The IS-LM model

1

The IS-LM model

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The model

The IS-LM model was developed in 1937 by John R. HicksJohn R. Hicks in an attempt to authentically interpret the “General “General Theory of Employment, Interest and Theory of Employment, Interest and Money”Money”, the famous book published by John Maynard KeynesJohn Maynard Keynes in 1936.

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The model

The model tries to explain the movement of output and interest rate in the short run.

To this end, it uses two curves: the IS (short for Investment and Saving) and the LM (short for Liquidity and Money).

The IS curve represents equilibrium in the goods market.

The LM curve represents equilibrium in the financial markets.

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The IS curve

We will try to use the goods market to establish a relationship between the interest rate and output.

We already know [from introductory macro…] that output in a closed economy is the sum of consumption (C), investment (I) and government expenditures (G).

Y = C + I + G

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The IS curve (the Keynesian cross) We also know that output (Y) is by definition equal

to income and that it represents the amount of spending undertaken by households, firms and the government.

But, how much do we want to spend? In other words, what is our demand for goods and services?

If we denote demand with Z, then: Z = C + I + G

So, demand (like output) is simply equal to the sum of consumption, investment and government expenditures.

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The IS curve (the Keynesian cross) If we try to elaborate a bit more on the form of

consumption, we can say that consumption must depend on our disposable income.

Our disposable income must be equal to total income (Y) minus the taxes that we pay to the government (T).

So, consumption is a function of our disposable income C(Y-T).

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The IS curve (the Keynesian cross) What if we want to be more specific about the functional form of the

consumption function. Let’s assume that we must cosume something anyway in order to

survive, like food. We call this amount autonomous consumption and let’s denote it by c0.

The rest of our consumption depends on our disposable income (Y-T). It is reasonable to assume that we consume a percentage of our disposable income and that we save the rest of it. We call this percentage marginal propensity to consume (MPC) and let’s denote it by c1. Since we consume less than our disposable income, c1 must be a number between 0 and 1. So, the non autonomous part of consumption must look like that: c1(Y-T).

Therefore, consumption in general must be equal to:

C = c0 + c1(Y-T)

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The IS curve (the Keynesian cross) If this is the form of consumption, then demand in total must be equal to:

Z = C + I + G =>Z = c0 + c1(Y-T) + I + G =>Z = (c0 - c1T + I + G) + c1Y

This last equation tells us that demand is equal to a sum of some variables that are exogenously given, namely:

c0 : the amount of autonomous consumption, c1T: the amount of taxes times MPC, I: investment, which for now we can assume that it is constant, and

G: government expenditures.We will call this whole expression (c0 - c1T + I + G), autonomous spending.

It also tells us that demand is a positive function of income (Y) and, moreover, that the slope of this positive function is c1, which is less than one. So the slope of the demand is flatter than the 45o line (the slope of which is 1).

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The IS curve (the Keynesian cross) Now we have the first building block of the

Keynesian cross. We are going to graph the demand as a function of income. We already proved earlier that the demand is a positive function of income and this is what we are going to graph now.

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The IS curve (the Keynesian cross)Z

ZZ

Y

1$

Slope: MPC

Vertical intercept: autonomous spending

This is a picture of the demand as a function of income. The vertical intercept of the line ZZ which represents the demand, is the autonomous spending and its slope is the marginal propensity to consume.

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The IS curve (the Keynesian cross) Our economy is in equilibrium when actual

production is equal to the demand, i.e. Y = Z. The only place that generally satisfies this

equilibrium condition is the 45o line in our previous graph. So, our equilibrium must be on that line.

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The IS curve (the Keynesian cross) If we assume further, that there is no

inventory investment, then output (= income) must always be equal to the demand.

So, in that case, not only are we always on the 45o line, but also always on the intersection of the demand function with the 45o line, which is our equilibrium point.

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The IS curve (the Keynesian cross)Z

ZZ

Y

This is a picture of the Keynesian cross. We observe that in equilibrium, demand is equal to income and production along the 45o line. In our model, since there are no inventories, we are always in equilibrium.

