Module 3

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Module 3 The Keynesian Model
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Contents
Background on the Model Real Vs. Nominal The
Product Market IS Equation Graphing the IS
Curve from the IS Equation The Money Market LM
Equation Graphing the LM Curve from the LM
Equation AD (IS-LM)/AS Workshop A Place to Put
the Model in Motion
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Background on the Model
Keynesian means different things to different
people. Its useful to think of the basic
textbook Keynesian model as an elaboration and
extention of the Classical macro model. Its
variable velocity of money and sticky prices
reflects Keynes belief that the Classical
models shortcomings arose from its
overly-strict assumptions of constant velocity
and highly flexible wages and prices.
Our 10 equation model of aggregate demand (AD)
can be split into two parts The IS model of the
product market (equations 1-6) and the LM model
of the money market (equations 7-10).
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Real vs. Nominal
Total spending on final goods and services at
current prices is called nominal or money GDP and
is denoted by y. It can change over time either
because there is a change in the amount (real
value) of goods and services (denoted Dy) or a
change in the prices of those goods and services
(denoted DP).
Hence, Y nominal GDP P y y real GDP Y/P
This distinction between real and nominal can
also be applied to other monetary values, like
wages. Nominal (money) wages can be denoted by W
and decomposed into a real value (w) and a price
variable (P).
Hence, W nominal wage P w w real wage
W/P
This conversion from nominal to real units allows
us to eliminate the problems created by having a
measuring stick (dollar value) that essentially
changes length over time, as the price level
changes.
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The Product Market IS Equation
To derive IS (which stands for Investment
Savings) we use 6 equations defined in real
terms.
1) y c i x g Equilibrium Condition 2) c
c0 c1(y-t) Consumption Function 3) t t0
t1y Tax Function 4) i i0 - i2r Net Real
Investment Function 5) x x0 - x1y - x2r Net
Export Demand Function 6) g g0 Government
Demand (assumed to be preset at level g0.)
The next few slides will break down each
equation
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Aggregate Demand
Remember that these are all measured in real
terms, i.e adjusted for inflation.
y c i x g
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The Consumption Function
c c0 c1(y-t)
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The Marginal Propensity to Consume
To understand the Marginal Propensity to Consume
(MPC) consider a shopping scenario. A person who
loves to shop probably has a large MPC, lets say
(.99). This means that for every extra dollar he
or she earns after tax deductions, he or she
spends .99 of it. This coefficient c1 measure
the sensitivity of the change in one variable (c)
with respect to a change in the other variable
(y-t).
Hence, it is the first derivative of the
consumption function with respect to a change in
real after-tax income.
c c0 c1(y-t)
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The Tax Function
t t0 t1y
If t1 is .2 or 20, then an increase in income of
2000 will create 400 in additional tax
revenue to the government and tax payments for us.
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Net Investment Spending
i i0 - i2r
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Net Export Demand Function
x x0 - x1y - x2r
Notice that x varies inversely with y r,
meaning that as y and r rise, the level of net
exports fall.
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Here is the rationale between r x in x x0 -
x1y -x2r
An increase in r reduces the demand for real
money balances as households and firms substitute
other assets for cash holdings. A higher real
rate of interest in the U.S. (relative to other
nations) attracts saving that would have gone to
other other parts of the world. This saving comes
in several forms (e.g. demand for stocks and
bonds and other securities) but regardless of
form, requires a a swap of foreign currency for
in order to buy the U.S. securities. Therefore,
an increase in the real interest rate, r via
events in the foreign exchange market leads to a
stronger dollar and thereby a reduction in net
exports, x.
In other words ?r ? ?D makes our goods more
expensive to foreigners, and their goods cheaper
for us ? ?x
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Government Demand
g g0
We take the level of government spending as given.
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After combining all 6 equations of the product
market into 1, and solving for y in terms of r,
we get the IS Equation!
y m(z0 g0 - c1t0) - m(i2 x2) r where z0
c0 i0 x0 and m (the Multiplier) 1/
1-c1c1t1x1
Notice that the IS equation contains two unknown
variables y and r. All the other terms
(m,i2,x2,z0) are parameters which can be
estimated statistically, or policy instruments
(g0,t0,t1) which we take as given. The IS
equation tells us the value of y for a given
level of r, or conversely, tells us the value of
r for a given level of y.
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The Multiplier
For our six equations, the expenditure multiplier
is m 1/ 1-c1c1t1x1.
