifts
aggregate demand: e.g.
• autonomous investment
• autonomous consumption
• government spending
• The position of the LM schedule depends
upon
– money supply
– (the price level)
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Fiscal policy in the IS-LM model
Y0, r0 represents the
initial equilibrium.
r
LM
r1
r0
Y0 Y1
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A bond-financed
increase in government
spending shifts the IS
schedule to IS1.
IS1 Equilibrium is now at
IS0 r1, Y1.
Some private spending
has been crowded out
Income
by the increase in the
rate of interest.
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Monetary policy in the IS-LM model
Y0, r0 represents the
initial equilibrium.
r
LM0
r0
r1
IS0
Y0 Y1
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An increase in money
LM1 supply shifts the LM
schedule to the right.
Equilibrium is now
at r1, Y1.
Income
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IS-LM Equilibrium Example 3 IS-LM
• The following example is simply a continuation of Example 3
from the commodity market, and Example 3 from the money
market.
Recall from these examples:
C = 300 – 30i + 0.80Yd
T = 100 + 0.25Y
(Solves as C = 220 – 30i + 0.60Y)
I = 250 – 20i
G = 480
Summing C + I + G gives us the demand curve:
AD  950 – 50i + 0.60Y
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IS-LM Equilibrium Example 3 IS-LM
And, setting demand equal to supply Y gives us the equilibrium:
Y  950 – 50i + 0.60Y
Which can be re-written as the IS-curve:
(IS-Curve) Y = 2,375 – 125i
From the money market, we have
Ms = 475
Md = 440 + 0.35Y - 70i
Which, when equated, gives us the money market equilibrium condition
(LM-curve) Y = 100 + 200i.
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IS-LM Equilibrium Example 3 IS-LM
The IS- and LM-curves are:
(IS-Curve) Y = 2,375 – 125i.
(LM-Curve) Y = 100 + 200i.
Setting the two equal to each other gives:
2,375 – 125i = 100 + 200i, or
ie = 7(%)
Inserting this equilibrium value for the interest rate back into the
LM-curve (or the IS-curve) gives:Ye = 1,500
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IS-LM Equilibrium Example 3 IS-LM
Graphically,
LM-curve
Interest
Rate
7%
IS-curve
Ye =1500
Output
In turn, all the other equilibrium values can be determined
T = 100 + 0.25 (1,500) = 475
Budget deficit = G - T = 480 - 475 = PSBR of 5
Yd = (1,500) - 475 = 1,025
C = 300 - 30(7) + 0.8 (1,025) = 910
I = 250 - 20(7) = 110
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And, to verify,
Md = 440 + 0.35 (1,500) - 70(7) = 475 (same as the Ms).
Also, recall that Y = C + S + T )or equivalently, S = Y - C –
T), so that saving S = 1,500 - 910 - 475 = 115.
Essentially, of the 115 being saved, 110 is going to firms
for investment, and the other 5 is being borrowed by the
government.
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Expansionary Monetary and Fiscal Policies
• Using the IS-LM framework we are able to solve for the
equilibrium, most importantly of Y. These values depend
explicitly on decisions by government; namely on fiscal
policy and on monetary policy.
• From the IS-LM diagram, it is clear that equilibrium output,
Ye , will increase when either the IS-curve or the LM-curve
shifts rightward.
• Therefore, any government fiscal policy which serves to
shift the IS-curve rightward, or monetary policy which
serves to shift the LM-curve rightward, will be expansionary,
i.e. cause Ye to increase and the economy to grow.
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Expansionary Monetary and Fiscal Policies
Expansionary fiscal policies include:
• Increasing government expenditure G or decreasing
personal taxation T.
Expansionary monetary policies include:
• Increasing the money supply Ms or (equivalently)
lowering the interest rate I.
So, the question naturally arises: What is the most
effective way for the government to induce the economy to
grow?
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Expansionary Monetary and Fiscal Policies
• Before looking at the Monetarist/Keynesian
debate on this issue, it is necessary to remind
ourselves that the model we’re working with
is a static, short-term model. This model will
enable us to understand the policy debate,
but (as we’ll see later) it sheds little light on
what are appropriate long-term strategies.
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Exercise 1
DO EXERCISE 1
• This exercise requires that you solve for the
equilibrium values associated with Examples
4a to 4d from note packet a. These should
verify the claims made above.
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Inflation is ...