Actual Production Y=Z

Y*

Y*

45o

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The IS curve (the multiplier)

If we combine the equilibrium condition Y = Z, with the expression for the demand that we derived earlier, Z = c0 + c1(Y-T) + I + G, we get:

Y = c0 + c1(Y-T) + I + G =>

Y = c0 + c1Y - c1T + I + G =>

Y - c1Y = c0 - c1T + I + G =>

Y(1 - c1) = c0 - c1T + I + G =>

Y = [1/(1 - c1)] (c0 - c1T + I + G)

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We have already called the (c0 - c1T + I + G) part of the above equation, autonomous spending.

Now, we will give a name to the 1/(1 - c1) part and we will call it the multiplier. The reason for that name is that this fraction is greater than one (remember that 0<c1<1).

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Therefore, whatever the change is in any of the parts of autonomous spending, the change in output is a multiple of that change.

So, if the government, e.g., decides to increase G by an amount x, this will result in an increase of Y by x times the multiplier.

Graphically, the demand will shift up by as much as the change in autonomous spending (the vertical intercept) but output will increase by more than that.

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The size of the multiplier obviously depends on c1, the marginal propensity to consume. The larger the MPC, the smaller the denominator and the larger the multiplier.

Graphically, a large MPC corresponds to a steeply sloped demand curve. Shifts of a steep demand curve have large effects on income.

A small MPC corresponds to a relatively flatter demand curve. Shifts of a flatter demand curve have relatively milder effects on income.

We will now graph those two cases.

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Z

ZZ1

Y


Y1

45o

ZZ2

Y2

Z

ZZ1

Y


Y1

ZZ2

Y2

Y1

Y1

Y2

Y2

45o

The Keynesian cross with a steep demand (large MPC). The shift in demand has a large effect on output.

The Keynesian cross with a flat demand (small MPC). The shift in demand has a milder effect on output.

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Deriving the IS curve

The Keynesian cross is an important building block toward the IS curve but our mission is not accomplished yet.

However, from this point the derivation of the IS curve is straightforward. It relies on the relaxation of an assumption that we made earlier, namely that the level of investment is constant.

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Constant investment is a clear simplification of the Keynesian cross model. We already know that investment is not constant but rather a negative function of the interest rate.

At this point we also add that investment is also positively related with output. The line of reasoning is that as firms see their volume of sales going up, they will undertake more investment to accommodate this increase. But the level of sales is just proportional to output, since if output is increasing, more goods are going to be sold and if output is decreasing less goods are going to be sold. So, the bottom line is that we observe a positive relationship between the level of investment and the level of output.

Therefore, investment is a negative function of the interest rate and a positive function of output. In symbols we write:I = I(Y,i)

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Focusing on the interest rate, we can say that if the interest rate increases, this reduces the level of investment, shifts down the demand and consequently, through the multiplier, reduces the level of income.

On the other hand, if the interest rate decreases, the level of investment increases, the demand shifts up and the level of income increases.

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We have therefore shown that there exists a negative relationship between the interest rate and income.

This negative relationship is what is known as the IS curve.

The mathematical form of the IS curve is called the IS relation and it is simply:Y = C(Y-T) + I(Y,i) + G

A more specific form of this equation is the already familiar to us equation:Y = [1/(1 - c1)] (c0 - c1T + I + G)

This is the graphical derivation of the IS curve.

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Y2

Z Actual Production Y=Z

Y1

45o

Y2

Y1

ZZ1

Y

ZZ2

IS

i

Y

I

i

I

i1

i2

i1

i2

Y1 Y2

A decrease in the interest rate increases the level of investment (Panel A), which shifts up the demand and increases income (Panel B). The IS curve sums up these movements in the goods market (Panel C).

I1 I2

Panel A

Panel B

Panel C

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Shifts of the IS curve

As always in economics, here too we are interested in curve shifts.

So, we are going to mix things up a bit, shift the curves around and see what happens.