When y m(z0 g0 - c1t0) - m(i2 x2) r
Suppose spending increases by 1, youd expect
equilibrium output (y) to also rise by 1.
y m(z0 g0 - c1t0) - m(i2 x2) r
?1
?1
But it doesnt! The multiplier shows that the
change in demand for output (y) will be larger
than the initial change in spending. Heres
why An increase in spending will increase
income. This increase in income will increase
spending some more. The increase in spending will
increase income again. This increase in income
will increase spending etc So, the multiplier
process helps explain fluctuations in the demand
for output. For example if something in the
economy decreases investment spending (found in
z0 c0 i0 x0) people whose incomes have
decreased will spend less, thereby driving
equilibrium demand down even further.
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Graphing the IS Curve from the IS Equation
y m(z0 g0 - c1t0) - m(i2 x2) r
The inverse relationship between r and y is built
into the downward slope of the IS curve. As we
move up and along the IS curve, y decreases
while r increases.
because the - m(i2x2) r drops out.
Also, note that when r increases, y decreases by
the amount Dy-m(i2x2)Dr.
Later, you can visit the AD (IS-LM)/ AS Workshop
to practice shifting IS. Throughout the course,
we will only alter terms found in the intercept
(e.g. z0), not the slope of the IS curve
(e.g.x2,i2)
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The Money Market LM Equation
Now that weve derived the IS part of AD, its
now time to complete the model of AD by adding a
money market equilibrium schedule, the LM curve.
We will use the following 4 equations to derive
our LM equation, and curve.
L/P M/P Equilibrium L/P j0 j1y - j2r Money
Demand M M0 Money Supply P P0 Fixed Price
Level
The next few slides will explain each equation.
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Money Market Equilibrium
L/P M/P
The next few slides will define the specifics of
the money market equilibrium.
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Money Demand
L/P j0 j1y- j2r
The positive sign is an indicator that as income
rises, real money demand also increases. The
negative sign is an indicator that as r rises,
real money demand will decrease. Remember that r
is the opportunity cost of holding moneyas r
rises that means its more expensive.
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Money Supply
M M0
We take the money supply as given at the level
of M0.
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Fixed Price Level
P P0
We assume that the price level is constant at the
level P0.
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After combine all 4 equations of the money market
in to 1, and solve for y in terms of r, we get
the LM Equation.
Notice that LM contains two unknown variables, y
and r. All the other terms in the equation are
parameters (j0,j1,j2) that are estimated statistic
ally or policy instruments (M0), except for the
price level (P0) which is held constant. Like the
IS equation, the LM equation tells us the value
of y for a given level of r, and conversely,
tells us the value of r for a given level of y.
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Graphing the LM Curve from the LM Equation
The LM Equation is a linear positive relationship
between AD (y) and real interest rate (r). It
shows all combinations of y and r such that money
demand (L/P) equals money supply (M/P).
Here is the rationale. Start with our money
market equilibrium condition where money demand
equals money supply. j0j1 y-j2 r M/P
Now increase income (y) in the equation and the
curve.
As a result, money demand exceeds money supply
(L/P gt M/P). Like in any market, when demand
exceeds supply, the price rises to clear the
market. The price is this case is r, the
opportunity cost of holding money. As the
interest rate rises, people reduce their money
holdings (according to the -j2 parameter) until
money demand and money supply are equal.
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The positive relationship between r and y is
built into the upward slope of the LM curve. As
we move up and along the LM curve, we see that y
and r both increase.
When r increases, money demand will decrease as
given by ?L/P j0j1y-j2?r. Here L/P lt M/P, so y
will rise by the amount Dyj2/j1Dr to equalize
money demand with money supply (L/PM/P).
When r is zero, the second term on the right-hand
side of the equation drops off, leaving the
horizontal intercept to be
Now lets put IS and LM together in order to
complete our model of aggregate demand.
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The IS-LM Model of AD
All the elements of our 10 equation model
compiled in our IS LM curves/solutions
determine the level of aggregate demand in our
economy.
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From IS-LM to AD
You probably noticed from the IS and LM diagrams
that r and y were on the two axes. Now were
going to bring a third variable, the price level
(P) into the analysis. We can accomplish this by
linking both two-dimensional graphs.
IS-LM Curves (in y r) AD Curve (in y P)
IS
r
To derive AD, start at point A in the top graph.
