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Chapter 7

IS-LM Model

7.1 Introduction

Now that we have reviewed the basic fundamentals of the goods and money markets we will construct the

IS-LM model. The IS-LM model shows the relationship between interest rates and income in the economy.

In the goods market we assumed both interest rates and price level were exogenous. In the money market

we looked at how the interest rate was determined and saw one of the key factors for determining the

interest rate was income. Combining the money market with the goods market will allow us to analyze how

the interest is determined (i.e. the interest rate will now be endogenous). The price level will remain

exogenous, which is in line with the Keynesian view of sticky prices and wages. The IS (or

investment-savings) schedule is derived from the goods market while the LM (or liquidity preference and

money supply equilibrium) is derived from the money market.

7.2 Money Market - LM Curve

The LM curve will show a positive relationship between income and the interest rate. The LM curve

represents all equilibrium values in the money market. Since money supply is exogenously determined by

the central bank we will primarily focus on money demand. We are interested in knowing how much does

the interest rate need to increase for a given increase in income to restore equilibrium in the money market

(holding money supply constant). One important clarification needs to be made: money demand refers to

the demand for real money balances (for simplicity we are going to assuming P=1). This simply means

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money demand and money supply are both real variables. Recall our equation for money demand is:

Md = L(Y, r + e).

More specifically we can write money demand in linear form:

Md

P= l0 l1

e + l2Y l3r. (7.1)

Money demand is positively related with income and negatively related to the interest rate. The LM curve

will trace out a line connecting different levels of income with the interest rate. To do this we will increase

income to Y1, Y2, and Y3 and observe how the interest rate changes to r1, r2, and r3. These points will make

up the LM schedule. As income increases, money demand shifts up, and the interest rate will increase. For

successively higher levels of income, the interest rate increases. Graphically, this is depicted in figures 7.1.

r

M

r

Y

Figure 7.1: Deriving the LM Curve

Mathematically we can solve for our LM curve by equating money demand with money supply and solving

for Y (or r):

Ms = Md = l0 l1e + l2Y l3r (7.2)

Solving for r we have:

r =l0l3

l1l3e +

l2l3Y

1

l3M (7.3)

Solving for Y we have:

Y =M l0 l1

e

l2+

l3l2r (7.4)

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The mathematical representation will help when we look at the slope and shift factors of the LM

schedule. Both are important to understand for policy effectiveness.

7.2.1 Slope of the LM curve

After solving for interest rates we can see the slope is

l2

l3 . The LM curve will become steeper (flatter) as l2

increases (decreases) relative to l3. The first parameter we will focus on is l2, the income sensitivity

(elasticity) of money demand. If l2 is larger than it takes a larger change in the interest rate to offset the

increase in money demand caused by the increase in income. The money demand curve will shift up by a

larger amount as l2 increases, causing the LM curve to be steeper. A small change in income will result in

a large change in the interest rate. The reverse is true for small values of l2. Interest rates will increase by

a small amount for a large change in income (money demand shifts up by a small amount for a change in

income). Graphically we can see this in figure 7.2.

r

M

r

Y

Figure 7.2: Determining the Slope of the LM Schedule

For the most part we take l2 as being a relatively stable parameter. Most of the debate among

macroeconomists concerns the value of l3 which we interpret as the interest sensitivity (elasticity) to money

demand. Recall the equation for money demand:

Md = l0 + l1e

l2Y l3r,

, where 1/l3 is the slope of the money demand line (see equation 7.3. Which means l3 tells us how much

the interest rate will change for a given change in the quantity of money. We already know from the

mathematical representation a higher value of l3 will make the LM curve flatter. As l3 increases, the slope

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(l2/l3) will become smaller. A large l3 means money demand is interest elastic; small changes in the

interest rate cause large changes in money demand, the money demand schedule is flat. When l3 is low, the

elasticity between money demand and the interest rate is relatively inelastic, the money demand curve is

steep. This means larger changes in the interest rate will not significant change the quantity

of money demand. Figure 7.3 will depict the case for a low value of l3.

r

M

r

Y

Figure 7.3: Money Demand - Low Interest Rate Elasticity (inelastic)

From figure 7.3 the LM curve is relatively steeper (inelastic) for lower values of l3. This should make

sense, because money demand does not respond significantly to changes in the interest rate (remember

inelastic) the interest rate must increase a lot to offset the increase in money demand. The interest rate

needs to increase in order to reduce the quantity of money demand back to the level of money supply

(which is vertical, fixed by the central bank). Now the opposite will hold for large values of l3. Figure 7.4

depicts a high elasticity between money demand and the interest rate.