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So, what could possibly move the IS curve? First, let’s recall the IS relation, Y = C(Y-T) + I(Y,i) + G, the

general equation that describes the IS curve. Which part of this equation could move the IS curve? Maybe, it’s better if we start by what could by no means

move the IS curve: income (Y) and the interest rate (i). Why? Because, these are the endogenous variables of our

model. These are the variable that we are trying to explain. They are the variables on the two axes of our graph (like price and quantity in a supply and demand diagram). So, if these two variables move, we move along the curve. We don’t shift it.

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So, what could move the IS curve is any of the other variables that are exogenous, i.e. they are taken as given outside the model, namely:

a) G, government expenditures (variable controlled by the government),

b) T, taxes (variable controlled by the government),c) C, consumption patterns that are independent of disposable

income, if for example, the households decide to consume more because an asteroid is going to hit the earth (variable controlled by household preferences), and

d) I, investment patterns that are independent of the interest rate and income, if for example firms go into an unexplained investing spree (variable controlled by the animal spirits of the investors).

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Out of those four parameters, we are mostly interested in the first two (G and T), because it is only those that policy makers can control. The other two cannot be affected directly by government policies.

So, our analysis will be primarily focused on government expenditures and taxes.

However, just bear in mind that changes in consumption and investment patterns affect the IS curve in exactly the same way as changes in government expenditures.

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What happens if the government decides to increase government expenditures (G↑)? We will use the Keynesian cross to explore the

effects of such a move. First, let’s recall the equation for the demand that we

derived earlier:

Z = (c0 - c1T + I + G) + c1Y If, ceteris paribus, the government decides to

increase G (by ΔG), then it is obvious that the demand curve would shift up by an amount equal to ΔG. The vertical intercept would move up by ΔG but the slope would remain the same.

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What happens if the government decides to increase government expenditures (G↑)? But would happen to income after this shift of the demand

curve? Now, we have to recall the IS relation in the specific form that

we also mentioned earlier:

Y = [1/(1 - c1)] (c0 - c1T + I + G) If G↑, then Y would go up by as much as ΔG times the

multiplier 1/(1 - c1), so by more than ΔG. So, it looks like it’s a good deal for the government to increase

G, since with an initial amount of increase, it can get income to increase more through the multiplier.

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What happens if the government decides to increase government expenditures (G↑)? But, what does this mean for the IS curve? It means that the increase in government

expenditures caused an increase in income for a given level of interest rate. Remember that the interest rate did not move at all.

This corresponds to a shift of the IS curve to the right. For a given level of interest rate now we have more income.

Let’s look at this effect graphically.

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The effects of G↑

Y2


Y1

45o

Y2

Y1

ZZ1

Y

ZZ2

IS1

i

Y

i*

Y1 Y2

ΔG An initial increase in G shifts up the demand by ΔG, which increases income by ΔG/(1 - c1) in Panel A. This means that for a given level of interest rate, the IS curve in Panel B must shift to the right by ΔG/(1 - c1).

Panel A

Panel B

IS2

ΔY=ΔG[1/(1 - c1)]

ΔY=ΔG[1/(1 - c1)]

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What happens if the government decides to decrease government expenditures (G↓)? The process that we follow must be clear by

now. Again we use the demand equation:


decrease G (by ΔG), then it is obvious that the demand curve would shift down by an amount equal to ΔG. The vertical intercept would move down by ΔG but the slope would remain the same.

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What happens if the government decides to decrease government expenditures (G↓)? Then we use the IS relation to see what happens to income:

Y = [1/(1 - c1)] (c0 - c1T + I + G) If G↓, then Y would go down by as much as ΔG times the

multiplier 1/(1 - c1), so by more than ΔG. This means that the decrease in government expenditures caused

a decrease in income for a given level of interest rate. This corresponds to a shift of the IS curve to the left. For a given

level of interest rate now we have less income.

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The effects of G↓

Y2


Y1

45o

Y2

Y1

ZZ1

Y

ZZ2

IS1

i

Y

i*

ΔG An initial decrease in G shifts down the demand by ΔG, which decreases income by ΔG/(1 - c1) in Panel A. This means that for a given level of interest rate, the IS curve in Panel B must shift to the left by ΔG/(1 - c1).

