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Mathematical Approach of the IS-LM Curve Model
We still maintain the assumption about the fixed price level: The price level P is assumed
to be fixed in the IS-LM model unless it is specified otherwise.
1. What Are We Trying to Do?
The IS-LM is the most broadly used frame of reference in macroeconomics theory.
In the IS-LM Curve Model, the interactions between the goods (output) market and the
financial market gives the equilibrium Y* and the equilibrium interest rate i*.
As this new Y* and i* satisfy the equilibrium conditions in the goods market as well as the
money market.
We would like to proceed in the following manner:
First, we will establish an inverse relationship between interest rates and investment in
the goods market. This eventually leads us to the IS curve or the various combinations
of i and Y, which satisfy the equilibrium condition in the goods market or make the
demand equal to the supply in the goods market.
Second, we will establish an inverse relationship between interest rates and (real)
money demand in the money market. This leads us to the LM curve or the various
combinations of i and Y, which satisfy the money market equilibrium or make the
demand equal to the supply in the money market.
Third, by equating the Ys or the i’s that we have obtained from the IS and the LM curves,
we will solve for the national income Y* or the interest rates i*, which satisfy the goods
and money market equilibrium conditions at the same time. Graphically, they are
obtained from the intersection of the IS and LM curves.
Fourth, we will examine various “comparative statics”, which is represented by the
multiplier. In this section, we examine the impact of exogenous changes in government
expenditures, money supply, monetary market conditions, etc.(these are only a few out
of many possible exogenous changes in the economy), on the equilibrium national
income Y* or the equilibrium interest rate i*.
2. IS curve
1) Components
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(1) Consumption Expenditure
Funtional Form of Consumption
C = C0 + c1 (Y-T)
For now, we assume that T = T0. However, later we should introduce a
more realistic assumption that T = T0 + t1 Y.
(2) Investment Expenditure
How does a high real interest rate dampen economic activities? Actually it works in two
ways; first it reduces the investment, and thus the AE, eventually reducing Y*. It also
reduces the real money demand. At this moment ignore the second impact.
The (real) interest rate constitutes a cost of obtaining (financial) capital for additions to
capital stock or investment. A higher interest rate means a higher cost, a lower
profitability and the lower rate of return on investment projects. Note well that the
investment is a decreasing function of real, not nominal, interest rates.
Some investment projects, which used to be marginally profitable or managed to make
both ends meet, are no longer profitable. So the desired investment will decrease as the
interest rate increases.
Functional Form of Investment
I = I0 – b i ,
I0 is the autonomous investment and b is the elasticity of investment with respect to
interest rates. b>0. Here b measures the responsiveness to changes in investment to
changes in the interest rate.
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The larger the value of b, the more responsive the investment with respect to changes in
interest rates. In other words, the larger the value of b, the more interest-rate elastic the
investment.
A numerical example would be I = 100 – 5 i: One percentage increases in investment will
bring about a 5% decrease in investment.
(3) Government Expenditure
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(4) Net Exports
X–M
As long as the prices are set to be constant (no changes in the relative price level or
competitiveness), and there is no change in Foreign exchange rates, they are
X = X0 or exogenous (as the domestic country has no control over its exports)
M = M0 - m 1 Y
*Question: Compare the consumption function and the import function. What is the
major difference? Why is M not a function of Y-T, but Y itself? – Why is T not deducted
from the Import Expenditure Function?
2) IS Curve: Goods Market Equilibrium
For simple illustration, for now, we assume that X-M =0 or that the
economy has no exports or imports. Later this should be relaxed.
The IS curve shows various combinations of national income and interest rates which
bring out the equilibrium, or the equality between demand and supply, in the goods
market.
Let’s plug the aforementioned modified investment function into the aggregate
expenditure function, and solve for Y* and i*.
(1) Algebraic Derivation
Recall there are three different cases of AE.
Case 1. All taxes are lump-sum or autonomous.
Under 3 unrealistic but simplying assumptions that T = T0, X-M =0 and all prices are
fixed.
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Suppose that we are dealing with the aggregate expenditures with only lump-sum taxes
and no exports or imports (This is Case 1 in the last chapter of the Keynesian Cross
Diamgram).
The AE will be
AE = C0 + c1 (Y – T0) + I0 – bi + G0
= c1 Y + (C0 - c1 T0 + I0 + G0 – b I0 )
At equilibrium,
Y= AE
Y = c1 Y + (C0 – c1 T0 + I0 + G0 – b i )
Y – c1 Y = C0 – c1 T0 + I0 + G0 – b i
Solve for Y* and i*: We can rewrite this equation as a functional relationship between Y *
and the interest rate i. That is, solving for Y* or i*, depending on what we need to know
about:
Y*=
1
( C 0 - c1 T 0 + I 0 - b i + G 0 )
1 - c1
or
i *=
1
1( C 0 - c1 T 0 + I 0 + G 0 ) - c1 Y
b
b
This is the algebraic expression of the relation between (i, Y) which represents
equilibrium in the final goods market.

The above two are identical. However, in economics, it is customary to put the
price or interest rate on the vertical axis, and the quantity on the horizontal axis
when drawing a graph or a diagram. So the second one is in line with the
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illustrative tradition. We can draw the IS curve by putting i on the vertical axis
and Y on the horizontal axis.