Now the relationship between money demand and the interest rate is highly sensitive. For the same

increase in income (the same horizontal shift in money demand) the interest rate does not need to increase

as much (relative to before) to bring the quantity of money demand back to money supply. The result is a

flat LM curve.

For now it is important to understand what factors determine the slope of the LM curve, later on we

will see the slope of the LM curve plays an important role for policy effectiveness (particularly with fiscal

policy).

7.2.2 Special Cases of the LM Curve

There are two special cases that apply to the LM curve.

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r

M

r

Y

Figure 7.4: Money Demand - High Interest Rate Elasticity (elastic)

Case 1: L3 = 0 - Classical View When the interest elasticity of money demand is zero changes in the

interest rate will have no affect on money demand. This means only income will affect money demand, in

the money market this implies the money demand line will be vertical. The equation for the LM curve

becomes Y = Ml0l1e

l2. The LM schedule is now vertical. This fits with the classical view of money.

r

M

r

Y

Figure 7.5: Money Demand - l3 = 0 - Classical View

Case 2: L3 - Liquidity Trap The alternative extreme occurs when the interest elasticity of money

demand becomes extremely large. In the money market this occurs at a relatively flat portion of our money

demand schedule. As l3 , a small change in the interest rate will cause a large change in the quantity

of money demanded. In terms of income, the interest rate only needs to increase by a small amount it

restore equilibrium in the money market due to the highly sensitive relationship between interest rates and

money demand. It will help to graph the money market with a nonlinear money demand function:

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r

M

r

Y

Figure 7.6: Money Demand - l3 - Liquidity Trap

From the above graphs we can see that when the money demand schedule is flat (steep) the LM curve

will also be flat (steep). When interest rates are highly (weakly) sensitive to changes in money demand it

takes small (large) changes to restore equilibrium given an exogenous shift. Keynes coined this situation

the liquidity trap. Recall the three motives for a holding money. The speculative motive emphasized at

low interest rates agents will choose to hold great quantities of money. Low interest rates signal future

increases which will cause bond prices to decrease. Shortly we will look into key policy implications of a

high elasticity between interest rates and money demand, but it is easily to see as the interest elasticity to

money demand increases equal increases in the money supply will have smaller affects on the interest rate.

7.2.3 Shift Factors

As we have discussed, the LM curve models equilibrium in the money market. The relationship between

interest rates and income is positive. Recall our linear money demand line was:

Md = l0 l1e + l2Y l3r (7.5)

and equilibrium in the money market was:

r =l0 l1e M

l3+

l2l3Y. (7.6)

The first term, l0l1eM

l3, represents the intercept and the second term l2

l3the slope. We have already

discussed the factors that affect the slope of the LM curve. Now we will focus on the shift factors which are

seen in the intercept.

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The LM curve will shift when any variable (other than interest rates or income) cause money demand

or money supply to shift. The most obvious variable we need to consider is M. When the central bank

increases the money supply the interest rate will decrease for a given level of income. This will correspond

with a downward shift of the LM curve. We can see a graph an increase in the money supply in figure 7.7.

r

M

r

Y

Figure 7.7: An Increase in LM - Increase in Ms

The second factor that will shift the LM curve will be autonomous changes in money demand ( l0).

The term l0 corresponds with changes in precautionary demand (Y2K, stock market concerns, financial

crises). When the money demand line increases at a given level of income then interest rates will also

increase. Income has remained unchanged, but interest rates have increased. This will cause the LM curve

to shift leftward (a higher interest rate for all levels of income). We can see this in figure 7.8.

r

M

r

Y

Figure 7.8: A decrease in LM - Increase in Autonomous Md

The third factor we need to consider is a change in expected inflation (3). The term l1 measures the

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impact a change in expected inflation will have on the interest rate. An increase in expected inflation will

cause the demand for money to decline. Households will shift assets into interest bearing securities. The

return on holding money will decline. The decline in money demand will lower interest rates for all levels of

income. This will result in the LM curve shifting to the right. We can see the effect of higher expected

inflation in figure 7.9.

r

M

r

Y

Figure 7.9: An Increase in LM - Increase in Expected Inflation e

An increase in expected inflation will lower the real interest rate at all levels of income.