Panel A

Panel B

IS2

ΔY=ΔG[1/(1 - c1)]

ΔY=ΔG[1/(1 - c1)]

Y1Y2

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What happens if the government decides to decrease taxes (T↓)?

Again we use the demand equation:


decrease T by ΔT (so ΔT is negative), then it is obvious that the demand curve would shift up by an amount equal to -c1ΔT. The vertical intercept would move up by -c1ΔT but the slope would remain the same.

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Then we use the IS relation to see what happens to income:Y = [1/(1 - c1)] (c0 - c1T + I + G)

If T↓, then Y would go up by as much as ΔT times [- c1/(1 - c1)].

The expression [- c1/(1 - c1)] is the version of the multiplier when taxes are changed by the government.

We observe that in the numerator of this expression there is c1, which corresponds to a number that is less than one. Therefore, if we compare this version of the multiplier with the general version [1/(1 - c1)], we conclude that the general version is larger. This means that expansionary fiscal policy is normally more effective if conducted through increases in government expenditures rather than decreases in taxation.

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So, in effect the decrease in taxes caused an increase in income for a given level of interest rate.

This corresponds to a shift of the IS curve to the right. For a given level of interest rate now we have more income.

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The effects of T↓

Y2


Y1

45o

Y2

Y1

ZZ1

Y

ZZ2

IS1

i

Y

i*

Y1 Y2

Panel A

Panel B

IS2

-c1ΔT

ΔY=ΔT[- c1/(1 - c1)]

ΔY=ΔT[- c1/(1 - c1)]

An initial decrease in T shifts up the demand by -c1ΔT, which increases income by

ΔT[- c1/(1 - c1)] in Panel A. This means that for a given level of interest rate, the IS curve in Panel B must shift to the right by ΔT[- c1/(1 - c1)].

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What happens if the government decides to increase taxes (T↑)?

Again we use the demand equation:


increase T by ΔT (now ΔT is positive), then it is obvious that the demand curve would shift down by an amount equal to -c1ΔT. The vertical intercept would move down by -c1ΔT but the slope would remain the same.

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What happens if the government decides to increase taxes (T↑)?

Then we use the IS relation to see what happens to income:

Y = [1/(1 - c1)] (c0 - c1T + I + G) If T↑, then Y would go down by as much as ΔT

times [- c1/(1 - c1)]. So, in effect the increase in taxes caused a

decrease in income for a given level of interest rate. This corresponds to a shift of the IS curve to the left.

For a given level of interest rate now we have less income.

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The effects of T↑

Y2


Y1

45o

Y2

Y1

ZZ1

Y

ZZ2

IS1

i

Y

i*

-c1ΔTPanel A

Panel B

IS2

ΔY=ΔT[- c1/(1 - c1)]

Y1Y2

ΔY=ΔT[- c1/(1 - c1)]

An initial increase in T shifts down the demand by -c1ΔT, which decreases income by

ΔT[- c1/(1 - c1)] in Panel A. This means that for a given level of interest rate, the IS curve in Panel B must shift to the left by ΔT[- c1/(1 - c1)].

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To sum up IS shifts…

Initial Change

Shift of IS

G↑ Right

G↓ Left

T↓ Right

T↑ Left

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The LM curve

To get to the LM curve, we have to use financial markets and go through the theory of liquidity preference. We have to understand why people decide to hold money in their pockets or in non- interest bearing bank accounts (checking accounts). In other words why we choose to forgo the interest rate that the banks offer us when we hold illiquid bank products (e.g. CDs, etc.).

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The LM curve

The answer is very simple: convenience and security.

It is true that having highly liquid assets, such as cash or immediately available, through an ATM, checking accounts makes our life easier.

Imagine if we had to go to the bank to liquidate part of our investments every time we needed to go to the grocery store. Also having liquid assets provide us with a sense of security, that we will, no matter what, have some money immediately available in case an emergency (or a new financial opportunity) occurs.

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The LM curve

Since we have answered why, now we have to answer how much money we hold.

To answer this question, first we have to define what is money.

Generally, for our purposes money is cash and checking (non interest bearing) bank accounts. This is known as M1.

There are also other measures of money but we are not really interested in them.