Now increase the price level from P0 to 2P0. This
shows up in our LM equation as a ? P.
LM(P0)
A
This lowers the real value of the money supply,
and y, shifting LM leftward to point B.
y
P
Notice that r increased. From equations 4 5
(?i i0 - i2 ?r) (?x x0 - x1y - x2?r) we know
that both investment and net export spending will
both decrease setting off a multiplier process
since - Di and -Dx, cause a -Dy. The - Dy
triggers -Dc as we move up the IS curve.
A
AD
The DP triggers a sequence of events that end
with a -Dy, the inverse relationship that defines
the downward slope of AD.
y
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Adding Aggregate Supply
Now that we have a theory of AD, we must
incorporate scarcity which can be done by adding
a model of Aggregate Supply. Recall from the
Classical Model the vertical AS which assumed
that changes in the price level left no lasting
impact on y (because of the market clearing
process). Well take this model and use it for
consideration of the long-term. Here well call
it ASLR. But we need a theory for the short-run,
defined as the interval of time during which
markets are not fully cleared.
ASLR
P
A simple, but useful first approach is to assume
short-run price rigidity. As AD shifts to AD? we
slide in an east-west direction to point B on
ASSR. Then, in the LR, we move from B to C
(move up and along AD).
C
B
P0
ASSR
A
AD?
AD
y
y
y f (n,k,inst)
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AD(IS-LM)/AS Workshop
A Place to Put the Model in Motion
IS-LM
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AD (IS-LM) /AS Mechanics
1) Most exam questions will revolve around the
impact of either a Policy Change (?g0, ?t0 or
?M0) or an Outside Event (?c0, ?i0, ?x0 or ?j0 or
?k, ?inst). 2) Read the question carefully to
figure out which of these variables change, hence
which of the underlying curves will shift. a)
?c0, ?i0, and ?x0 all shift IS AD (via the z0
term). b) ?g0 and ?t0 also shift IS AD (but in
opposite directions). c) ?j0 shifts LM AD
(with ?j0 shifting LM to the left). d) ?M0 also
shifts LM AD. e) ?k, ?inst shift AS 3) Make
the appropriate shifts in the diagram to either
IS AD, LM AD, or AS. 4) Now you can read
the short and long run effects on y, r, and P
directly from the diagram. 5) Once you determine
how y, r, and P are affected, you can plug in
those effects into equations 1-10 to determine
how the rest of the economy is affected.
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Suppose there is a Dx0.
Look at the appropriate equation that captures
the x0 term
Notice that z0 was increased, thus increasing the
value of the horizontal intercept which
translates into a rightward shift of the IS and
AD curves.
IS
r
LM(P0)
In the short-run, we move along ASSR from point A
to point B.
A
But as the output market clears, in the
long-run, the price level will increase from P0
to P2.
This DP decreases the value of the LM
equations horizontal intercept which translates
into a leftward shift of the LM curve.
y
ASLR
P
ASSR
P0
A
AD
y
Finally, this leaves us at point C in both
diagrams.
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Now its time to determine the effects on the
variables in the economy.
For the variables y, P, and r, you can read the
effects right off the diagrams.
The other variables c, i, x, and b require you to
plug in the effects of y and r to determine what
happens.
Remember that SR is the movement from A to B.
Short-run Impacts
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For the variables y, P and r, you can read the
effects right off the diagrams.
The other variables c, i,x, and b require you
to plug in the effects of y and r to determine
what happens.
Remember that LR is the movement from A to C.
Long-run Impacts
LM(P2)
IS
r
LM(P0)
A
y
ASLR
P
ASSR
P0
A
AD
y

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Suppose there is a DM0.
Look at the appropriate equation that captures
the M0 term
Notice that M0 was increased, thus increasing the
value of the horizontal intercept which
translates into a rightward shift of the LM and
AD curves.
(P2)
In the short-run, we move along ASSR from point A
to point B.
C
But as the output market clears, in the
long-run, the price level will increase from P0
to P2.
This DP decreases the value of the LM
equations horizontal intercept which translates
into a leftward shift of the LM curve.
C
Finally, this leaves us at point C in both
diagrams.
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Now its time to determine the effects on the
variables in the economy.
For the variables y, P, and r, you can read the
effects right off the diagrams.
The other variables c, i, x, and b require you to
plug in the effects of y and r to determine what
happens.
Remember that SR is the movement from A to B.