7.2.4 LM Curve Summary

1. The LM schedule is the schedule giving the combinations of values of income and the interest ratethat produce equilibrium in the money market

2. The LM schedule slopes upward to the right

3. The LM schedule will be relatively flat (steep) if the interest elasticity of money demand is relatively

high (low).

4. The LM schedule will shift downward (upward) to the right (left) with an increase (decrease) in the

quantity of money

5. The LM schedule will shift upward (downward) to the left (right) with a shift in the money demand

function that increase (decreases) the amount of money demanded at given levels of income and the

interest rate.

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7.3 Goods Market - IS Curve

I hate to tell you this, but we finished the easy part (well at least on paper). I believe the IS schedule is

easier to interpret but more complicated to derive. The IS schedule stems from the relationship between

investment and savings. From the goods market recall equilibrium was represented as:

Y = C+ I+ G (7.7)

Using the GDP equation and Y = C+ S+ T we can write equilibrium as:

S+ T = I+ G (7.8)

Our objective is to map the relationship between the interest rate and income through equilibrium in the

goods market. Essentially we are asking the following question: when interest rates increase how doesincome change. For now changes in the interest rate will only affect investment (for simplicity we are going

to assume the consumption function is independent of interest rates), I= I i1r. So an increase in the

interest rate will decrease investment by an amount of i1. Through our equilibrium condition,

Y = C+ I+ G a decrease in investment will cause income to fall. The IS curve has a negative

relationship between interest rates and investment. We can graph this approach using the

Keynesian Cross, see figure 7.10.

E

Y

r

Y

Figure 7.10: Deriving the IS Curve with the Keynesian Cross

A second approach is to derive the IS curve through the relationship between saving and investment.

At first this approach will be slightly more complicated but will allow us to easily extend the model to the

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r

I

S

Y

Figure 7.11: IS Curve - Saving and Investment Schedules

open economy. The IS curve represents the relationship between investment and savings (S+ T = I+ G).

Investment takes the same form as before, I= I i1r or r = Ii1 1i1 I and personal savings is derived from

the consumption function, S= a + (1 b)YD. Since we are assuming the consumption function is

independent of the interest rate, it follows that saving is also independent of the interest rate. Studies have

shown the relationship between changes in the real interest rate and personal saving rates is extremely

week. This assumption is not that extreme. The slope of the investment function depends on i1, the

investment sensitivity to the interest rate. When i1 is small (large), investment is interest inelastic

(elastic), and the investment function is steep (flat). For now we are going to assume T = G = 0 which

gives us S= I. The investment and savings functions are shown in figure 7.11.

For a given interest rate, r0, we find the quantity of investment. In equilibrium I= S which allows us

to use the savings function to determine the equilibrium level of income. To construct the IS curve we must

change the interest rate and observe what happens to income. As the interest rate decreases, the quantity of

investment increases, which will increase saving and output. Graphically this can be seen in the figure 7.12.

Again to construct the IS curve we start at an initial interest rate and observe the level of investment.

Because investment equals saving this allows us to determine the level of income. In order to graph the IS

schedule we repeat this process for successively higher levels of the interest rate.

7.3.1 Slope of the IS curve

From the above graphs we can see the slope of the IS curve will depend on the slope of the investment

schedule (1/i1) and the slope of the savings function (1 b). We will start by looking at i1, the interest

sensitivity of investment. In the above graphs we have interest rates on the vertical axis so it might help to

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r

I

S

Yr

YFigure 7.12: Deriving the IS Schedule - Saving and Investment

define the investment function in terms of the interest rate: r = I 1i1I. If the investment schedule is

steep, i1 small (inelastic), then investment is not very sensitive to changes in the interest rate which implies

for given decrease (increase) in the interest rate, investment will not increase (decrease) by a large quantity.