Note that the slope has a negative sign and thus the IS curve is downward sloping.
This means that in equilibrium, of the goods market, the interest rate and income
move in the opposite direction; if interest rate increases for some reason, in order
to stay at the same equilibrium in the goods market, national income should
decrease.
(2) Intuitive Explanation of the IS curve.
We can also give the following intuitive explanation about the negative slope of the IS
curve;
Let us start from one equilibrium: Y = YS = AE = C + I + G. Here let us change the
interest rate and examine the responsive changes in Y. If i and Y turn out to be moving in
the same direction, the slope of the IS curve will be positive, and vice versa.
Let us suppose that the interest rate decreases from i0 to i1. If investment is inversely
related to the interest rate, there will be an increase in investment and thus an increase in
the AE. This means that there will be an excess aggregate demand (now Y < AE’). How
can we re-establish the equality between AE and Y? The answer is by increasing Y. In
the equality of AE and YS, or the equilibrium of the goods market, when interest rates
goes down and national income goes up. The interest rate and national income should
move in the opposite direction.
We can express the above relationship with a curve in a graph with Y* on the horizontal
axis, and the interest rate i* on the vertical axis. This curve is called the IS curve because,
at equilibrium, AE = Y, which means C + I + G = C + S + T . As C in both side cancels
out, the equilibrium condition of the goods market can be expressed as I + G = S + T. S
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is the houholds’ savings. The first letter of each side of the equality read ‘I’ and ‘S’. So
along the IS curve, I + G = S + T. So comes the word ‘IS curve’.
This equation can be used to show the relationship between the ‘national’ savings and
investment.
I = S + (T –G), and
S is the househlds’ savings, and T-G is the government’s budget surplus or ‘public’
savings. Thus S + T-G is the sum of the ‘national’ savings. It is the total savings in a
closed economy with no trades.
(3) Modification with International Trade for an Open Economy
So far, we have ignored the exports(X) and imports(M).
In an Open Economy with international trade, the IS curve is derived by equating Y(supply
side) with AE = C + I + G + X-M(expenditures for domestic goods and services).
Whenever there is a change in AE or its components, the IS curve shifts around. Now the
X-M has to be specified.
X-M is the Net exports (NX), which is approximately equal to the Current Account balance:
X-M = NX = CA.
So we can rewrite into AE = C + I + G + NX. Whatever affects the components of the AE
shifts the IS curve: Now an improving current account will shift the IS to the right, and a
deteriorating current account to the left.
What determines the Net Exports or Current Account Balance?
X = M*(Y*, S P*/P)
Our exports are the imports by the foreign country. How much the foreign country
imports from us depends on their income (foreign country's national income), and
the relative price level of the foreign country to our country (S P*/P).
P* is the price level of the foreign country in terms of the foreign currency. S is `our'
price of `their' dollar. So the product of S P* is the relative price level of the foreign
country to our (the domestic country) in our currency terms. For instance, suppose
that a hamburger in the U.S. is $1.00 in U.S. dollar terms (P*), a Canadian
hamburger is $1.30 in Canadian dollar terms (P), and the Canadian dollar price of
U.S. $1 is $1.40 (S). The U.S. hamburger costs Canadian $1.40 as S times P* = 1.4
X 1. The Canadian hamburger costs Canadian $1.30. So the relative price level of
the foreign to the domestic country is 1.4 to 1.3, that is, 1.076. The foreign price
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level is 1.076 times as high as the domestic price level. In our model we assume that
the price level, domestic and foreign, is fixed. An increase in the exchange rate or S
makes the foreign good dearer and more expensive, and raises the foreign price level
compared to the domestic price level. This will in turn make consumers, domestic
and foreign, switch from foreign to domestic goods: our exports of domestic goods
rise and our imports of foreign goods fall. Our current account and the balance of
payment will improve: S  SP*  SP*/P  Foreign price level  
Demand for domestic goods  and Demand for foreign goods  X and M
 Net Exports(X-M) (doubly improving)  CA.
M = M(Y, SP*/P)
Our imports are an increasing function of our national income, and a decreasing
function of the relative price level of the foreign to the domestic country: The more
money we have, the more of foreign goods we can afford to import. The higher the
foreign price level, the less we would like to import.
Combining the above two as NX = X-M, we get
NX = X(Y*, SP*/P) - M(Y, SP*/P)
Ultimately, the current account is a function of Y, Y*, SP*/P;
NX = f(Y, Y*, SP*/P)
Let's review the impact of each variable on the net exports or current account:
i)
Y  M  NX  
moves along the IS curve to the right in the dimension of Y and i
ii) Y*  X  NX  IS curve moves to the right
iii) S  SP*/P   M and X  NX   IS curve moves to the right
This suggests that the IS curve becomes endogenous under the flexible exchange
rate system. A changing exchange rate leads to a change in the AE curve, which in
turn shifts the IS curve around.
This works fairly well for an economy in a short-run when S moves around in a country
with a flexible foreign exchange rate. In the long-run, S may change further as a result of
the initial impact on Y.
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Suppose that S or foreign exchange rate rises for reasons unrelated to the domestic economy.
The foreign currency is more expensive in terms of the domestic currency. All foreign goods
are now more expensive in terms of the domestic currency while all domestic goods are
cheaper in terms of the foreign currency. Thus M falls, X rises, NX rises(call it ‘A’) and the
IS curve shifts to the right. In a new equilibrium of the IS-LM, Y rises and the interest rate i
rises as well. This is the first round of changes. And it is not the end of the story.
An increase in Y leads to an increase in M, and thus a decrease in NX(call it ‘B’). The IS
shifts to the right? Not so fast. Something else is working on NX in an open economy
where not only goods but capital flows freely. And capital flows are a function of relative
interest rates between the domestic and the international money markets. A rising r attracts
international capital into the (domestic) country, and leads to an increase in NX(call it ‘C’).
How much would this be in comparison to the afore-mentioned decrease in NX?
It depends on the sensitivity or elasticity of capital flows to interest rate changes, or in a
word, the degree of capital mobility. What determines the degree of (international) capital
mobility is a topic for a separate discussion. We can think of the two extreme cases, and all
possibilities of the real world fall somewhere within the continuum between these two
extremes. In one extreme where there is a perfect capital mobility, ‘C’ exceeds ‘B’, and the
net NX rises, and the IS curve moves to the right further from its initial move. Y rises
further. On the other hand, in the case of a perfect capital immobility, there is no ‘C’, but
only ‘B’. And the net NX falls, and the IS curves shifts back from the initial move. Y falls
back as well.
Can you illustrate these two different cases in two steps of the initial impact and the
secondary self-adjustment?
We need some model to explain this secondary self-adjustment of economy. How about the
case where the government fixes S or adopts fixed foreign exchange rate system? In fact, in
this case as the government buys or sells the foreign currency with the domestic currency,
the volume of the domestic currency in circulation leads to changes in money supply. In
other words, the LM curve moves as a result of the government’s intervention in the foreign
exchange market. Thus we need something else. Bob Mundell came up with the model
with a new ‘Balance Payment curve’ or BP curve. We will discuss this in a separate chapter.
3. LM Curve for Money Market Equilibrium
LM cure shows the combinations of the interest rate and the income (i, Y) which
satisfies the equilibrium in the money market.
1) Components
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(1) ‘Nominal’ versus ‘Real’ Money Supply/Demand
We should make distinction between Nominal Supply or Demand and Real Supply or
Demand. The first one is in monetary terms, and the second in quantity terms.
In microeconomic analysis of equilibrium, we define the demand and supply in real
terms, not in monetary or nominal terms. For instance, if we say that $20,000 worth of
hamburgers are demanded (or supplied), the statement is not clear enough. This $20,000
is nominal demand in monetary terms. What about the real demand or quantity? If the
price is $1 per hamburger, in real terms, 20,000 units of hamburgers are demanded. If the
price is $10, in real terms 2,000 hamburgers are demanded.
In the same vein, for the analysis of the money market equilibrium, the quantity of money
should be also defined in real terms, not in nominal or monetary terms. The nominal
quantity of money is the face value of the money, and the real quantity of money is the
face value divide by the price level;
Real quantity of money = Nominal quantity of money/Price level.
m = M/ P
The real quantity of money supply m is the nominal money supply divided by the price
level. For instance, nominal money supply is 2,000,000,00 dollars or $ 2 billion. The
price level is measured by a price index. Suppose that the price index is 100 (or 1.00)
right now. The real money supply m = 20,000,000,000/100 or 20/1.0 (units do not matter
as long as there is a consistency).
(2) Money Supply
The nominal quantity of the money supply is determined by the monetary authority,
which usually is the central bank.
MS = M0
Money supply varies depending on the scopes of money: it may include only cashes (in
circulation) in a narrow scope, and may include cashes and all deposits in a broad
scope.such as M2. The different scopes of money supply will be discussed in full in the
separate chapter.
For instance, M0 = $20,000,000,000 or $20 billion.
The monetary authority does not have to determine the nominal money supply on the
basis of any variables in any given manner over time. Thus, we regard the nominal
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money supply as an exogenous variable, and regard it as arbitrarily determined by the
monetary authority.
Mathematically, this means that the nominal money supply curve is vertical, being
independent of interest rates. As the money supply is independent of the interest rate,
when drawn in the interest rate and real quantity dimension, the money supply curve is
vertical, being the same regardless of the level of the interest rate.
At one point of time it is fixed. However, of course, over time it can be changed by the
monetary authority. In fact, the monetary authority sets the nominal money supply in
each period.
. * Can we have a Money Supply ‘Function?
For instance, depending on circumstances, the monetary authority may increase or decrease the
nominal money supply when there is an increase in the national income. If the monetary
authority wants to accommodate the booming or growing economy, it would increase the
nominal money supply in the face of a rising national income. The logic is that a larger economy
has a larger volume of economic transactions and needs a larger amount of medium of
exchanges, i.e., money. On the other hand, if the monetary authority judges that the rising
national income may touch off inflation and thus decides to fight the inflation, it will decrease the
money supply in the face of a rising national income. This is called ‘leaning-against-wind’
monetary policy.
All in all, the monetary authority can choose any of these policies. Mathematically, this means
that
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relationshipthe
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If this
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economy, it would increase the nominal money supply in the face of a rising
national income. The logic is that a larger economy has a larger volume of
economic transactions and needs a larger amount of medium of exchanges, i.e.,
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(3) Real Money Demand
(a) Uniqueness of Real Money Demand
A few important things to remember about real money demand:
First, note that the money market equilibrium should be defined in terms of real money
supply and demand;
Nominal money supply is equal to nominal money demand at all times, i.e., at and out of
equilibrium. The nominal quantity of money demanded by the society as a whole is
always equal to the nominal quantity of money supplied by the government; MS = MD at
all times. Suppose the government is handing out newly printed paper monies or notes on
the street. IS there anyone who would refuse them? Every dollar of money supply will
be gladly demanded.
Second, while an individual cannot control real money demand, the general public as
opposed to the monetary authority can control real money demand;
When an individual receives some new paper monies, her/his nominal (and real) balances
increase. S/he may succeed in decreasing the nominal money demanded or the real
money balanced back to the initial level by spending the excess money holdings.
However, because her/his expenditures will become someone else’s receipts, some other
members are getting the increased money supply. So from an individual’s view point the
nominal money demanded may be controllable, while it is not controllable from the entire
society’s viewpoint. What is true for individuals is not necessarily true for the society as
a whole. This is the ‘fallacy of composition’ commonly founded in macroeconomics.
As individuals are busy getting rid of the excess of money holding over the desired level
of demand (“I would like to have $200 in my pocket, but as government gives me a new
$100 bill, now I have the excess of money holding by $100. I would like to go back to
the desired level of money demanded, that is $200 by spending $100 away.”) The
increased money becomes a kind of ‘hot potato’. What does this mean in terms of the
real money demand? The real money demand, which is the nominal money demand ( =
the nominal money supply) divided by the price level, is going back to the initial level.
The increased speed o spending and expenditure will eventually push up the price level.
The general public are collectively changing the price level and thus controlling the real
money demand.
Suppose MS = M = MD = $200 billion and P = 1.00 initially in the equilibrium; the real
money demand is MD/P = 200/1 = 200 and should be equal to the real money supply at
the equilibrium. This real money demand is at the desired level at the equilibrium in light
of all the determinants of the demand including the income level and the interest rate.
Now the monetary authority increases the nominal money supply MS to $400 billion.
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First, all the increased nominal money supply will be demanded. So the nominal money
demanded is equal to the new nominal money supply; MD’ = MS’ = M’ = $400 billion.
In the short-run, the price does not change, and thus the actual amount of the real money
holding will be m’ = m’’ = M’/P = $400/1.00 = 400. This is much larger than the desired
real money demand, that is, 200. As there are no change in the determinants of the real
money demand, there should not be any change in the level of real money balances the
general public wish to hold. There is an excess of real cash balances over the desired real
money demand; ‘actual’ real money balances > ‘desired’ real money balances.
As individuals with excessive money balances try to recover the desired real money
balances by spending the excess money receipt, the price level is going up to P’. At this
new price level, the new ‘actual’ real money balances (M’/P’) become equal to the
desired level of real money balances.
Specifically, the price level will go up to the level of 2 (or the index number 200). The
actual real money demand will be 400/2 = 200, the same level as before any changes.
However, if P is fixed, there have to be permanent changes in real money demand, which
is only possible when there is a change in its determinants such as interest rates and real
income. The idea is that if there is an excess of liquidity, in the money market interest
rate should fall and this should in turn boost investment and national income. This is the
case in hand.
(b) Functional Form of Real Money Demand
The real money demand is given a functional form such as
md = L ( i, Y ).
The above equation defines the real money demand as a decreasing function of interest
rates and a increasing function of national income. What determines the desired level
(quantity) of real money demand? Just as the desired quantity of hamburgers is
determined by the consumers’ income and the price of hamburger, the real demand for
money is determined by the income level of the economy, that is the national income, and
the price of the money, that is, the interest rate.
Let us examine the second point in the above statement: the price of money is the interest
rate. In other words, the opportunity cost of holding money balances is the interest rate.
Money is one of many assets, which include bonds, stock, equities and real assets.
Money and other assets are substitutes. The major difference between money and other
assets is that money does not bring in any positive pecuniary returns. Actually it is very
often subject to the erosion of real value due to inflation, and other assets do have
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pecuniary returns. However money, or cash balances in a precise term, renders a unique
non-pecuniary service, which is known as ‘liquidity’. Money is the most generally
accepted medium of exchange and most ‘liquid’. So when you decide to hold assets in the
form of cash balances instead of any other, you are showing your preference for liquidity
over pecuniary returns. This is the reason why the money demand is called’ liquidity
preference’, and the money demand function ‘liquidity preference function.’
The interest rate represents the foregone pecuniary return or the economic sacrifice you
have to take when you are choosing cash balances over other assets, as your mode of
holding assets; in other words, the interest rate is the opportunity cost of holding cash
balances. When the interest rate goes up, the cost of holding cash balances increases and
naturally you would like to hold less assets in the form of cash balances and more interest
bearing assets. This means that the demand for money is inversely related to the interest
rate.
Now we have another major factor to be considered, which affect the real money
demand; the income level. When real income increases, in most cases, the demand for
money increases in real terms, too. To name one reason, when real income increases,
there occur more transactions, and then more cash balances should be held to back up the
increased transactions.
We can give the liquidity preference function the following specific functional form;
md = kY – h i + u,
where K is the elasticity of real money demand with respect to the national income; h is
the elasticity of real money demand with respect to interest rates; and u is the random
component of real money demand.
The liquidity preference curve is negatively sloped when drawn with the interest rate on
the vertical axis and the amount of real money on the horizontal axis. The variables Y
and u are the shift parameters of the real money demand curve.
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Also, we can draw a set of liquid preference curves for different levels of income; the
higher the level of national income, the larger the demand for real money balances. You
may remember, from the class of introductory economics, that an increase in income
shifts the demand curve to the right.
2) LM Curve as the Money Market Equilibrium
As emphasized, the money market equilibrium should be defined in real terms; the
money market is in equilibrium when real money supply is equal to real money demand
ex-ante. If the demand is larger than the supply, the price will go up. With an increased
price some people will give up their demand. The price, which adjusts to equate the
supply and demand, is nothing but the interest rate. The money market interest is set at
such a level as to make the supply equal to demand ex-ante.
(1) Algebraic Solution
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LM Curve: Money market equilibrium condition ms = md yields the following
equations. And then you can solve for Y* or i*.
In line with the illustrative tradition of economics (what was it?; do you recall?; if
not go back to the IS curve illustration as shown above), rearranging the equation with ‘i’
on the left hand side and ‘Y’ on the right hand side, we get a LM Curve.
M0
= kY - h i + u
P0
h i= i=
M0
+k Y +u
P0
M0
1
k
(+ u )+ Y
h
h
P0
We can draw a LM curve with the interest rate on the vertical axis and the national
income on the horizontal axis. The LM curve is upward-sloping, or in other words, it as a
positive slope.
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Of course, as we have discussed in the case of IS, the above LM can be expressed in
terms of Y as well:
M0
P0
= kY - h i + u 0
kY =
Y=
M0
P0
M0
+ hi  u 0
1
h
(
 u0 ) + i
k P0
k
If you draw a curve from this, you will have an inverse curve of the above LM curve.
(2) Intuitive Explanation
Why is the LM curve upward-sloping LM?