46

The LM curve

Then we have to come up with a measure of money. We call the measure of money with the interesting name: real money balances or real money stock (M/P).

To determine how much money we hold, as always in economics, we will look for an equilibrium.

The equilibrium between the supply of real money balances and the demand for real money balances.

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The LM curve (Money supply) The supply of real money balances is easy

because it is exogenously given. It is controlled by the central bank through the ways that we learned in introductory macro (open market operations, discount rate, required reserves ratio). So the supply is just a number decided by the central bank and we do not need to worry about it.

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The LM curve (Money supply)

i

M/P

Since money supply (Ms) is independent of the interest rate, it can be represented by a vertical line. The amount of money supplied only depends on the decision of the central bank and nothing else.

Ms

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The LM curve (Money demand) The demand for real money balances is more complicated. The

amount of real money balances that we demand, depends on what?

Well, first it depends on income (Y). The more income in an economy, the more transactions will occur and the more money we will demand to effect these transactions. So, there is a positive relationship between demand for real money balances and income.

But also, it depends on the interest rate. The higher the interest rate on illiquid financial products (e.g. CDs), the less money we will demand, since money pays no interest whereas these illiquid products do. Because we do not want to lose a lot of interest, as interest rates go up, we will hold less and less real money balances. So, there is a negative relationship between demand for real money balances and interest rate.

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The LM curve (Money demand) If we wanted to write down in symbols what we

just said in words, we would write this expression for money demand:(M/P)d = L(i,Y)

Demand for real money balances is a function L of the interest rate and income.

Or, if we want to assume that money demand is exactly proportional to the level of income in an economy, we can even more simply write:(M/P)d = YL(i)

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The LM curve (Money demand)

iSo, if we want to graph the relationship between money demand (Md) and the interest rate, it must be represented by a downward sloping curve. As we just said, money demand depends negatively on the interest rate.

M/P

Md = YL(i)

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The LM curve (Money supply and money demand in equilibrium) So, now that we have all the pieces, we can equate money

demand and money supply and find the equilibrium in the money market, i.e. the equilibrium amount of real money balances in our economy and the equilibrium level of interest rate.

Mathematically:Ms = Md =>(M/P)s = (M/P)d =>(M/P)s = YL(i)

This expression is what is called the LM relation. It is the mathematical representation of the LM curve.

Note that for the purposes of these notes, the symbols Ms and Md

refer to real money supply and real money demand, unless otherwise specified.

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The LM curve (Money supply and money demand in equilibrium)

iTherefore in equilibrium if we equate money supply and money demand, we get the equilibrium level of real money balances and the equilibrium level of interest rate.

M/P

Ms

(M/P)*

i*

Md = YL(i)

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Deriving the LM curve

From here the crucial step in order to derive the LM curve is to bring income (Y) into play.

We have already said that money demand depends positively on income.

This means that for a given level of interest rate, a higher income would result to a shift of the money demand to the right. If income increases, for a given level of interest rate, I engage in more transactions and I demand more real money balances.

The picture is as follows:

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iSo, we notice that a higher level of income (Y2 >Y1), by shifting the money demand to the right, is associated with a higher level of interest rate.

M/P

Ms

(M/P)*

i1

i2

Md = Y1L(i)

Md = Y2L(i)

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Therefore we have proved that, through the channel of financial markets and the liquidity preference theory, there is a positive relationship between the interest rate and output.

This positive relationship between interest rate and output is represented by the LM curve.

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Y2

i

Y

i1

Y1

LM

i2

i

M/P

Ms

(M/P)*

i1

i2

Md = Y1L(i)

Md = Y2L(i)

Panel A Panel BIn Panel A, a higher level of income (Y2 >Y1) shifts the money demand to the right and results in a higher level of interest rate. In Panel B, the LM curve sums up this positive relationship between income and interest rate.

58

Shifts of the LM curve

Now we will explore what shifts the LM curve. To this end, we have to recall the LM relation,

(M/P)s = YL(i), the equation that describes the LM curve.

Starting again by what could by no means move the LM curve, it is now very easy to say: income (Y) and the interest rate (i). Exactly like in the IS case, if these two variables move, we move along the curve. We don’t shift it.