If investment only responds by a small amount, then income will only change by a small amount. The IS

curve will be steep. A change in the interest rate will have little affect on investment and income. We can

see this effect in figure 7.13.

Using the same analysis but with a flat investment schedule, i1 large, then investment will be very

sensitive to changes in the interest rate (elastic). Now that same change in the interest rate will have a

large affect on investment and conversely income will increase by a large amount. We can show the effect of

a large value of i1 in figure 7.14.

An extreme case does emerge when the interest sensitivity to investment is zero. The slope of the

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r

I

S

Yr

YFigure 7.13: IS Schedule - Small i1 (inelastic)

investment function approaches infinity (becomes vertical) and changes in the interest rate will not change

the quantity of investment, and consequently income will not change. The IS curve will also be vertical.

The second factor that will affect the slope of the IS curve is the marginal propensity to consume.

Normally the MPC is relatively constant which means the savings function is fairly stable. One factor

worth exploring in the future will be how to incorporate taxes when they are a function of income. This

will change both the slope of the consumption and savings function. For now we will restrict our discussion

to the MPC. If the MPC increases then the slope of the savings function (1 b) will decrease. This implies

for a given increase in investment a higher MPC (a flatter savings function) will cause output to increase

by a larger amount. The IS curve will be flatter. We can graph this outcome in figure 7.15.

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r

I

S

Yr

YFigure 7.14: IS Schedule - Large i1 (elastic)

7.3.2 Shift Factors

Now that we understand the determinants of the IS function we are going to analyze variables that shift

the IS schedule. Remember we used the equation, S+ T = I+ G, to begin our analysis. One way to view

this equation is through leakages and injections. The left hand side (S+ T) are leakages from GDP. When

we add taxes to the model the savings function will increase. There are more leakages in the system for a

given level of income. The right hand side of the equation has what we call injections (G + I). Saving and

taxes remove income from the system and are injected through investment and government spending.Adding government spending to the model will shift the investment function to the right.

Now it is easy to see how a change in government spending and taxes will affect the IS curve. If

government spending increases, the investment function will shift to the right. At a given interest rate,

I+ G and S+ T will increase causing the IS curve to shift rightward. The size of the rightward shift will

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r

I

S

Y

r

YFigure 7.15: IS - MPC large

be equal to the autonomous expenditure multiplier (we will explore this below). Figure 7.16 shows the

effects of an increase in government spending.

Instead of increasing government spending, suppose the government decides to increase taxes. The

increase in taxes will cause the saving function to shift left. There are now more leakages from the system.

The IS curve will also shift left. The IS curve will decrease by the size of the tax multiplier ( b/(1 b)).

The increase in taxes is modeled in figure 7.17.

7.3.3 IS Curve Summary

1. The IS schedule slopes downward to the right

2. The IS schedule will be relatively flat (steep) if the interest elasticity of investment is relatively high

(low).

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r

I

S

Y

r

YFigure 7.16: IS Curve - An Increase in Government Spending

3. The IS schedule will shift to the right (left) when there is an increase (decrease) in government

expenditures.

4. The IS schedule will shift to the left (right) when taxes increase (decrease).

5. An autonomous increase (decrease) in investment expenditures will shift the IS schedule to the right

(left).

7.4 Mathematical Derivation

In the previous sections we primarily focused on the graphical representations of the IS/LM curves. Now

we are going to explain both figures through math. We are going to start with the LM curve. Recall our

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r

I

S

Yr

YFigure 7.17: IS Curve - An Increase in Taxes

key equation for the LM curve:

Ms = Md = l0 l1e + l2Y l3r (7.9)

and the equilibrium interest rate is:

r =l0 l1

eMs

l3+

l2l3Y (7.10)

The equilibrium level of income is:

Y =Ms l0 + l1e

l2

+l3

l2

r (7.11)

The slope of the LM curve is the change in r per unit change in Y, holding constant the factors that fix the

position of the schedule. In equation 8.20 our slope is:

r =l2l3

Y

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r

Y=

l2l3

As we discussed above, the LM schedule will be steep (flat) for higher (lower) values of l2 and lower

(higher) values of l3. A high l2 can be interpreted as a greater increase in money demand for a given

change in income. The money demand line will have a larger shift for a given change in income. A small

value of l3 can be interpreted as a low interest elasticity to money demand. The money demand line is

steep, small changes in the quantity of money demand will have large affects on interest rates.