• Inflation is a rise in the average price of
goods over time
• One of the first acts of the Labour
government in 1997 was to make the Bank
of England independent
– with a mandate to achieve low inflation.
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Some questions about inflation
• Why is inflation bad?
– Inflation does have bad effects, but some popular
criticisms are based on spurious reasoning
• What are the causes of inflation?
• What can be done about it?
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Inflation in the UK, 1950-99
30
% p.a.
25
20
15
10
5
19
90
19
70
19
50
0
Source: Economic Trends Annual Supplement, Labour Market Trends
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The Monetarist v. Keynesian Debate
• The first models we introduced (in the commodity
market) did not include interest rates or prices of any
kind, and equilibrium output was entirely demanddetermined. In these simple models (Models 1 and 2),
the government could increase output either by cutting
taxes or by increasing its own expenditure.
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The Monetarist v. Keynesian Debate
• When interest rates and the money market were included
(Model and Example 3), however, we introduced a third
way of inducing economic growth; by increasing the
money supply (or, identically, cutting the interest rate). An
additional implication of this more complicated model is
that fiscal policies are less effective than we had
previously thought: As the government spends more, the
interest rate rises and private investment and consumption
fall; thus partially offsetting the expansionary effects of the
government’s policy.
• So which of these policies - fiscal or monetary - is best?
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The Monetarist v. Keynesian Debate
• Essentially, the answer is an empirical one.
Theory doesn’t really tell us. Rather, it will
depend upon how strongly households and
firms respond to changes in the interest rate
and income.
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The Monetarist v. Keynesian Debate
• Essentially, Monetarists believe that (1) money demand is not very
responsive to interest rates. Graphically, this means that the money
demand curve is very steep. Monetarists also believe however, that
(2) investment, in particular, is very responsive to interest rate
changes. this makes the IS curve relatively flat.
• According to the monetarist assumptions, changing the money
supply would have a great effect on output, but fiscal policy would be
relatively ineffective. Ironically, monetarists promote a cautious,
stable monetary policy rather than an activist one, largely because of
the practical and political difficulties of conducting an appropriate
monetary policy.
• In any event, in the longer term any positive effects of expansionary
monetary policy are offset by higher prices, which cause demand for
money to increase, the LM curve to shift back, and output to return
roughly to its original level. Thus, once the picture is completed,
neither policy is very effective, (according to monetarists!).
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Monetarism
• Monetarism has its roots in the old “quantity theory” of
money, which is embodies in the equation:
money x velocity = price x real output.
• In words: the amount of physical money, multiplied by the
number of times each coin or note is circulated (i.e., its
velocity) must equal the total amount of money spent in
the economy, which is simply price (per unit of output)
times the amount of output.
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• Monetarists do not assume, as do Keynesians, that
supply can adjust to meet any increase in demand.
•
Rather, they assume that markets clear, and therefore
that supply (i.e. output Y) is already at its full-employment
level. Output is thus more or less fixed irrespective of
government policy.
• Monetarists also assume that monetary velocity is
relatively constant. If so, then the quantity theory
equation above implies that increasing the money supply
affects mostly the price level (proportionately) and does
little to affect real output.
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Monetarism
• Thus, the completed IS-LM model, with price changes
added in (see below), is compatible with the old quantity
theory of money, in that both imply no active role for
government in stimulating economic activity. (Indeed, this
is why noted monetarists generally believe in a laissez-faire
government economic policy).
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Monetarist v. Keynesian: Graphically
With respect to expansionary fiscal policy, the Keynesian v.
Monetarist debate can be illustrated as follows.
Monetarist monetary expansion (before price increases):
Ms
Ms1
i
i
LM
LM1
i
Md1
Ms
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Ms’
IS
Y
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A Keynesian Monetary Expansion
Ms
Ms1
i
IS
i
LM
i
Md1
i
M
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Y
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Exercise 2
DO EXERCISE 2
• Exercise 2 shows the effectiveness of various
fiscal and monetary policies under both the
monetarist and Keynesian assumptions.
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The Money Market & Price
• Before considering production and supply, it is necessary
to introduce the price level explicitly, and show how it
relates to IS-LM. In practice, the price level “p” is an
aggregate or average price level for the economy as a
whole. When it increases, inflation is said to occur. In our
model, however, we interpret “p” as the price for our
(homogeneous) output good; i.e. “p” is the price per unit of
“Y”.