Let us start with an equilibrium, ms = md.

When the interest rate increases there will be a decrease in the real quantity of
money demanded, (a new md < an old md = ms).
How can we recover the equality between the real money demand and the real
money supply? The real money supply cannot change unless the government
changes the nominal money supply MS or M to a higher level, or the price level
changes. So the real money demand should rebound back to the initial level in
order to re-establish the equality. One way of doing it is to increase Y*. When
the national income increases, the real money demand will increase. This
increase in real money demand offsets the previous decrease in real money
demand. So we can observe that the interest rate and the national income move in
the same direction.

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4. (Expanded) Equilibrium National Income and Interest Rate in the ISLM Framework
Now we would like to get Y* and i* which encompass both goods and money markets.
The intersection of the IS and LM Curves give the equilibrium national income and the
interest rate that satisfy the market clearing condition in both goods markets and money
markets; ex-ante all the goods produced are demanded, and real money supply is equal
to the real money demand.
1) Graphic Solution
2) Algebraic Solution
Case 1 with Three Simplifying Assumptions: All taxes are lump-sum or autonomous
T = T0, Closed Economy NX= 0, and Prices are fixed
The strategy here is to bring up the IS and the LM, and solve for Y* and i* that satisfy
both IS and LM. So we go:
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Step 1: Recall the IS Curve: Goods market equilibrium condition AE = Y yields
1
( C 0 - c1 T 0 + I 0 - b i + G0 ),
1 - c1
or
Y=
1
1 - c1
i = ( C 0 - c1 T 0 + I 0 + G 0 ) Y
b
b

Step 2: Recall theLM Curve: Money market equilibrium condition ms = md yields
M0
P0
= ky - h i + u 0
h i= i=
M0
P0
M0
+ k Y + u0
1
k
(+ u0 ) + Y
h
h
P0
or
Y=
1 M0
h
(
 u0 ) + i
k
k
P0
where K is the elasticity of real money demand with respect to the national income; h is
the elasticity of real money demand with respect to interest rates; and u is the random
component of real money demand.

Step 3: Equate the above two equations for i or Y: The Simultaneous Equilibrium
of Goods and Money Markets yields:
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In practice, we may go either ways. First, when we equate Y of the IS and Y of
the LM as shown above:
1
( C 0 - c1 T 0 + I 0 - b i + G0 )  1 M
h
0
1 - c1
(
 u0 ) +
i
k
k
P0
Alternatively, we may equate i of the above IS and i of the above LM:
1
1( C0 - c1 T 0 + I 0 + G0 ) - c1 Y = 1 M 0
k
(+ u0 ) + Y
b
b
h
h
P0
The first equation will yield to the equilibrium Interest Rate. And the second will
yield to the equilibrium National Income. We have to get both. For now, we
focus on Y*:
*
Y =
M
h
b
( C 0 - c1 T 0 + I 0 + G 0 ) +
( 0 - u0 )
h(1 - c1 ) + kb
h(1  c1 ) + kb P0
Rewriting the above we get,
*
Y =
1
kb
1 - c1 +
h
( C 0 - c1 T 0 + I 0 + G 0 ) +
b
h
kb
1 - c1 +
h
(
M0
P0
- u0 )
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* Can you solve for i* by yourself?
Steps
1. Get the IS and LM curve
2. Solve for Y*
3. Substitute the solution of the Y* for the variable Y and the
LM equation to get the value for i*;
4. Differentiate the above equations for multipliers.
3) Comparative Statics of IS-LM: Multipliers:
i) Impacts of Exogenous Changes in Variables on Y* (or i*)
We may remember that in the simple Keynesian model of income determination (the
Cross-Diagram with Y = YS and AE) the multipliers were obtained by differentiating the
equilibrium national income equation.
Now, in the IS-LM curve model, another set of the multipliers can be obtained by
differentiating the first equation, which describes the equilibrium national income in the
goods and money market, with respect to the Autonomous components of AE ( C, T, I, G
and M). The result of differentiation is the coefficient of each variable in the above
equation.
Y
=
C 0
*
Y
=
I 0
*
1 - c1 +
kb
h
1
1 - c1 +
Y
=
 G0
*
1
kb
h
1
1 - c1 +
kb
h
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
The first two multipliers have something to do with business cycles as the C0 and
I0 show cyclical movements over time beyond the control by government.

The third one is called the ‘Fiscal Policy Multiplier’. It measures the ratio of the
change in the goods and money market equilibrium national income to a change
in government expenditure. Note that this new multiplier or the fiscal policy
multiplier in the IS-LM framework is smaller than the government expenditure
multiplier in the Cross-Diagram setting. Both measure ∆Y* due to ∆G. However,
the fiscal policy multiplier takes account of the resultant change in interest rate
and the consequent crowding out effect while the government expenditure
multiplier does not; The thus difference between the government expenditure
multiplier and the fiscal policy multiplier is the crowing-out effect which results
from an increase in interest rates and its suppression of private investment.
Because of the secondary feedback in the money market, the magnitude of fiscal
policy multiplier is smaller and thus ∆G has a smaller impact on Y*.
Y
=
T 0
*

 c1
1 - c1 +
kb
h
The above multiplier measures the change in income to a change in a lump-sum
taxes responsible for it.
b
Y *
h

M
kb

1 - c1 +
p
h

The above multiplier is called the ‘Monetary Policy Multiplier’. It measures the
ratio of the increase in income to an increase in money supply –recall that the
price level or P is constant, and thus any changes in M/P or real money supply
come from changes in M or money supply.
ii) Impacts on Interest Rates: Solve for the equilibrium interest rate, and examine its
coefficient
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Appendix1: Complicating the Tax Function
So far we have assumed a very simple model where all taxes are lump sum and there are
no exports or imports. Now, let’s extend our model to more complex cases of aggregate
expenditures as we have seen before.
1. Now we may assume that there are Autonomous and Proportional Taxes. T = T0 +
t1Y, and there are no imports or exports.