The shift factors of the LM curve can be seen through the intercept terms of equation 8.20. These

terms represent money supply and autonomous demand for money. Both variables will have the same

affect on the LM schedule. Taking the change in these variables yields the following:

r =1

l3Ms (7.12)

rMs

=1l3

(7.13)

The negative sign implies the intercept for the LM curve will be smaller, an increase in money supply will

cause the LM curve to shift downward.

We can find the slope and the size of the shift factors in a similar fashion for the IS curve. We are

going to maintain the assumptions that consumption and saving are independent of the interest rate, taxes

are lump sum, and NX= 0. The starting point for our IS schedule is:

S+ T = I+ G

Recall our savings function was S= a + (1 b)(Y T) and investment was I= I i1r. Using these

equations we have:

a + (1 b)(Y T) + T = I i1r + G

Solving for income we have:

Y =1

1 b(a + I+ G bT)

i1r

1 b(7.14)

Equation 8.17 looks very similar to the equilibrium condition found in the simple Keynesian model. We

can also find the equilibrium interest rate as:

r =1

i1(a + I+ G bT)

1 b

i1Y (7.15)

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demand (the money demand curve increases by l2. The increase in money demand will cause interest rates

to increase (which depends on the size of l3. An increase in the interest rate will decrease investment

(which depends on i1).

Intuitively, an increase in government spending will cause income to increase, but by a much smaller

amount than previously discussed in the goods market. The following chain diagram will be useful in our

analysis:

As we can see through the chain diagram, the multiplier will be larger when the MPC is big (people

spend their extra income), the income sensitivity to money demand, l2, is small (money demand does not

respond to changes in income), the interest sensitivity to money demand, l3, is large (at the initial interest

rate, it only takes a small increase in rates to restore equilibrium in the money market) and finally the

interest sensitivity to investment, i1, is small (interest rates will increase in the money market for the

multiplier to be large investment cannot respond to the increase).

We can also do a similar diagram for an increase in the money supply.

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In the above chain diagram an increase in the money supply will lower interest rates (depending on the

size of l3), increase investment (depending on the size of i1), increase income, and then the standard affects

on consumption. Also the increase in income will cause money demand to increase (depending on the size

of l2), the interest rate will increase (depending on the size of l3), investment will decrease (depending on

the size of i1), and income will fall. We can see the role each parameter has through our multipliers.

7.4.2 Multipliers

Our focus will be on the effects of fiscal policy (changing government spending and taxes) and monetary

policy. The government spending multiplier is:

Y

G=

1

(1 b) + i1l2l3

. (7.18)

As we can see in equation 7.19, fiscal policy is more effective for larger value of b and l3 and smaller valuesof i1 and l2. The tax multiplier has the same intuition as the government spending multiplier:

Y

T=

b

(1 b) + i1l2l3

. (7.19)

Notice that if i1 or l2 approach zero, the multiplier reduces down to the standard Keynesian multiplier. In

other words the money market become irrelevant. The investment schedule becomes nearly vertical,

changes in the interest rate have no affect on investment, and money demand line no longer responds to

change in income. Essentially there will be no crowding out effect. The LM curve would be horizontal forl2 = 0. When l3 becomes extremely small, the second term in the multiplier becomes very large. This will

make the LM curve vertical and fiscal policy ineffective.

The multiplier for monetary policy will be slightly different:

Y

Ms=

1

(1 b) + i1l2l3

i1l3

rewriting:

Y

Ms = i1

(1 b)l3 + i1l2. (7.20)

As we can see from our multiplier equation, monetary policy is more effective if l3 is relatively small, the

LM curve is steeper. As l3 becomes smaller, the denominator of the money multiplier becomes smaller,

making monetary policy more effective. A small l3 also corresponds with a steep money demand curve

(slope ofMd = 1/l3), meaning small changes in the money supply lead to large changes in the interest rate.