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Shifts of the LM curve

So, what could move the LM curve is any of the other variables that are exogenous, i.e. they are taken as given outside the model, namely:

a) Ms, the money supply controlled by the central bank (note that the central bank controls the nominal money supply, but given that we can assume constant prices, effectively the central bank can control the real money supply),

b) P, the level of prices, andc) Md, the demand for real money balances, BUT only to the extent that this is

affected by factors other than the interest rate and income. So, if just like that, for some weird reason, we start demanding more or less money for a given level of interest rate and income. E.g. because an asteroid is going to hit the earth and we want to engage in more transactions in the last days of our earthly existence, we increase our demand for money.

Since, out of those factors, the policy maker can directly control only the money supply (case (a)) through monetary policy, we are mostly interested in changes in this first factor. However, for reasons of completeness, we will examine here the other two factors as well (cases (b) and (c)).

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What happens if the central bank decides to increase the money supply (Ms↑)?

If the central bank decides to increase the money supply, this would certainly mean that the interest rate would decrease.

So, for a given level of income, now we would have a lower level of interest rate.

This necessarily means that the LM curve must shift down.

61

The effects of Ms↑

i

Y

i1

Y*

LM1

i2

i

M/P

(Ms)1

(M/P)1

i1

i2Md = YL(i)

Panel A Panel BIn Panel A, the increase in money supply shifts the money supply to the right and results in a lower level of interest rate. In Panel B, the LM curve shifts down since, for the same level of income, now we have a lower level of interest rate.

(Ms)2

(M/P)2

LM2

62

What happens if the central bank decides to decrease the money supply (Ms↓)?

If the central bank decides to decrease the money supply, this would certainly mean that the interest rate would increase.

So, for a given level of income, now we would have a higher level of interest rate.

This necessarily means that the LM curve must shift up.

63

The effects of Ms↓

i

Y

i1

Y*

LM1

i2

i

M/P

(Ms)1

(M/P)1

i1

i2

Md = YL(i)

Panel A Panel BIn Panel A, the decrease in money supply shifts the money supply to the left and results in a higher level of interest rate. In Panel B, the LM curve shifts up since, for the same level of income, now we have a higher level of interest rate.

(Ms)2

(M/P)2

LM2

64

What happens if the level of prices goes down (P↓)?

Since we are interested in real money balances, a decrease in the level of prices effectively means that the supply of real money (M/P)s increases. The supply of real money balances increases without the intervention of the central bank but only due the price change.

Therefore, because of the increase in money supply, the interest rate decreases.



65

The effects of P↓

i

Y

i1

Y*

LM1

i2

i

M/P

(M/P1) s

(M/P)1

i1

i2Md = YL(i)

Panel A Panel BIn Panel A, the decrease in

prices (P2< P1) causes the money supply to increase and shift to the right. This results in a lower level of interest rate. In Panel B, the LM curve shifts down since, for the same level of income, now we have a lower level of interest rate.

(M/P)2

LM2

(M/P2) s

66

What happens if the level of prices goes up (P↑)?

An increase in the level of prices effectively means that the supply of real money (M/P)s decreases. The supply of real money balances decreases without the intervention of the central bank but only due the price change.

Therefore, because of the decrease in money supply, the interest rate increases.



67

The effects of P↑

i

Y

i1

Y*

LM1

i2

i

M/P

(M/P1) s

(M/P)1

i1

i2

Md = YL(i)

Panel A Panel BIn Panel A, the increase in

prices (P2>P1) causes the money supply to decrease and shift to the left. This results in a higher level of interest rate. In Panel B, the LM curve shifts up since, for the same level of income, now we have a higher level of interest rate.

(M/P)2

LM2

(M/P2) s

68

What happens if money demand decreases (Md↓)?

If money demand decreases for a given level of income and interest rate (i.e. the asteroid case), then the money demand curve shifts to the left. This results in a lower interest rate.



69

Effects of Md↓

i

YY*

i

M/P(M/P)*

i1

i2

Panel A Panel BIn Panel A, a decrease in the demand for money shifts the money demand to the left and results in a lower level of interest rate. In Panel B, the LM curve shifts down since, for the same level of income, now we have a lower level of interest rate.

