Download 14 - The Citadel

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14. Aggregate Demand and IS-LM Analysis
Question:
34. Be able to describe the short run effects of an increase or a decrease in
consumption, saving, investment, government spending, taxes, budget deficit,
trade deficit, base money, money supply or demand shocks, price level and
illustrate with an IS-LM diagram. (these are the effects on the real market
interest rate and real income. These effects must be shown!)
Aggregate Demand
Aggregate Demand is the real volume of final goods and services that
households, firms, and government choose to buy. That is, the planned
purchases of consumer goods and services by households are added to the
planned purchases of capital goods by firms. That is private expenditure.
That is added to purchases of goods and services by the government. This
total amount of nominal expenditure is then corrected for changes in the price
level. The result is aggregate demand.
IS-LM Analysis
IS-LM analysis is a method of understanding the relationships between money
supply and demand, interest rates and aggregate demand. It allows us to
develop of theory of aggregate demand, but it is based on the implicit
assumption that firms will always produce whatever they can sell at a given
price level. (This is a very incomplete theory of the macroeconomy--but
aggregate supply will be added later.)
Changes in the LM curve
Changes in money supply, money demand shocks, or the price level are
analyzed using shifts in the LM curve.
An increase in the LM curve is a
shift to the right. A decrease in the LM curve is a shift to the left.
Factor
Base Money Supply
Money Multiplier
Money Supply Shock (βt)
Money Demand Shock ( αt )
Price Level
Relationship to LM
Positive
Positive
Positive
Negative
Negative
The explanation is simple. An increase in the money supply tends to lower
interest rates, given money demand. That means that the real interest rate
consistent with a given level of real income is lower--the LM curve shifts to
the right. If people just choose to hold more money or else the higher price
level causes people to hold more money, the result is a shift of the money
demand curve to the right. The nominal and real interest rates that go with a
given level of income are higher. The LM curve has shifted to the left.
IS Relationship
An increase in income causes an increase in savings. The interest rate at
which saving and investment are equal is lower. This relationship is
represented by the IS curve.
I stands for investment. S stands for saving. The IS curve shows
combinations of income and interest rates consistent with saving and
investment being equal in the short run.
An alternative approach looks at the relationship between the real
interest rate and total real expenditure--consumption plus investment plus
government spending. A lower real interest rate tends to stimulate
consumption and investment spending. The increase in total spending, tends to
cause firms to sell more. Assuming they expand their production, output and
income rise.
A log linear function representing the is function would be:
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lnyt = co - c1tt - c2r
bt
+ c3 lngt+ c4 lnxt - c5 lnnt + γt
where: co, c1, c2, c3, c4, c5 are positive coefficients, and γt is a real
expenditure shocks. t is the tax rate, rbt is the real interest rate on bonds,
x is exports and n is imports. Permanent changes in consumption or investment
would be represented by a change in c0 in the same direction. Temporary
increases in investment and consumption or decreases in saving are positive
real expenditure shocks. Temporary decreases in investment or consumption or
increases in saving are negative real expenditure shocks.
The IS curve is the graph of this relationship.
IS and LM Together: Equilibrium Real Income and Interest Rate
The IS curve and LM curve together seem to show the equilibrium interest
rate and real income in the short run. It is the level of the interest rate
and real income consistent with the supply of money being equal to the demand
for money and the supply of saving being equal to the demand for investment.
An alternative statement is that given the equilibrium level of real
income, the money demand and money supply are consistent with the equilibrium
real interest rate and given the equilibrium interest rate, sufficient
spending is generated to purchase just the amount output equal to the
equilibrium income.
But always remember--this income in IS-LM is actually real spending on
final goods and services. There is enough spending to buy that amount of
output. There is no guarantee that firms can produce that much output or that
they are willing to sell that amount.
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By solving the real expenditure (IS) function and the LM function, real
income and the real interest rate can be found.
Start with the LM and the IS relationships:
.
rbt = 1/b2(1-b3)*(lnPt + bo + b1lnyt - lnBt - lnmt + βt - αt) - Pet
lnyt = co - c1tt - c2r
bt
+ c3 lngt+ c4 lnxt - c5 lnnt + γt
Solve the IS relationship for the real bond interest rate:
rbt = 1/c2 (c0 - c1 + c3 lngt + c4 lnxt - c5 lnt - lnyt)
Set them equal and solve for real income:
lnyt = b2(1-b3)/(b1c2+b2(1-b3)) * (co-c1tt+c3lngt+c4lnxt-c5lnnt+γt)
+ c2/(b1c2+b2(1-b3)) *(lnBt+lnmt-lnPt -bo -βt+αt)
.
+ c2b2(1-b3)/(b1c2+b2(1-b3)) * Pet
Substitute this solution for real income into the IS relationship above,
and that gives the solution for the real bond interest rate.
Changes in the LM curve
Changes in money supply, money demand shocks, or the price level are
analyzed using shifts in the LM curve.
An increase in the LM curve is a
shift to the right. A decrease in the LM curve is a shift to the left.
Factor
Base Money Supply
Money Multiplier
Money Supply Shock (βt)
Money Demand Shock ( αt )
Price Level
Relationship to LM
Positive
Positive
Positive
Negative
Negative
Short Run Effects of Increase in Base Money
Other things being equal, an increase in base money increases the money
supply. Assuming money demand is unchanged, that tends to create a surplus of
money. The excess money is spent and at least some of it is spent on bonds.
Bond prices rise and the nominal and real interest rate falls. The lower real
interest rate tends to stimulate investment and consumption spending. There
is enough spending to buy more output. Assuming firms would actually produce
that extra output, real income rises. The short run effects of an increase in
base money are a lower real interest rate and higher level of real income
(actually, aggregate demand.) This can be illustrated by a shift of the LM
curve to the right.