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It is difficult to isolate the effects of i1 on the money multiplier. The smaller i1 becomes then investment

becomes less sensitive to changes in the interest rate (the investment and IS schedules become steep), which

makes monetary policy ineffective. This is seen in our multiplier through the nominator becoming small.

7.5 Adjustment to Equilibriumr

YFigure 7.18: Adjustment to Equilibrium in the IS/LM Model

7.6 Policy Effectiveness

As we learned in the last section, the slope of the IS curve depends on the interest sensitivity to investment

and the marginal propensity to consume. The size of IS curve shifts depend on changes to the exogenous

variables (notably government spending and taxes). The slope of the LM curve depends on the interest

sensitivity to money demand and the income sensitivity to money demand. The LM curve shifts depend on

changes in the money supply. We can graph an increase in government spending in figure 7.19

The IS curve will shift horizontally by the size of our simple multiplier 1/(1 b). The increase in

income will cause money demand to increase, interest rates to increase, investment to decrease, and income

to decrease. This reduces the overall effectiveness of our spending program. In the above graph will can see

the secondary effects as we move up our new IS curve to equilibrium. The government spending program

will increase output and interest rates. The same reasoning holds for a decrease in taxes, expect the initial

shift in the IS curve will be smaller. The horizontal shift will be b/(1 b). Autonomous changes in

investment will act in a similar manner with government spending. As you can probably tell the

effectiveness of fiscal and monetary policy will depend on the slopes of both LM and IS curves.

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r

YFigure 7.19: An Increase in Government Spending

7.6.1 Fiscal Policy Effectiveness

To start our analysis we will begin by looking graphically as the effects of an expansionary fiscal policy

when the IS schedules are flat and steep. For starters, fiscal policy will be most effective for large values of

the MPC. We want our multiplier to be as large as possible. Referring to the chain diagram above, the first

and primary effect is through the MPC. When government spending increases, income increase, followed by

changes in consumption. Given we want the MPC to be large, what else will increase fiscal policy

effectiveness. Graphically we can see for a given increase in government spending, the change in income is

largest as the IS curve becomes steeper (see figure 7.20).

r

Y

r

Y

Figure 7.20: Fiscal Policy Effectiveness - Steep IS

What makes the IS curve steep. Recall the slope of the IS curve is 1bi1

, for a given MPC, the IS

curve will be steeper as i1, the interest sensitivity to investment, becomes small. This implies investment is

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relatively interest-inelastic. This parameter captures the crowding out effect of government spending.

Looking back to our chair diagram. An increase in income will cause money demand and interest rates to

increase. In order for fiscal policy to be effective investment needs to be relative insensitive to

the increase in the interest rate (i1 small). The IS curve will be steep. Fiscal policy will be most

effective when the IS curve is vertical, investment does not respond to an increase in the interest rate.

Next we turn to the LM curve. Looking back to our chain diagram, an increase in government

spending will increase income which in turn will cause money demand to increase. The increase in money

demand will cause the interest rate to increase. Fiscal policy is most effective when money demand does

not respond to changes in income (the upward shift in money demand is minimal), and interest rates are

highly sensitive to money demand (for a given shift of money demand, interest rates are highly elastic and

therefore need to increase a small amount to restore equilibrium in the money market). Both of these

effects can be seen in the slope of the LM curve, l2l3

. The relationship between income and money demand

is represented by l2. If we dont want money demand to increase in response to an increase in income then

we need l2 to be small. Next, when money demand does increase following a change in income we want the

interest rate to be highly sensitive. This implies that we only need a small change in the interest rate to

restore equilibrium, in other words we need l3 to be large. A small l2 combined with a large l3 will give us

a flat LM curve. We can compare these results in figure 7.21.

r

Y

r

Y

Figure 7.21: Fiscal Policy Effectiveness - Flat LM Curve

As we can see above, fiscal policy is most effective when money demand does not respond

to change in income and the interest rate is highly sensitive to changes in money demand. At

the extreme fiscal policy will be completely ineffective when the LM curve is vertical. This can occur as l3

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approaches zero, the interest elasticity to money demand becomes extremely small. The interest rate no

longer responds to movements in money demand (this was the classical case we presented earlier.