(Md)1

(Md)2

LM1

LM2

i1

i2

Ms

70

What happens if money demand increases (Md↑)?

If money demand increases for a given level of income and interest rate (again the asteroid case), then the money demand shifts to the right. This results in a higher interest rate.



71

Effects of Md↑

i

Y

i1

Y*

i2

i

M/P(M/P)*

i1

i2

Panel A Panel BIn Panel A, an increase in the demand for money shifts the money demand to the right and results in a higher level of interest rate. In Panel B, the LM curve shifts up since, for the same level of income, now we have a higher level of interest rate.(Md)1

(Md)2

LM1

LM2

Ms

72

To sum up LM shifts…

Initial change Shift of LM

Ms↑ Down

Ms↓ Up

P↓ Down

P↑ Up

Md↓ Down

Md↑ Up

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The IS-LM model in all its glory…

i*

IS

Y*

i

Y

If we put the IS and the LM curves together in a diagram we are able to determine the equilibrium level of output and interest rate in a closed economy.

LM

74

So, what happens if we shift the curves in the full scale model? Now it’s time to use our model to see what

happens when we use fiscal or monetary policy in order to affect different macro variables.

We will examine in turn fiscal expansion and contraction and monetary expansion and contraction.

75

Fiscal expansion

As we already know, a fiscal expansion is a situation where the government increases government expenditures (G) or reduces taxes (T).

As we have mentioned, this corresponds to a shift of the IS curve to the right.

The result is a higher a level of output and a higher level of interest rate.

76

Fiscal expansion

IS1

If the government engages in a fiscal expansion, the IS curve shifts to the right. The LM stays still. The equilibrium moves from A to B indicating a higher level of output and a higher level of interest rate.

IS2

A

B

A

B

LM

i

i1

i2

Y2 YY1

77

Fiscal expansion elaborated… Now, let’s ask ourselves why did this happen? The first move was made by the government that chose to

embark on a fiscal expansion (by raising G or cutting T). What’s the result?

Either way (G↑ or T↓), the demand (Z) increases and therefore output (= income) increases (remember the Keynesian cross). What’s next?

The increase in income, through the LM relation, increases the demand for money leading to a higher interest rate (remember the money supply and demand graph). What’s next?

The higher interest rate, by reducing private investment, reduces demand and output but not enough to offset the positive effect of the fiscal expansion on them.

78

Fiscal expansion elaborated… So now, we have a clear picture of how all our variables moved:a) C: consumption is positively affected either the fiscal expansion

was effected by an increase in G or through a reduction in T (disposable income increases in both cases).

b) I: the movement of investment is ambiguous because on the one hand output went up and we know that this boosts I, but on the other hand the interest rate increased and we also know that this shrinks investment. So the net effect is ambiguous.

c) G: government expenditures went up if the fiscal expansion was effected by an increase in G or were unaffected if the fiscal expansion was effected by a decrease in T.

d) T: taxes went down if the fiscal expansion was effected by a decrease in T or were unaffected if the fiscal expansion was effected by an increase in G.

79

Aggregate effects of a fiscal expansion conducted by G↑

Y i C I G T

↑ ↑ ↑ ? ↑ 0

80

Aggregate effects of a fiscal expansion conducted by T↓

Y i C I G T

↑ ↑ ↑ ? 0 ↓

81

Fiscal contraction

As we already know, a fiscal contraction is a situation where the government decreases government expenditures (G) or increases taxes (T).

This corresponds to a shift of the IS curve to the left.

The result is a lower level of output and a lower level of interest rate.

82

Fiscal contraction

IS1

If the government engages in a fiscal contraction, the IS curve shifts to the left. The LM stays still. The equilibrium moves from A to B indicating a lower level of output and a lower level of interest rate.

IS2

B

A

LM

i

i1

i2

Y2 YY1

83

Fiscal contraction elaborated… Now, let’s ask again ourselves why did this happen? The first move was made by the government that chose to

embark on a fiscal contraction (by reducing G or increasing T). What’s the result?