IS Curve: Goods market equilibrium condition AE = Y yields
Y =
i=

1
( C 0 - c1 T 0 + I 0 - b i + G 0 )
1 - c1 (1 - t 1 )
1
1 - c1 (1 - t 1 )
( C 0 - c1 T 0 + I 0 + G 0 ) Y
b
c1 (1 - t 1 )
LM Curve: Money market equilibrium condition ms = md yields
M0
P0
= ky - h i + u 0
h i= i=
M0
P0
M0
+ k y + u0
1
k
(+ u0 ) + y
h
h
P0
Alternatively,
Y 

1
M
h
(
 u )+
i
k
k
P0
Simultaneous Equilibrium of Goods and Money Markets
By equating the IS and LM curves, we solve for Y* (we can solve for i* as well;
how?) as follows:
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M
h
b
( C 0 - c1 T 0 + I 0 + G0 ) +
( 0 - u0)
h(1 - c1 (1 - t1 )) + kb
h(1 - c1 (1 - t1 )) + kb P0
or,
1
*
Y =
kb
1 - c1 (1 - t1 ) +
h

( C 0 - c1 T 0 + I 0 + G0 ) +
b
h
(
M0
kb P0
1 - c1 (1 - t1 ) +
h
- u0)
Note: compared with the equilibrium national income equation without the
LM curve (in the previous handout), there is an additional term kb/h in the
multiplier for the autonomous expenditures.
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Chapter V. Aggregate Supply & Aggregate Demand Curve Analysis
1. Aggregate Demand
1) Algebraic Derivation
You may remember that the equilibrium national income from the IS-LM curve is
*
Y =
h
b
M
( C 0 - c1 T 0 + I 0 + G0 ) +
(
- u)
h(1 - c1 ) + kb
1 - c1 + kb P0
Let’s focus on the relationship between Y and P.
If all variables are constant except for Y and P, we can get an equation showing the
relationship between the two variables Y and P, such as Y = 500 + 200/P. This equation
carves up the relationship between two variables, Y and P, is called the Aggregate
Demand Curve.
P
( C 0 ; T 0 ; I 0 ; G 0 ; M ) s h i f t p a r a m e t e r s
AD
YP
In the discussion of monetary policy which involves a change in money supply M and its
impact on P and Y, we deliberately drop the intercept A, which is related to fiscal
policies, and frequently use Y = B/P = B’ (M/P) to carve up the relationship between the
three key variables, M, P, and Y (real income).
If we draw the graph of the above equation with Y on the horizontal axis and P on the
vertical axis, this is a hyperbola.
We know that Y = 1/X is a rectangular hyperbola. Y = A + B/X is simply Y = 1/X
shifted up by A and outward along the Y =X line by B.
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The quantity theory of money postulates that the equation of exchange is M V = P Y,
or Y = V (M/P), where M is the supply of money, and V the velocity of circulation of
money. This equation is exactly the same as Y = B’ (M/P). This is a special case,
featuring monetary aspects, of the AD curve which embodies the impact of fiscal
policies along the others (∆C, ∆I) in the first term and that of monetary policies along
with monetary shocks (∆u) in the second term of the equation Y
2) Graphic Derivation
We derive the AD curve by examining the impact of a changing price level on the LM
curve and consequently on the AD.

When the price level falls from P1 to P2, the real money supply rises from M/P1
to M/P2. This shifts the LM curve to the right.

The equilibrium national income level rises in the IS-LM curve.
The corresponding point shifts in the AD setting. By linking the two points, we
get the AD curve.

LM (M/P1)
LM (M/P2)
P1
P2
AD
3) Shift of AD curve

∆ C0, ∆I0, ∆G0, - ∆T0  ∆IS  ∆AD

∆ M ∆LM  ∆AD

∆ md = ∆u  ∆LM  ∆AD
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In summary, the AD has six shift-parameters, C0, I0, G0, T0, M, and u.
 Out of them, C0, I0 and u are beyond the control of the government;

C0, I0 and u are called Aggregate Demand Shocks;
specifically, C0 and I0 (X0 and M0 as well in the open economy) are
goods market shocks, and
u is a monetary shock;

G and T are fiscal policy instruments;

M is monetary policy instrument.
To countervail the Aggregate Demand Shocks and thus to eliminate any impact on the
equilibrium national income, the government may control G, T, and M in countercyclical ways. This is called ‘the Counter-cyclical policy’ or ‘Income stabilization
policy’.
2. Aggregate Supply
1) What is the aggregate supply?
AS versus YS
The aggregate output is the sum of all the supplies of goods and services in the economy.
You may remember the 45 degree line of YS = Y in the Keynesian Cross Diagram.
When the aggregate output YS is drawn against a particular price level, that is the
aggregate supply. The only difference is that the AS is drawn again at the price level
while YS is not. In a sense, AS comes from YS. Then, our next question is, what
determines YS?
2) Aggregate Production Function
AS is the aggregate outputs at a particular price level. Output results through production
process from inputs. The production function shows the relationship between the inputs
and the outputs: production combines production factors with a certain technology. The
production function summarizes all three aspects of the supply: Inputs, outputs, and
technology.
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(1) Functional Form
In microeconomics theories, an individual production function, say, a hamburger or i
industry, is given by
th
Qi = f (K,L),
where K and L are capital and labor inputs, and Q output at the firm or industry level.
Technology is implied in the functional form.
The aggregate production function is obtained by summing up the production functions
of all industries. The aggregate production function shows the aggregate output YS as an
increasing function of capital and labor inputs. Again technology is implied in the
functional form. We use notation K for the capital stock or the amount of capital, and N
for labor input at the aggregate level of economy.
YS = F (K, N; T ).
Note that unlike the microeconomics which uses L for labor input, we use N for the
aggregate labor inputs, which is called the ‘level of employment’ in an economy. N may
be measured in total hours worked for a given period of time, which is equal to the
number of workers employed times the number of hours worked by each worker. Here T
stands for Technology employed in production.
(2) Derivation of the Aggregate Production Curve
Note that in the short-run, K remains fixed and T does not change. Thus the short-run
aggregate production function can be expressed as an increasing function of one variable
N or the level of employment of existing workers: the more workers employed for longer
hours, and then more aggregate output.
YS
Aggregate Production Curve
N
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(3) Shift of Aggregate Production Function
In the long-run, i) an increase in N, ii) an increase in K, and iii) the enhanced level of
technology are all possible, leading to an increase in Aggregate Output. However, an
increase in N leads to a movement along the Aggregate Output Curve, and the two others,
such as an increase in K or/and T leads to a shift of the Aggregate Output Curve.
i) Capital Accumulation: ∆K
With more capital inputs, each level of employment will lead to a larger amount of
aggregate outputs: With more capital equipment, each worker can produce more outputs.
This will send the Aggregate Production Curve outward, or upward.
YS
N


Capital naturally wears and tears over time and it is called ‘Depreciation’
Capital can be destroyed during a war.
ii) Technical Innovation, or Technological Advances: ∆T
With an improved production technology, each level of employment will lead to a larger
amount of aggregate outputs.

Therefore, technological advances also lead to a upward shift of the production
curve. The marginal product of labor rises, too.
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YS
N
iii) A Growing Number of Workers: ∆Ns
This is a rightward shift of the labor supply curve. The equilibrium nominal wage rates
fall: So does the real wage rate. The equilibrium level of employment rises, which
increases the aggregate outputs along the aggregate production function.
This can happen in the long run due to population growth, or open-door immigration
policies. As N is on the horizontal axis, this leads to a movement along the aggregate
production curve.
3) Aggregate Labor Supply and Demand Curve: Labor Market
Then, the question in order is how the level of employment or N* is determined to enter
the aggregate production function. N* is determined in the labor market through the
interplay of the aggregate labor supply and aggregate labor demand. Now, we note that
we are introducing one more market into the picture, and that is the labor market.
The supply of labor is an increasing function of real wages, which are money wage over
the price level ( w = W/P), and the demand for labor a decreasing function of real wages.
(1) Aggregate Labor Supply
The labor supply is an increasing function of real wages, which are equal to nominal
wages divided by the price level;
Ns = f (W/P; other variables)
For a given level of P, as W rises, Ns rises as well.
If you put Ns on the horizontal axis and W on the vertical axis, the curve should be
positively sloped. And P becomes a shift parameter.
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Numerical Example:
Ns = 100 + 3 (W/P).
If the nominal wage or money wage (rate per hour) is $10 per hour and the price
level is equal to 1, then the real wage (rate per hour) is 10/1 = 10, and the
aggregate labor supply would be 100+ 3 times 10/1 = 130.
The above is sufficient for the labor supply curve in macro. Note that the vertical axis is
in the real wage W/P. The labor supply is an increasing function of real wage.
However, in the macroeconomics, we would further separate real wage W/P into nominal
wage W and price level P. If we draw the aggregate labor supply curve N s against the
nominal wage W, we can see impacts of P more clearly.
How can we do that? First, hold P = 1 constant, then W/P becomes W, and draw the N s
curve of the same shape:
(for P=1)
Note that now the vertical axis is W or nominal wage, and the horizontal axis is the level
of employment or N, and finally that the Ns curve or the aggregate labor supply curve is
drawn with the fixed price level of 1. Thus we should note that the price level is now the
shift variable of the Ns curve.
What will happen to the Ns curve for P =1 if the price level rises from 1 to, say, 2 while
the nominal wage (rate for hour) is held constant?
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A Shift of the Ns curve:

In the short-run, a change in the price level shifts the Ns curve. As P rises, the Ns
curve shifts up as well; As P rises, for a given level of W, the real wage of W/P
falls, and thus labor supply falls.
When P rises from P=1 to P=2,
Ns (for P=2)
Ns (for P=1)
W
Ns decreases
There are other variables that shift the Ns curve.