7.6.2 Monetary Policy Effectiveness

An increase in the money supply will cause the LM curve to shift right. It will help to start our analysis bylooking at a detailed chain diagram reflecting the change in the money supply. An increase in the money

supply, which causes the interest rate to decrease. A decrease in the interest rate will cause investment to

increase and income to increase. An increase in income will cause consumption to increase in the goods

market but at the same time money demand will increase. The increase in money demand will cause

interest rates to increase and investment to decline. How does all of this relate to the parameters of our

model. Graphically we can see that monetary policy is more effective for a relatively flat IS curve (see

figure 7.22). Remember the horizontal shift in the LM curve is held constant.

r

Y

r

Y

Figure 7.22: Monetary Policy Effectiveness - Flat IS Curve

Recall the slope of the IS curve was: 1bi1

which means the IS curve will be flat for large values of b

and i1. This makes perfect sense, a large MPC is needed to ensure households spend their added income.

This is seen in the above chain diagram after the initial increase in income. Secondly we also need i1 to be

large. Since the Federal Reserve is increasing the money supply, the interest rate decreases and investment

will increase. The more sensitive investment is to changes in the interest rate the more effective monetary

policy becomes. Monetary policy is most effective when the MPC is large, and investment is

highly sensitive to changes in the interest rate, the IS curve is flat. At the extreme case, if i1

approaches zero the IS curve become vertical and monetary policy is completely ineffective.

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r

Y

r

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Figure 7.23: Monetary Policy Effectiveness - Steep LM Curve

Now for a given IS curve is monetary policy most effective for a steep or flat LM curve? We can start

our analysis by looking at the graphs for the same change in the LM curve (see figure 7.23).

In the above figures we can see monetary policy is most effective when the LM curve is steep. Recall

the slope of the LM curve is l2l3

and the LM curve will be steep for large values of l2 and small values of l3.

In other words we want a money demand to be highly sensitive to changes in income, but more

importantly we want money demand to be interest inelastic. To understand this logic it will help to look at

our money market. A small measure of interest elasticity is reflected in a relatively steep money demand

line. For a given change in the money supply, interest rates will decrease by a larger amount when interest

rates are highly inelastic. The larger decrease in the interest rate will cause investment and income to

increase by larger amounts. Monetary policy is most effective when the LM curve is steep, which

occurs when money demand is interest-inelastic.

Ironically, the condition that makes monetary policy most effective (money demand being interest

inelastic, a small l3) corresponds with fiscal policy being least effective. The monetary authority wants

interest rates to be highly inelastic, they want small changes in the money supply to create large changes in

the interest rate. Conversely, the fiscal authority wants to be able to increase income without having to

worry about large increases in the interest rate. An expansionary fiscal policy will cause interest rates to

increase, but an expansionary monetary policy will cause interest rates to decrease. The following tablewill sum up monetary and fiscal policy effectiveness.

As we can see in table 7.1 the conditions for monetary policy and/or fiscal policy to be effective are

very different.

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Table 7.1: Monetary and Fiscal Policy EffectivenessMonetary Policy

IS Schedule LM ScheduleSteep Ineffective EffectiveFlat Effective Ineffective

Fiscal Policy

IS Schedule LM ScheduleSteep Effective IneffectiveFlat Ineffective Effective

7.7 Limitations of the IS-LM Model

The IS-LM model was the workhorse model in macroeconomics starting in 1937 (with Hicks) through 1980.

Even today, most economists picture the IS-LM when thinking about the effects of policy. Compared to

new models, it is relatively simple to understand and can explain a number of relationship in the economy.

Further is has proven to do a good job at depicting business cycle movements.

Even with all the successes of the IS-LM model, there are limitations. Three primarily limitations fall

along the lines of expectations, microfoundations, and prices. Starting with the idea of rational

expectations. Keynes assumed agents formed expectations adaptively (essentially projecting the past into

the future). In the 1970s a group of Chicago School economists (Robert Lucas) developed the idea of

rational expectations. Agents use all relevant information when making future projections. Agents are

foreword looking.

Another limitation of the IS-LM model stems from the failure to account for supply side effects and

microfoundations in supply and demand. In the classical model we saw the important of real variables.