• As was suggested above, in the IS-LM model the price
level enters through the money demand curve. Intuitively,
as the price level increases, so too does money demand.
(As a first approximation, if prices double, households and
firms will seek to hold twice as much money).
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The Money Market & Price
We’ve already seen an example of how the price level
affects IS-LM:
1. An increase in P causes Md to increase.
2. An increase in Md implies a leftward shift in the LM-curve.
3. As a result, output Ye will decrease.
4. Combining 1 and 3 above, a higher P implies lower Ye.
5. The combinations of P and Ye that form an IS-LM
equilibrium is an inverse relationship which we interpret as
the “Price-Determined Demand Curve” (DD).
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Deriving Price-Determined Demand “DD”:
Example
• To see how one would obtain a price-determined
demand curve from the IS-LM model, we will
combine Examples 3 and 4d.
• Recall that Example 4d was the same as example 3,
except that money demand had increased by 10%.
• We will now suppose that this increase in Md was
due to a corresponding 10% increase in the price
level, from P = 1 to P1 = 1.10.
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• From Example 3:
• IS-curve: Ye = 2,375 – 125i.
•
•
•
•
Ms = 475
Md = 440 + 0.35Y – 70i
Implies
old LM-curve: Y = 100 + 200i
• Solving IS and LM simultaneously gave the
equilibrium values
• Y = 1,500 and i = 7% (at P = £1.00).
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• From Example 4d:
• old IS-curve: Y = 2,375 – 125i
• old Ms = 475
• new Md = 484 + 0.385Y – 77i
• Setting Ms = Md gave the new LM-curve
• New LM- Curve Ye=-23.38+200i
• Now, setting the old IS-curve equal to the new LM
curve gives
• 2375-125i =-23.38+200i
• which solves for ie=7.38 and Ye=1453 (at P= £1.10)
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The price determined demand schedule
LM0
r
Real money supply is nominal
LM1 money supply divided by the
price level – it influences the
position of LM.
IS
P
P0
Income
P1
DDS
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Y0 Y1
Income
With price at P0, LM is located
at LM0, and given IS, real
income is in equilibrium at Y0.
At a lower price P1, LM is at
LM1, and real income at Y1.
The price determined demand
schedule (DDS) connects
these points ...
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The price determined demand schedule
LM0
r
P
P0
P1
Y0
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The DDS shows the different
LM1 combinations of the price level
and real income at which
IS1 planned spending equals
actual output once interest
IS0 rates are set to keep money
market equilibrium.
Income
Notice that a fall in price may
also shift IS by increasing the
DDS' value of household wealth via
the real balance effect.
DDS
The effect of this is to produce
Y1 Y2 Income a flatter schedule DDS'.
© Stephen Hall, Imperial College London
Price-Determined Demand “DDS”
There are several things to note about this demand
curve:
• In most macroeconomic textbooks, this demand
curve is known as the “aggregate demand curve”.
• Also note there can be only one equilibrium output
level. Visually, then the Ye’s on the IS-LM diagram
and on the DD-curve diagram must be the same.
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• While an increase in the price level will affect the
money demand and LM-curves as described above,
the causality can also work in the other direction.
That is, changes in the IS-LM equilibrium (due to,
say, a fiscal policy change) will have corresponding
effects on the DD-curve.
• As far as visually manipulating the DD-curve is
concerned: In general, anything that causes the ISLM equilibrium to shift to the right will also cause the
DD curve to shift to the right!
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Review
Until now, we have assumed that equilibrium output was
entirely demand determined. Before we introduce supply, it
is useful to review our progressively more complicated
models.
• Models 1 and 2: No interest rate or price level. Output
determined entirely by demand. Implication: increase G to
increase Y.
• Model 3, Interest rate introduced. Output still demanddetermined. But increasing G pushes up interest rate and
“crowds out” private investment. Therefore higher G
implies lower I. Implications: depends upon investment
responsiveness, but increasing G still a good idea.
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Review
• Model 3 (money market): Money supply introduced as new
variable under government control. Increasing Ms
increases Y and lowers i.
• Implications: Isn’t expansionary monetary policy thus
better than expansionary fiscal policy?
• Answer: Not necessarily, as we’ll show below. Increasing
M may lower the interest rate. But it also leads to
inflation, which reduces investment. There are also longterm problems (to be discussed), relating mostly to supply.
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