The analysis of an increase in the money multiplier, a positive shock to
moeny supply, a decrease in the price level, or a negative shock to money
demand are much the same. And a decrease in base money or the money
multiplier, an increase in the price level and a negative shock to money
supply or demand are just the opposite. Remember that both a money demand
shock or an increase in the price level imply an increase in money demand.
That leads to a shortage money, sales of bonds, etc.)
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Changes in Real Expenditure: shifts of the IS curve
Changes in real expenditure shocks are represented by shifts in the IS
curve. Examples include changes in consumption, saving, investment,
government spending, taxes, the budget deficit, and the trade deficit. In the
short run, they cause changes in real income and the real interest rate.
An increase in the IS curve is a shift to the right. A decrease in the
IS curve is a shift to the left. (To remember the relationships, note that
increases in spending tend to increase production and income in the short run.
More consumption, more production, IS curve shifts right.)
Factor
Relationship to IS
Consumption (c0)
Positive
Saving (negative c0)
Negative
Investment (c0)
Positive
Government Spending
Positive
Taxes (tax rate)
Negative
Budget Deficit (govt. spending - taxes) Positive
Exports
Positive
Imports
Negative
Trade Deficit (imports -exports)
Negative
The explanation is simple. The increase in real expenditure implies that
there is more spending at any given real income. That means enough spending
so that more can be sold. Assuming, firms can produce and are willing to sell
that extra output, income rises. A given real interest rate is consistent
with higher real income--this IS curve shifts to the right.
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Short Run Effects of an Increase in Government Spending
Suppose government spending increases and everthing else remains
unchanged. The increase in government spending leads to an increase in total
spending. Assuming that firms adjust output to match the increased sales,
then the increase in output implies a equal increase in real income. But
people with higher income demand more money. The increase in money demand
leads to a shortage of money. To obtain the needed funds, people sell bonds.
Bond prices fall and the nominal and real interest rate on bonds rises. So
the short run effect of an increase in government spending is to raise real
income (actually aggregate demand) and raise the real interest rate. (This is
illustrated by a shift of the IS curve to the right.)
An increase in consumption, investment, or exports is analyzed in much
the same way. A decreaes in taxes implies an increase in disposable income
and consumption. A decrease in saving is an increase in consumption. A
decrease in imports implies more domestic consumption or investment spending.
An increase in the budget deficit implies more government spending or lower
tax rates. A lower trade deficit implies higher exports or lower imports.
The opposite analysis would apply to a decrease in consumption, increase
in saving, decrease in government spending, increase in taxes, decrease in the
budget deficit, decrease in exports, increase in imports, or an increase in
the trade deficit.
Dynamic IS-LM
A growing supply of base money matched by a growing price level might
leave the LM curve unchanged. But if real income is growing, steady-state
equilibrium requires that both the IS and LM curves shift to the right at the
same rate. Real consumption and investment expenditures tend to grow with
capacity, so a dynamic IS relationship would be:
.
.
.
.
.
yt = c0 - c1 Δtt - c2 Δrbt + c3gt + c4 xt + c5 nt + γt
For this kind of equilibrium to develop, the growing real expenditure and
income must be matched by either an increasing money supply (say, growing base
money) or else a decreasing price level. Of course, sufficiently rapid growth
in base money would make this sort of equilibrium consistent with a rising
price level.
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The Aggregate Demand Function and Curve
IS-LM analysis is a theory of aggregate demand. It shows the real volume
of purchases, assuming that firms will actually produce the output. But when
the real volume of sales change, firms will almost certainly adjust prices and
well as output. But when prices change, so does the price level. The price
level is negatively related to LM, which implies that a lower price level
tends to raise real income. What that really means is that the lower price
level tends to result in more spending, so that that firms could sell more
output if they could produce the output and wanted to sell it.
The equilibrium income from the IS-LM model is the aggregate demand
relationship. Everything is given, except the price level. The negative
relationship between the real income and the price level is highlighted. A
d superscript is used to note that this is really a relationship between
the price level and spending.
lnydt = b2(1-b3)/(b1c2+b2(1-b3))*(co-c1tt+c3lngt+c4lnxt-c5lnnt+γt)
+ c2/(b1c2+b2(1-b3))*(lnBt+lnmt-lnPt -bo -βt+αt)
.
+ c2b2(1-b3)/(b1c2+b2(1-b3)) * Pet
The aggregate demand curve shows the relationship between the price level
and real income, that is, the total amount households, firms, and the
government is willing to buy. The lower the price level, the higher the
amount of real income demanded and vice versa.
All the factors that influence the IS or LM curves imply shifts in the
aggregate demand curve in the same direction as the change in equilibrium real
income. For example, IS-LM analysis suggests that real income increases when
the money supply increases. That means that the aggregate demand curve
increases--shifts to the right. Similarly, IS-LM analysis suggests that real
income decreases when saving increases. That means the aggregate demand curve
shifts to the left.
Dynamic Aggregate Demand
The growth rate of real expenditures can be found by taking the difference
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between the log of aggregate demand in period t and period t-1. That gives:
.
.
.
.
.
ydt = b2(1-b3)/(b1c2+b2(1-b3))*(co-c1 Δt t+c3gt+c4xt-c5nt+γt)
. . .
+ c2/(b1c2+b2(1-b3))*(Bt+mt-Pt -βt+αt)
.
+ c2b2(1-b3)/(b1c2+b2(1-b3)) * ΔPet
Notice that the growth rate of aggregate demand is negatively related to
the inflation rate. (Dont get confused with the positive relationship to the
change in the expected inflation rate.)