For example, in the long-run, as population grows, the aggregate labor supply
curve shifts to the right.
When population grows or more immigrants come, the Ns shifts to the right
Ns
Ns’
W
Ns increases
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In summary, for the dimension of W and N, we can write the aggregate labor supply
curve as:
Ns = f (W(+) : P(-) , other variables such as population, immigration, etc.)
All other variables, except W and Ns, become shift variables. A change in these shift
variables leads to a shift of the Ns curve.
Remember that an increase in the price level or P leads to the visually upward movement
of the Ns curve or a decrease in Ns.
(2) Aggregate Labor Demand:
Let us examine the labor demand first:
The aggregate labor demand is a decreasing function of real wages:
Nd = g (W/P; other variables).
If we draw a curve which shows the relationship between Nd and W. It will be
downward-sloping; as W goes up, the entrepreneurs demand for labor falls. The third
variable P becomes a shift parameter.
W/P
Nd
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By holding P = 1 constant, we can get a Nd curve corresponding to P=1.
W/1
Nd (P=1)
Nd
Background-You may recall the following Microeconomics theory of labor
demand:
The entrepreneur does demand labor and hires workers. If s/he is maximizing
profits, at the margin or for the last worker hire, the cost is equal to the benefit.
The cost of hiring the last worker in monetary terms is the money wage W, and
the benefit from hiring the worker is the marginal product MP (units of output the
worker produces) times the price of the output P. So at the profit maximizing
level of employment, W = P x MPL.
Numerical example) It costs $10 to hire a worker because W = $10. The last
worker increases the total products or outputs by 5 (5 units of outputs), and each
unit of output has the price of $2 in the market. The cost of hiring the last worker
is $10, and the benefit from hiring her/him is 5 times $2, being equal to $1.
We now know that at the equilibrium for the profit maximizing firm
W = P x MPL in dollar terms, or W/P = MPL in physical terms.
MPL is a decreasing function of the amount of labor inputs.
The real wage w= W/P is set by market forces, and is paid uniformly to all
workers, regardless of whether there are many or few workers.
When the real w = W/P is set at a certain level in the labor market, the
entrepreneur who is a price taker will hire workers in such a number that the last
worker’s marginal product is equal to the real wage set in the market. The
entrepreneur is making profits from hiring intra-marginal workers (all the workers
except the last worker hired) as their marginal products are higher than the real
wage. S/he is not marking any profit from hiring the last or marginal worker (MP
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= W/P) This implies that the MPL curve itself drawn against real wages is the
labor demand curve.
A Shift of the Nd curve:

As P or the price level rises, the real wages (W/P) falls for a given level of W.
And thus Nd rises: this is a rightward movement or upward movement of Nd curve.
As P rises, say from 1 to 2, while W is held constant,
W
Nd(P’)
Nd(P)
N
Nd rises
where P =1, and P’ = 2 in this case.
There are other variables that shift the Nd curve:
 In the long run, ∆K or an enhanced technology increases each worker’s
productivity or marginal product. The MPL shifts up, and the labor demand curve
shifts up (or to the right): some workers who used to be unproductive and thus
unemployable become now productive due to technical innovations and become
employable. There is an increase in the aggregate labor demand by the
entrepreneurs.
W
Nd’
Nd
N
Nd rises
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In summary, for the dimension of W and N, we can write the aggregate labor supply
curve as:
Nd = g(W (-) : P(+) , other variables such as population, immigration, etc.)
All other variables, except W and Ns, become shift variables. A change in these shift
variables leads to a shift of the Nd curve.
Remember that an increase in the price level leads to the visually upward movement
of both Nd and Ns curves.
(3) Labor Market Equilibrium
The interplay of the Nd and NS determines the equilibrium level of employment N* and
the equilibrium level of real wages w*;
At equilibrium,
f(W/P) = g(W/P), or
f(W: P ) = g (W: P)
We can solve for the real wages or W/P at this equilibrium in the labor market.
And then, for a given price level, we can also get the nominal wages W for this
equilibrium.
Graphically,
W
W*
N*
Nd
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By plugging the value of W* back into the aggregate labor supply or demand function,
we can get N*
In summary, As – YS – N*- w* - W for a given level of P.
(4) Responses of Nominal Wages to Changing Price Levels: Flexible or Not?
We would revisit the question of what will happen to the equilibrium real wage W/P = w
when the price level rises? This depends on what will happen to nominal wage or W
when the price level rises.
In the microeconomics, which belongs to the world of classical economics, there is an
assumption of flexibility of nominal wage. In other words, the nominal wage W will rise
in an exact proportion to the increase in P. As P rises, W rises by the same amount. Thus,
W/P = w or real wage does not change. There will be no change in the level of
employment N, and thereby no change in aggregate output YS or real national income Y.
The flexibility of nominal wage W ensure the separation of the world of nominal
variables such as W and P, and the world of the real variables such as N, YS, and Y.
There is a dichotomy between the real and the nominal variables.
However, in macroeconomics, there are different schools which have different
assumptions about the degree of flexibility of nominal wage. And the different degrees
of flexibility of nominal wage opens up the possibility of W not exactly following the
movement of P and thus lead to a change in real wage or w =W/P, level of employment N,
aggregate output YS, and real national income Y. An increase in the price level, which
is a change in nominal variable, can affect the real variables.
Let’s elaborate on this point:

If W is viewed to be flexible, just as assumed in the classical economics, and
follows the movement of P, a change in P will be accompanied by an equal
movement of W, leaving w unchanged.
First, the rising P shifts both the labor supply and demand curves up;
The new equilibrium occurs at E;
The new equilibrium nominal wages are proportionally higher than the previous
one: In other words, the increase in W is proportional to the increase in P;
Therefore the real wages (w= W/P) do not change;
The level of employment is the same as before.
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E
W1
W0
Nd
This flexibility of money wages and thus the consequent constancy of real wages belong
to the classical world, where i) there is no information asymmetry between the
entrepreneurs and the workers: There is no money illusion on the part of workers (it goes
without saying that any working, let along successful, entrepreneurs should NOT have
any money illusion at all); ii) there is no structural rigidity which hinders flexible changes
of money wages in response to a change in price level, particularly of downwards
changes or falls to a falling price level in the case of recession, such as labour unions,
and finally iii) it is in the long-run – enough of time has passed to make a full adjustment
of money wages to a changing price level.
However, John Maynard Keynes saw the real world differently: First, he argues that yes,
in the long-run, the money wages will adjust fully to a changing price level and
everything will be fair and square, but that in the long-run ‘we are all dead’. We may live
through a series of short-terms, and constant changes in equilibrium. In the short-run,
money wages can be rigid for many reasons. For one thing, it may be confusion on the
part of the workers, such as money illusion. Even in the long-run, money wages can be
rigid even amid recession, and they are so mainly due to institutional elements such as
labor unions. Why did the Great Depression last for such a long period of time – 10 years
or so? It was mainly due to the rigidity of money wages backed by labor unions, and also
due to ‘confusion’ by a political leader. Let’s listen to Professor G. Smiley in her
contribution of ‘The Great Depression” in the Concise Encyclopedia of Economics:
“….In previous depressions, wage rates typically fell 9-10 percent during a oneto two-year contraction; these falling wages made it possible for more workers
than otherwise to keep their jobs. However, in the Great Depression,
manufacturing firms kept wage rates nearly constant into 1931, something
commentators considered quite unusual. With falling prices and constant wage
rates, real hourly wages rose sharply in 1930 and 1931. Though some spreading
of work did occur, firms primarily laid off workers. As a result, unemployment
began to soar amid plummeting production, particularly in the durable
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manufacturing sector, where production fell 36 percent between the end of 1929
and the end of 1930 and then fell another 36 percent between the end of 1930 and
the end of 1931.
Why had wages not fallen as they had in previous contractions? One reason was
that President Herbert Hoover prevented them from falling. He had been appalled
by the wage rate cuts in the 1920-1921 depression and had preached a “high
wage” policy throughout the 1920s. By the late 1920s, many business and labor
leaders and academic economists believed that policies to keep wage rates high
would maintain workers’ level of purchasing, providing the “steadier” markets
necessary to thwart economic contractions. When President Hoover organized
conferences in December 1929 to urge business, industrial, and labor leaders to
hold the line on wage rates and dividends, he found a willing audience……”
Perhaps, it wasn’t Mr. Hoover who found the audience, but it was the general public
(workers) that found Mr. Hoover as a populist politician. He meant to have represented
the workers by supporting an artificially high money wages, but in the end, he prolonged
the depression into the Great one in history.
Thus the Keynesian world goes as follows:

If W is fixed, particulary downwardly rigid: An increase in P may or may not
be accompanied with a commensurate increase in money wages or W, and thus
may lead to a decrease in real wages or w. However, more apparently, a decrease
in P during the recession may not lead to a corresponding fall in money wages or
W. It may be due to three things: money illusion on the part of workers; labor
unions, and/or in the short-run. In any case, it will lead to an increase in real
wages or w: an increase in the real labor cost on the part of entrepreneurs and thus
their demand for labor decreases.
First, the increasing P shifts both the labor supply and demand curves visually up.
However, the nominal wages are set at a fixed level, shown by the horizontal line;
nominal wages cannot be nothing other than the fixed level.
The new equilibrium should come at E where the labor demand curve and the
horizontal nominal wage line (effective labor supply curve) intersect.
At the new equilibrium, compared with the previous equilibrium, the nominal
wages are the same, and the equilibrium level of employment N is lower.
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Ns
W
E
E
(effective labour supply)
Nd
N
*
N
*
0
Nd
The first position is taken by the classical economics, which is the same as the
microeconomics, and the second is by the Keynesian economists. The second is true
when there is structural impediment to the flexible mobility of W or nominal wage.
This is the case when there is a union which insists on having fixed nominal or
monetary amount of wage. In other words, when workers’ unions have ‘money
illusion’ and thereby focus on the nominal value of wage instead of real value or
purchasing power of the wage. This is also the case when the time-period of
observation is too short. In a very short-run, the change in the price level is not
reflected in the wage level. The third possibility is when the people (= the workers)
have some kind of ‘money illusion’. The money illusion refers to the situation where,
being faced with a changing price level P, the people really should focus on the real
wages w = W/P but they in fact have ‘hang-up’ on the nominal wages, and thus they
try to stick to the fixed nominal wage( W bar). The end result is that real wage instead
changes and so do N*, YS, and Y.
On the other hand, if there are no impediments on the mobility of nominal wage W
and workers are more or less fully employed W will move in the same direction as the
changing P in the long-run. ∆P means an increase in living –costs for workers, and
workers will eventually demand a higher money wage or ∆W.
Basically, the AS analysis hinges upon what is happening when the price level changes:
What is the impact of a change in the price level on real wages and on the equilibrium
employment level?
4) Derivation of Aggregate Supply Curve
(1)Different Aggregate Supply Curves
You may remember that the AS is assumed to be vertical in the classical economics, and
horizontal or upward sloping in the Keynesian economics.
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You may recall that the classical AS curve is vertical; the AS is fixed at a certain level.
The fixed level of AS is called ‘the full employment level’.
Note: The full employment does not mean zero unemployment, but a low yet
positive rate of unemployment. A certain positive rate of unemployment is
inevitable for an economy where new comers are looking for best-fitting jobs and
some workers are upgrading their skills and consequently searching for another
jobs. Some unemployment is even desirable as it provides some reserves in the
economy; without it the man/women-power situation is too tight, and a firm
which is faced with even temporary rise in the demand for its products would
have extreme difficulties in hiring extra workers. As a consequence, we will
observe a shortage of the good or a rise in its price. We need a small ‘buffer’ of
unemployed workers. This positive rate of unemployment compatible with a
smooth working economy at the ‘full employment level’ is called ‘the natural rate
of unemployment’. The corresponding national income is the ‘natural real
national income.’
In the short-run, there may be some temporary deviation of the actual national income
from the full employment N.I., but the price level will adjust to push the economy back to
the equilibrium. The Business Cycles can occur due to the demand shocks. However, it
is only temporary, and is of no big concern as the economy, if left alone, automatically
gravitates toward a unique equilibrium N.I.
What is the role of the government in the economy?
If there is no factor in the economy which blocks the above tatonnement, the government
should not create anything which can get in the way of this natural adjustment process of
recovering the equilibrium. Actually it should eliminate any impediments in this process
and facilitate the adjustment process by promoting competition.
You may also recall that the Keynesian Aggregate Supply curve is upward-sloping; the
AS responds positively to the (output) price level.
(2) Fundamental Cause of Different AS curves.
Flexible Nominal/Money Wages  A vertical AS curve.
(Neo Classical)
Rigid Nominal./Money Wages  a Positively Sloping AS curve. (Keynesian)
The reasons for rigidity:
Money Illusion; a kind of stupidity at the individual level
Union, etc: a kind of ‘social’ and ‘structural’ rigidity
To derive the Aggregate Supply Curve, first you need a Four-Panel graph of AS-AD, Ns
and Nd, and Aggregate Production Curve and a 45 degree-line of converting YS into Y.
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The AS curve shows the relationship between the different levels of prices, or Ps, and the
corresponding levels of real national income, orYs. Thus, you have to kick up and down
the price level or P, and to find the corresponding Y.
(3) Classical Aggregate Supply Curve: A Vertical AS Curve
Under what circumstances would the money wage be flexible?
i)
The economy is at full employment level: all available workers are fully
employed; there are no other workers who are willing to work for the real
wage lower than the prevailing rate;
ii)
There is no structural rigidity of money wage: no impediment on the
equilibrating force in the labor market;
iii)
The workers are free of ‘Money Illusion’;
iv)
In the long-run: an enough amount of time has elapsed since ∆P.
This is a graphic and somewhat mechanical derivation:

1.) Choose a price level, say, P1.

2.) For this given price level, we can have the labor supply and demand curves;
Ns = f (W/P); and Nd = g (W/P) become
Ns = f (W: P1); and Nd = g (W: P1).
Or, by simply showing the shift variables, we can write down
Ns (P1); and Nd (P1).

3.) The intersection of the labor supply and demand curves gives the equilibrium
real wage w= W/P, in the labor market; N* and W* for a given P (thus w*).

4.) The equilibrium N* feeds into the aggregate production function of
YS = F (K, N*; T) for a given K and T in the short-run.

5.) YS = Y the third panel.

6.) Y goes down to the fourth panel and matches the starting price level P1.
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
7.) Suppose that the price level goes up to P2.

8.) As P rises, both labor supply and demand curves shift up.
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Now we get Ns (P2); and Nd (P2).
These are shown with broken lines in the graph below.

9.) We get the new equilibrium. At this new equilibrium, the new nominal wages
are higher than the previous nominal wage by the same proportion of the increase
in P. And thus, the real wages do not change; the level of employment does not
change, either.

10.) The same level of employment feeds into the aggregate production function,
and leads to the same level of YS.

11.) The same level of Y in the third panel.

12.) The same Y goes down to the fourth panel and matches the new price level
P2.

13.) By linking the two points in the fourth panel, we get the AS curve.
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Note that along this AS curve the real wage is constant but money wage is not: at
point 1 the corresponding money wage is W*1, and at point 2 the corresponding
money wage is W*2. However, at both points, the real wage is equal to w.
An intuitive explanation is as follows:
When P rises, W will rise proportionately. The revenues (P Q) and the costs (W
L) are increasing proportionately, and thus the profit margin does not change.
There is no reason for entrepreneurs to attempt to expand production scale. The
AS remains constant at the macroeconomic level, too.
P increases and W increases  W/P remains unchanged  N remains
unchanged YS remains unchanged  Y remains unchanged, and thus a
vertical AS we get.
(Supplement: Why does W/P determine the profit margin?)
Production decisions are made ultimately by producers, or entrepreneurs who weigh the
situations in the output market (which determines revenues) and the input market (which
determines costs).
Entrepreneurs make supply decisions by weighing the ratio of output price to input price,
which is the key variable for their profits which constitute their prime motivation.
Entrepreneurs are orchestrating production processes (borrowing capital, hiring workers,
etc.) in order to earn profits.
Formally, the aggregate production function shows the relationship between inputs such
as capital (K) and labor (L), and outputs. These aggregate outputs are the aggregate
supply or Y in Y – YS: Y = F (K,L)
We know that an increase in K and L leads to an increase in Y. However, it does not
happen by itself. In order to have a larger amount of inputs and consequently more
outputs, entrepreneurs should exert themselves to organize more K and L. What would be
the incentive for entrepreneurs to produce more? They respond to a larger profit margin.
Profit is revenues minus costs. Revenues are Output Price times Quantity.
Costs are Input Price times Input Quantity. Profit = Total Revenue – Total Cost = P Q – (
r K + W L). In the short-run, P and W determine the magnitude of profits; an increase in
P increases profits, and an increase in W decreases profits.
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(4) Keynesian Aggregate Supply Curve
Basic assumptions are as follows:
i)
ii)
iii)
The time is too short for W to change, or
There are impediments on the flexibility of W, or
There is unemployment; there are other workers other than the present
employees, who are willing to work for less than the present real wage.
Graphic Derivation is as follows:












Start with P1.
For the given price level, get the labor supply and labor demand curve in the
second panel.
The intersection of the labor supply and demand curves gives the equilibrium
level of employment N1.
This feeds into YS1 in the aggregate production function.
YS1 = Y1 in the third panel.
Now in the fourth panel, Y1 matches with P1.
Suppose that the price level goes up to P2.
This sends both the labor supply and demand curves up.
However, the level of nominal wages does not change due to unions or money
illusion. It is the effective labor supply curve; note that it replaces the shift labor
supply curve, which is meaningless.
The new equilibrium level of employment is given at N2.
This feeds into the aggregate production function to give YS2 = Y2.
Y2 goes down to match P2.
By linking the two points of Y in the fourth panel, we get the Keynesian
Aggregate Supply Curve. It is upward-sloping.
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Along the Keynesian AS curve, the nominal wage rates are fixed at W*. However,
real wages vary along the AS curve. That is because the money wage is fixed
along the AS curve, but the price level varies: The real wage (=W/P) must vary
along the curve.
This contrasts with the fact that along the previous classical AS curve, which is
vertical, the real wage is fixed but money wage varies.
Suppose that there is a huge excess capacity of production: this is possible as the
economy is just coming out of a big recession. Even a very small increase in the
price level leads to some increase in the revenues of companies (= P x Q), and the
entrepreneurs will respond to this increase in revenues in a big way by hiring a lot
of new workers back to the production process. We can have a very flat AS
curve as well.
Depending on the elasticity of the supply side, we can get the almost horizontal
SAS curve as we have seen in Chapter 1.
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Intuitive Explanation for the upward sloping AS curve is as follows:
When P rises, W remains constant. The revenues increase while the costs are fixed, and
thus the profits increases. The larger profits will give a greater incentive for
entrepreneurs or employers to expand production scale by hiring more workers. If this
expansion of output happens to all firms, the aggregate supply will increase.
P increases with W being fixed  w(=W/P) decreases  Nd increases  N*
increases  AS = y = F (K, N) increases
The opposite can happen, too.
P decreases with fixed W w(=W/P) increases  Nd decreases  N* decreases
 AS = y = F (K, N) decreases
Let us explain the same thing in terms of real wages, which is nothing but the ratio of W
and P or W/P. The profitability is related to the ratio of W to P (=W/P), which is real
wage or constitutes ‘real’ cost of hiring workers.
1) When W/P falls, the real cost of hiring workers is falling, the profit margin
widens, and thus more (incentive for) production (on the part of the
entrepreneurs):
Real wage (W/P) decreases  Nd increases  Actual N* increases  AS = y = F
(K, N) increases
2) When W/P rises, the real cost of hiring workers is rising, the profit margin is
reduced, and thus less (incentive for) production (on the part of the
entrepreneurs).
W/P increases  Nd decreases  Actual N* decrease  AS = y = F (K, N)
decreases
Note: a larger W/P sounds like good news for the workers. You may be wrongly
reasoning: “a larger W/P means a larger incentive for the workers to work. The
longer and harder the workers are working, the larger the output. And the workers
will have more money to spend.” (This is the very wrong idea that Mr. Hoover
had during the Great Depression).
But it is not workers but entrepreneurs that make production decision. In the
above case, who will hire the larger number of more willing workers at such a
high real wage level? The willing workers will not be hired as they cannot force
the entrepreneurs to hire them above and beyond the latter want to.
So we are assuming that the actual amount of employment is determined along an
entrepreneur’s labor demand curve, not along the worker’s labor supply curve,
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and the effective labor supply curve, which is basically the horizontal line from
the fixed money wage or W.
Can you mathematically express the AS curves of the Keynesian and the Classical
economists?