Either way (G↓ or T↑), the demand (Z) decreases and therefore output (= income) decreases (remember the Keynesian cross). What’s next?

The decrease in income, through the LM relation, decreases the demand for money leading to a lower interest rate (remember the money supply and demand graph). What’s next?

The lower interest rate, by increasing private investment, increases demand and output but not enough to offset the negative effect of the fiscal expansion on them.

84

Fiscal contraction elaborated… So now, we have a clear picture of how all the variables moved:a) C: consumption is negatively affected either the fiscal contraction

was effected by a decrease in G or through an increase in T (disposable income decreases in both cases).

b) I: the movement of investment is ambiguous because on the one hand output went down and this decreases I, but on the other hand the interest rate decreased and this boosts investment. So the net effect is ambiguous.

c) G: government expenditures went down if the fiscal contraction was effected by a decrease in G or were unaffected if the fiscal contraction was effected by an increase in T.

d) T: taxes went up if the fiscal expansion was effected by an increase in T or were unaffected if the fiscal expansion was effected by a decrease in G.

85

Aggregate effects of a fiscal contraction conducted by G↓

Y i C I G T

↓ ↓ ↓ ? ↓ 0

86

Aggregate effects of a fiscal contraction conducted by T↑

Y i C I G T

↓ ↓ ↓ ? 0 ↑

87

Monetary expansion

We already know that a monetary expansion is a situation where the central bank increases the money supply.

We also know that this shifts the LM curve down.

The result is a higher a level of output and a lower level of interest rate.

88

Monetary expansion

IS

If the central bank engages in a monetary expansion, the LM curve shifts down. The IS stays still. The equilibrium moves from A to B indicating a higher level of output and a lower level of interest rate.

LM1 LM2

A

BBB

Y2 YY1

i

i1

i2

89

Monetary expansion elaborated… Now we have to tell the story again. The first move was made by the central bank that

chose to expand the money supply. What’s the result?

By remembering the money supply and money demand graph, we conclude that this leads to a lower interest rate. What’s next?

The lower interest rate in turn leads to higher investment and thus, higher demand and output (remember the Keynesian cross).

90

Monetary expansion elaborated… So now, we have a clear picture of how all our

variables moved:a) C: consumption increases since income went up and

so our disposable income (Y-T) went up. b) I: investment unambiguously increased because we

saw that the interest rate went down (this increases investment) and also income went up (this also increases investment). So a monetary expansion gives a twofold boost to investment (compare that to the fiscal expansion which had an ambiguous effect on investment).

c) G: government expenditures are unchanged.d) T: taxes are unchanged.

91

Aggregate effects of a monetary expansion

Y i C I G T

↑ ↓ ↑ ↑ 0 0

92

Monetary contraction

We already know that a monetary contraction is a situation where the central bank decreases the money supply.

We also know that this shifts the LM curve up.

The result is a lower level of output and a higher level of interest rate.

93

Monetary contraction

If the central bank engages in a monetary contraction, the LM curve shifts up. The IS stays still. The equilibrium moves from A to B indicating a lower level of output and a higher level of interest rate.

IS

LM1

LM2

A

B

Y2 YY1

i

i1

i2

94

Monetary contraction elaborated… Let’s tell the story for one last time. The first move was made by the central bank that

chose to contract the money supply. What’s the result?

By remembering the money supply and money demand graph, we conclude that this leads to a higher interest rate. What’s next?

The higher interest rate in turn leads to lower investment and thus, lower demand and output (remember the Keynesian cross).

95

Monetary contraction elaborated… So now, we have a clear picture of how all our

variables moved:a) C: consumption decreases since income went down

and so our disposable income (Y-T) went down. b) I: investment unambiguously decreased because we

saw that the interest rate went up (this decreases investment) and also income went down (this also decreases investment). So a monetary contraction gives a twofold blow to investment.

c) G: government expenditures are unchanged.d) T: taxes are unchanged.

96

Aggregate effects of a monetary contraction

Y i C I G T

↓ ↑ ↓ ↓ 0 0

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The IS-LM model

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