Short-run Impacts
35
For the variables y, P and r, you can read the
effects right off the diagrams.
The other variables c, i,x, and b require you
to plug in the effects of y and r to determine
what happens.
Remember that LR is the movement from A to C.
Long-run Impacts
Notice that the only LR impact of an increase in
the money supply was an increase in the price
level.
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If...
1) y c i x g 2) c c0 c1(y-t) 3) t t0
t1 y 4) i i0 - i2 r 5) x x0 - x1y -x2 r 6) g
g0 7) L/PM/P 8) L/Pj0j1y-j2r 9)
MM0 10SR) PP0 10LR) yF(n,k0,i0nst)
What happens if there is a Dc0 ?
What is the impact on y,P,r,c,i,x,b?
Note b is net real borrowing by the government
(the deficit) defined as bg-t.
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1) Dc0 causes the IS curve to shift right to IS'
due to the ?z0 in the IS equation (increasing
the value of the horizontal intercept).
r
IS
2) This leads to a rightward shift in AD to AD.
Short Run Move from A to B.
y
Long Run Market clears at P0 to P2 from B to C.
P
ASLR
3) DP causes LM(P0) to shift leftward to LM(P2)
due to the lowering of the real value of the
money supply (decreasing the value of the
horizontal intercept.)
P0
ASSR
AD
y
IS-LM
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Now, try to determine the short and long run
impacts for yourself.
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0 -- - 0
y P 0 r c i - x - b -
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What is the impact of a Dg on the macroeconomy?
It depends on 1) Initial position yy or
ylty 2) Short-run or Long-run 3) How the
government finances its spending

• It has three options for financing government
  spending
• (Dg Dt0) Taxes coercion now (theft if we
  did it)
• (Dg Db) Borrowing (bonds coercion later)
• (Dg DM0) Printing money (counterfeiting if
  we did it)

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• Tax-Financed Increase in
• Government Spending
• (Dg0Dt0)

U.S. Tax
1040
42
Tax-Financed Increase in Government Spending
(Dg0Dt0)
r
IS
Result A small rightward shift in both IS (IS
to IS'') and AD (AD to AD'') and a movement along
ASSR to point B.
A
Given our IS equation ym(z0g0-c1t0)-m(i2x2)r
Dg shifts IS to IS'.
y
But, Dt shifts IS back to the left (to IS'').
Note the shift leftward from IS' to IS'' is less
than the original rightward shift because the tax
multiplier (-c1t0) is less than the expenditure
multiplier (m).
P
ASLR
As the market clears, the rising price level
contracts LM and the economy moves to point E.
ASSR
P0
AD
y
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Bond-Financed Increase in Government Spending
(Dg0Db)
US. Treasury Bond
44
Bond-Financed Increase in Government Spending
(Dg0Db)
r
IS
A
Given our IS equation ym(z0g0-c1t0)-m(i2x2)r
Dg shifts IS to IS'. Note Db is not part of
our 10 equation AD/AS model, and therefore it
doesnt impact AD (IS-LM) or AS.
y
P
ASLR
In the short run, the Dg causes a rightward
shift in both IS (IS to IS'') and AD (AD to
AD'') and a movement along ASSR to point B.
ASSR
P0
As the market clears, the rising price level
contracts LM and the economy moves to point E in
the long run.
AD
y
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Money-Financed Increase in Government Spending
(Dg0 DM0)
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Money-Financed Increase in Government Spending
(Dg0DM0)
r
IS
A
The DM0 causes a rightward shift in both LM
(LM(P0) to LM(P0)') an AD (AD to AD''') and a
movement along ASSR to point C.
Given our IS equation ym(z0g0-c1t0)-m(i2x2)r
Dg shifts IS to IS'.
P
y
ASLR
The Dg causes a rightward shift in both IS (IS
to IS'') and AD (AD to AD'') and a movement along
ASSR to point B.
As the market clears, the rising price level
contracts LM(P0)' to LM(P2) and the economy moves
to point E in the long run.
ASSR
P0
AD
y
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Financing Gov't Spending
DgDt
DgDb
DgDM
SRstrongest impact on y with Dr indeterminately
small (without additional info). LR strongest
impact on P Dr same as for deficit-financing
Dy0.
SR relatively small Dy and Dr DP0. LR
relatively small impact on P, r Dy0.
SRstronger impact on y and r DP0. LRstronger
impact on r,P Dy0.