Classical AS curve: Y = F(K, Nf) = Yf, say, 1000.
Keynesian AS curve: Y = F(K, Nf + dN) = Y – a (W/P), say = 1500 – 100 (W/P):
(W/P) increase then dN <0, so N < Nf and Y decrease,
(W/P) decrease then dN >0, so N > Nf and Y increase.
If W/P goes up, the real cost of hiring workers is higher now, and thus entrepreneurs
would like to hire less workers. The resultant output or AS will be smaller. If W/P falls,
the real cost of hiring workers is lower now, and thus more workers will be put into
production process and the resultant AS will be larger than the previous equilibrium or the
full employment level national income.
Some may argue that the Classical AS curve is valid in the long-run; and the Keynesian
AS curve is valid in the short-run;
Short-run AS = Keynesian AS
Long-run AS = Classical AS
One might have the SAS curve in the short-run when the time is too short for W to
change and the LAS curve in the long-run when enough time elapses for the adjustment
of W.
5) Shift of Aggregate Supply Curves

i)
ii)
iii)
iv)
The Long-run AS shifts(to the right) when
∆K
∆Technology
∆Population
Positive Supply shocks
As the long-run AS shifts to the right, the level of long-run real national income
or full-employment real income rises.
The first two shifts the Aggregate Production Curve up and, at the same time, the
Aggregate Labor Demand curve up.
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Population growth shifts the aggregate labor supply curve to the right (downward
visually).
The last one, positive supply shocks, may send the aggregate production curve up.
Combined or not, the shifts of the aggregate production curve and the
corresponding aggregate labor supply or demand lead to an increase in YS and Y
as we can easily illustrate on the 4 panel graph.
Over time, the first three happen to a growing economy. And it is called
‘economic growth’, and the annual economic growth rate is measured by a
percentage change in real national income.
These issues will be examined in details in a later chapter of economic growth
theories.

The Short-run AS shifts (to the right) when
The above four shift factors, and
v) ∆ Decreases in Money Wage
When the LRAS curve moves, the SRAS shifts, too, at all times.
However, it is not necessarily the case that when the SRAS shifts, the LRAS shifts:
When there is an increase in money wages, the SRAS shifts to the left (visually up), but
the LRAS stays put.
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(1)An Increases in Money Wages or W:
Suppose that unions raise the fixed nominal wages to a higher level;

Along the AS curve, the nominal wage rates are fixed at W*.
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(2)Technical Innovation
If we assume that there is no change in labor demand, but the technical innovation shifts
up the aggregate production function only, then N1* remains to be the equilibrium level of
employment in the labor market. However, the corresponding out level is higher and thus
the long-run AS curve as well as the SR AS will shift to the right to a new point of Y2.
We can see that the LAS and SAS curves all shift to the right by the same amount and at
the same time: the height of the intersection of the SAS and LAS curves stays the same.
However, most technical innovations increases the productivity of labor forces as well.
Thus the demand for labor forces increases. In other words, technical innovation shifts up
the aggregate production function as well as labour demand curve. In this case, the
equilibrium level of employment will be at N2, and the corresponding level of national
income is Y3. And thus the SAS and LAS shift more to the right than the previous case.
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(3)An Increase in Production Cost(except for money wages) such as Oil Shock
In general, this is called ‘adverse or negative supply shock’. It shifts the aggregate
production function downward.
This permanently shifts the LRAS and SRAS to the left by the same amount.
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3. ‘Grand Equilibrium’ of Aggregate Demand and Supply
1) Grand Equilibrium
Long-run AS
Short-run AS
P
P*
AD curve
Y*
Y
The intersection of the AD curve and the Long-run Aggregate Supply curve gives
the long-run equilibrium.
The intersection of the AD curve and the Short-run Aggregate Supply curve gives
the short-run equilibrium.
There are the corresponding equilibrium national income and the equilibrium
price level for the short-run and the long-run equilibrium respectively.
2)Short-run Adjustment to the Long-run equilibrium
What if the long-run equilibrium and the short-run equilibrium do not coincide with each
other?
The long-run adjustment depends on the flexibility of Money Wage: If nominal wage or
W is flexible, then the SAS curve will move around so that the intersection of all three
curves, i.e., LAS, SAS, and AD, come to one point.
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However, please note that the above adjustment of the SAS to the LAS is not automatic.
It critically depends on the background of the economy, particularly on the flexibility
versus rigidity of nominal wages.
If for some reasons money wage or nominal wage is not flexible in the long-run, the SAS
will stay suspended. This was the case of the Great Depression.

Suppose that the short-run equilibrium Y < long-run equilibrium Yf;
P
workers
AD
Y1
LAS
SAS
-- deflationary gap  Y leads to more competition among
For instance, Yf is below the long-run equilibrium or full employment income Yf.
The deflationary gap leads to a competition among unemployed workers and thus
lower nominal wages. The falling nominal wages shift the short-run aggregate
supply curve to the right. Eventually, a new short-run equilibrium will coincide
with the long-run equilibrium.
However, if there is an impediment to the flexibility of money wages, the SAS
will stay suspended, and will not move to the new position given by the solid
broken line as shown above. And the equilibrium national income Y1 will last for
a long period of time, which is below the full employment national income Yf. It
is a sustained economic recession.

If initially short-run Y*>long-run Yf* and money wages are flexible, then
there will be an inflation gap developing, which will lead to upward pressure
on money wage. As money wage goes up, the SAS goes up as well. Eventually
all the three curves of SAS, LAS and AD, intersect at one point:
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P
---
inflationary gap
The short-run equilibrium national income exceeds the long-run or full
employment national income. This inflationary gap leads to an increase in the
price level. The labor supply in the market is tight. The competition for workers
leads to a rising nominal wage. Thus the labor supply curve will shift to the left
until it passes through the long-run equilibrium point where the AD and the Longrun AS curves intersect.
3) Applications of the AS-AD Curve Model: Economic History of the U.S.
(1) Industrial Revolution (1869 – 1897)
Statistical data shows:
Y*
100.00
299.00
Y*
1869
1897
P
LAS0
LAS1
P*
100.00
63.40
P*
SAS0
SAS1 SAS2
P1869
(100.00)
P1897
(63.40)
Yf1869
(100.00)
Yf1897
(299.00)
AD
Y
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mainly due to LAS (SAS), which was in turn due to K, L, T during the
American Industrial Revolution
AD was stable due to no (slow) increase in (gold) money supply
An increase in population might have added, through an increase in C, I, and so
forth, but the overall it is no stronger than an increase in AS.
When LAS0 moves to LAS1, SAS0 moves to SAS1 by the same amount at the
same time(note that the intersections of the LAS and SAS before and after have
the same height). That is not the end of the story.
Note that the SAS moves once again from SAS1 to SAS2: Because the short-run
equilibrium national income given by the intersection of SAS1 and AD leads to a
short-run equilibrium national income Y (not indicated above: you may do so),
and it is below the new full employment or long-run equilibrium national income
Yf 1987.
In this case, just as we have learned, the SAS should move to the long-run
equilibrium. As SAS moves to the right for this reason, there is an additional
increase in Y and a fall in P.
(2) The Great Depression (1929 – 1939)
Y*
100.00
70.00
105.00
1929
1933
1939
P
LAS
P*
100.00
75.00
100.00
SAS
AD19
AD19
3919
AD
Y
Y << Yf
*
- puzzling question: Why SAS did not shift to the right when P level fell
between 1929 and 1933?
33
29
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The answer lies in the institutional downward rigidity of money wages that kept
the SAS there for a long period of time.
If the money wages had fallen, YSR* would not have stayed below Yf for such a
long period of time:
P
LAS
SAS
099
SAS
1
AD29
Y f  YSR  YLR
*
*
AD39
Y
(This situation did not happen in 1929-1939)
(3) Pax Americana (1945 – 1962)
-
a resumed economic growth, shifting LAS and SAS (and is coupled with an increase
in AD due to the post-war expansion of government expenditures, consumption, and
investment)
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LAS 0
L A S1
P
SAS 0
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SAS1
E'
e
Y 1*
Yf
Y f'
Y
(4) Evolution of Inflationary Spiral (1968 – 1969 – 1980’s)
-:
:
:
Where people to do not have inflationary expectations, the economy
moves from (a) to (b) in the SR. As the general public catch on what
is happening to the price level, they demand a higher money wage and
the higher wage is reflected in the shift of the SAS curve from (b) to
(c) in the LR.
When people revise inflation expectations at the same time along with
the actual increase in the price level: one movement is from (c) to (d).
When inflation expectations are excessive, being higher than the
actual increase in the price level, and, in addition, the excessively
higher money wages are actually obtained by strong labour unions,
one movement is from (a) to (e)  The result is a decrease in Y below
Yf, and it is called STAGFLATION, which is the combination of
STAG(nation) plub (in)FLATION.
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LA S 0
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SAS3 LAS1
e

SAS2

d
SAS1
SAS 0

c
b
a
AD3



AD0
Y
*

Yf
AD2
AD1
Y
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(5)Oil Shocks (1972 – 1975)
:
:
P
Oil shocks – permanent (negative) AS shocks, shift LAS and SAS to
the left
Additional adjustment of AS curve
LAS1
LA S 0

SAS2

SAS1
 SAS 0
AD0
Y
'
f
Yf
Y
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4. Rational Expectations Revolution and New Classical Model
1) Assumptions
(1) Revised Labor Supply and Demand Curves
The entrepreneurs make a decision on labor demand on the basis of the actual real wages,
which are equal to nominal wages divided by the actual price level;
Nd = f (W: P, other variables).
This is the same as any previous models.
On the other hand, the workers make a labor-supply decision on the basis of their
‘perceived real wages’, which are equal to nominal wages divided by the ‘expected price
level’ of the current period, being carried from the last period.
Ns = g (W: Pe, other variables).
We draw Ns curve with W or money wages on the vertical axis and N on the horizontal
axis. Pe becomes a shift parameter.
W
Ns (Pe1)
W1
Nd (P1)
N1
Y
(2) Information Asymmetry is a norm for Unannounced Policies.
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At time period t-1, workers and employers do form expectations as to the price level to
prevail at time period t, that is, Pe.
At time t, the actual price level turns out to be equal to P. Of course, there is no guarantee
that Pe = P.
As soon as the price level reveals, the employers or entrepreneurs are updated, and do
have correct information about the current price level P. On the other hand, the workers
do not have information about it. The workers do have just the expected price level Pe,
which is carried from the last period.
Derivation of Lucas Aggregate Supply Curve for a fixed Price Expectations on the
part of Workers:
i) Information Asymmetry and the New Classical Labor Supply and Demand
Curve:
Suppose that there is an increase in P, which the entrepreneurs recognize but the workers
do not. In other words, let us assume that there is information asymmetry between the
employers and the employees about the price level.
In this case, what will happen to the Nd (P1) and Ns (Pe1) curves?

This increase in P is unexpected on the part of workers, and thus Pe remains
unchanged. Thus the labor supply curve stays put.

However, the entrepreneurs are updated on the increase in P. Thus the labor
demand curve shifts up.
W
Ns (Pe1)
Nd (P2)
Nd (P1)
Y
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ii) Information Asymmetry and the New Classical AS Curve:
P > 0
Pe = 0
W* >0
P > W* > Pe = 0
Lucas’s
AS

Along the Keynesian AS curve, the nominal wage rates are fixed at W*.
The resultant AS is called “Lucas’s AS curve” or “Expectations-Augmented AS
curve”.

Note that along this Lucas AS curve, the expectations about the price level are
constant. In other word, the expected price level is the shift variable for Lucas
Aggregate Supply Curve. As the workers or the general public revise their
expectations as to the price level (up: it is a numerical increase), Lucas’s AS
curve shifts (it is visually a upward movement, but a numerical decrease in AS).

Note that the increase in the nominal wages W is smaller than the increase in P.
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As a result, in the mind of a worker, the perceived real wages have gone up: The
expected price level remains unchanged while the actual nominal wages have
gone up somehow. The labor supply rises along the curve.
However, the actual real wages, the nominal wages divided by the actual price
level, have gone down; the numerator has changed less than the denominator has.
iii) Revised Expectations and the Shift of Lucas Aggregate Supply Curve
Recall that, as P1 goes up to P2, Nd curve shifts up on the part of entrepreneurs but Ns
remains constant reflecting a constant Pe on the part of workers: This is needed to derive
LAS(Pe1 ) curve.
Now what will happen if the workers revise their expectations? The Ns will shift up as
shown below, there will be two corresponding points to the two different price level P1
and P2.
Lucas AS (
)
Lucas AS (
)
Note that Y1 here coincides with the full employment national income.
iv)A vertical Long-Run Aggregate Supply Curve or LRAS is still valid here as well. This
is the line passing through the points where expected price levels are the same as actual
price level. In the long-run the perception will come in line with the reality.
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(3) Policy Invariance Theorem for Fully Anticipated Government Policies
How convincing is the assumption of Information Asymmetry as assumed above?
Generally it did make a sense prior to the 1980s. However, in today’s world of the postinformation-revolution society where the general public has access to all kinds of
information including government policies, information asymmetry may not be
sustainable. The general public has the same access to information of the government’s
policy model and all the input data. With this parity-of-information between the general
public and the government or the policy maker, the assumption of information
asymmetry between the employers(entrepreneurs) and employees(workers) is
unsustainable. It is all the more so in a democratic society where every has equal access
to all kinds of information and information is efficiently propagated. This is particularly
so when government announces its proposed policy and its forecast economic impacts in
advance. The ‘honest’ government may be educating the general public in this case.
A well-announced economic policy with deterministic rules will not have any impact
on the real variables such as real national income- Policy Invariance Theorem
Suppose that even the workers are fully updated on a change in the price level: The
government announces its policy well in advance to the general public and carries out the
policy in the honest and open way. The general public have time to understand the
impact of the proposed policy on the price level and thus to revise their expectations
about the price level. What will happen to the labor supply and demand curves?
Ns (Pe2)
W
Ns (Pe1)
Nd (P2)
Nd (P2)
P
Note that P = Pe = W* > 0 in this case.
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What is the resultant AS curve in this case?
AS

Along the Keynesian AS curve, the nominal wage rates are fixed at W*.
The resultant AS is the same as the long-run AS curve.

Note that the increase in the nominal wages W is proportional to the increase in P.

This happens in the long-run when the workers are fully updated on what is
happening to the price level, and the money wages become flexible even if they
are not so in the short-run.

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Another way of looking at the above is as follows:


We can think of the above vertical long-run AS curve as Lucas’s AS curve shifts
up as the expectations are revised as given below:.
LAS (
)
LAS (
)
Along the Keynesian AS curve, the nominal wage rates are fixed at W*.
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4. New Keynesian AS curves
1) Assumptions
i)Rigidity of Nominal Wages;
In the New Keynesian model of labor market, the nominal wage is set at t-1 through
labor contracts, and the level of employment is to be determined at time period t.
ii) Long-term Non-indexed Labor Contract: Just like the Keynesian AS curve model,
the wages are set in advance through the long-term non-indexed contract.
iii) The labor contract sets nominal wages at time t-1. The workers are bound by the
contract to work at the set wage rates as much as is required by the entrepreneurs.
The level of employment is flexible to be determined according to the labor demand
at time t.
Ex-post revisions of expected price levels do happen, and shift the labor supply and
demand curves around. However, the labor supply curve is redundant as it is
effectively replaced with the wage line, which is set through the contract. The
equilibrium takes place where the horizontal nominal wage line intersects the newly
shifted labor demand curve.
2) Derivation of New Keynesian AS curve
Graphic Derivation is as follows:











Start with P1.
For the given price level, get the labor supply and labor demand curve in the
second panel.
The intersection of the labor supply and demand curves gives the equilibrium
level of employment N1.
This feeds into YS1 in the aggregate production function.
YS1 = Y1 in the third panel.
Now in the fourth panel, Y1 matches with P1.
Suppose that the price level goes up to P2.
This sends both the labor supply and demand curves up.
However, the level of nominal wages does not change due to unions or money
illusion. It is the effective labor supply curve; note that it replaces the shift labor
supply curve, which is meaningless.
The new equilibrium level of employment is given at N2.
This feeds into the aggregate production function to give YS2 = Y2.
Y2 goes down to match P2.
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By linking the two points of Y in the fourth panel, we get the New Keynesian
Aggregate Supply Curve. It is upward-sloping.
P2
Fixed W*
P1
N1*
N2*
Y1
Y2
3) Comparison of the New Classical and the New Keynesian AS curves

Note that the slope of New Keynesian AS curve is flatter than the corresponding
New Classical AS curve: if we look at the labor market only for a unexpected rise
in the price level, the comparison is as follows:
New Classical Eq.
Ns (Pe1)
New Keynesian Eq.
Nd (P2)
Nd (P1)
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Comparison of New Classical and New Keynesian equilibriums:
YS = Y
450
P2
Fixed W*
New
Classical
P1
NKAS
N1*

N2*
Y1
Y2
Note that the slope of New Keynesian AS curve is flatter than the corresponding
New Classical AS curve: if we look at the labor market only for a unexpected rise
in the price level, the comparison is as follows:
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5. Putting them all together in a complete macroeconomic model with the AS and
AD curves.
So far we just assume that there is an increase in the price level P. Why or how does it
happen, or what causes this rise in the price level?
In reality a rise in the price level or inflation is most likely the result of government’s
expansionary fiscal or monetary policies, which shift the AD curve.
Suppose that government increases nominal money supply or MS. It will put a train of
economic sectors in motion:
First, the real money supply curve ms will shift to the right.
Second, the LM curve will shift to the right.
Third, the AD curve will shift to the right.
Now, when it comes to the response of the AS side, there are different assumptions for
different circumstances:
1) If the increase in Money Supply is unanticipated or unexpected for the
workers or the general public, then the SAS curve does not move at all in the
short-run.
2) Even if the expansionary monetary policy is unexpected, eventually in the
long-run the general public will figure out the consequent increase in the
price level. Suppose that there is no institutional wage rigidity in the labour
market. As they demand a higher money wage so as to recover the real wage,
the money wage will rise and the SAS will reflect the wage(labour cost)
increase and thus decrease(shifting to the left or up visually).
3) If the expansionary monetary policy is announced well in advance and is
executed by the monetary authority as announced, and at the same time, if
there is no institutional money wage rigidity, then there is the Policy
Ineffectiveness Theorem holding once-for-all, i.e., in the short-run as well as
in the long-run.