Stemming from the assumption of sticky wages, Keynes ignored the effects of the supply side on

determining equilibrium output. Additionally, the IS-LM model does not account for individual optimizing

behavior. Current macroeconomic models start at the household level and model labor, consumption, and

investment through household and firm behavior. The macroeconomy is simply an aggregate of all

households and firms. To correctly understand movements in the macroeconomy we need to understand

how households and firms make decisions. Macro models shifted focus in the 1990s and looked closely at

the households decision process between working and consumption and the firms capital decisions. These

models include what economists call microfoundations.

The next limitation of the IS-LM model deals with the effects of nominal shocks, inflation, and policy

responses. Since the IS-LM model does not incorporate supply side effects, policy makers had a difficult

time conducting policy following the oil shocks in the 1970s. As oil prices spiked, the demand for money

increased. To offset the higher demand for money the Federal Reserve increased the money supply. They

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were able to maintain their interest rate target. Unfortunately the model was unable to gauge the impact

their actions would have on inflation. The result was extreme inflation throughout the 1970s and 1980s.

Today we know the policy response was incorrect, the Federal Reserve has shifted policy into more

inflation targeting opposed to interest rate targeting. Had this been the norm in the 1970s then we would

probably see the IS-LM at the forefront of macroeconomics.

7.8 Monetarists Rebuttal to Keynes

A monetarists is someone who thinks it more important to regulate the supply of money in an economy

than to influence other economic instruments. This is thought very wicked by those who cant be bothered

by what it means.

The monetarist counterrevolution began shortly after Keynes death in 1946 and can be characterized

by four propositions:

1. The supply of money is dominant influence on national income.

2. In the long run, the influence of money is primarily on the price level and other nominal magnitudes.

In the long run, real variables, such as output and employment are determined by real, not monetary,

factors.

3. In the short run, the supply of money does influence real variables. Money is the dominant factor

causing cyclical movements in output and employment.

4. The private sector is inherently stables. Instability in the economy is primarily the result of

government policies.

The take away is the stability in the growth of the money supply is crucial for a stable economy. Milton

Friedman, the primary intellectual force behind monetarism, is known for always advocating the central

bank should follow a monetary policy rule. Monetary policy governed by discretion would result in excess

volatility.

By looking at the four propositions we can see where monetarists borrowed and expanded on the

ideals of classical economists. The first and third propositions stem from the Keynesian view of the IS-LM

where money could influence output. The second proposition follows directly from the classical view of the

economy.

As we discussed earlier, the Great Depression primarily brought an end to the Classical school and

quantity theory of money. Friedman argued the events of the Great Depression were not properly analyzed.

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That instead of a failure in the quantity theory of money, the instability was a result of government policy

(proposition 4).

7.8.1 Keynesian View of Monetary Policy During the Great Depression

In the IS-LM model weve already seen the role money plays. An increase in the money supply will resultin lower interest rates and higher levels of income. However, many early Keynesians believed money was of

little importance. Most early Keynesians were influenced by the Great Depression. During the Great

Depression the LM schedule of very flat (high interest rate elasticity of money demand), while the IS

schedule was very steep. This fits with the characterization of low output and low interest rates during the

Depression. The money market feel into a liquidity trap, but early Keynesians believed the interest rate

elasticity of investment was very high. In other words, small changes in the interest rate would stimulate

investment. Combining these two features with a very low rate of resource utilization causing excess

capacity early Keynesians thought investment would be unlikely to respond to changes in the interest rate.

We can see figure 7.24

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Figure 7.24: Early Keynesians on the Great Depression

As we can see in figure 7.24 the highly elastic LM schedule left money having little importance when it

came time to conduct policy.

7.8.2 A Monetarists View of the IS-LM Model

Friedman countered the early Keynesians by arguing that money demand was stable and the interest

elasticity was not infinite. Instead he argued the interest elasticity of money demand was quite small. To

understand Friedmans position we need to reinstate the quantity theory of money. Friedmans positions

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starts with the Cambridge money demand equations:

Md = kPY, (7.21)

where money demand is expressed as a proportion of nominal GDP (PY). Friedman accepted Keynes

view that money was an asset and the amount of money demand depends on the rate of return. But

critiqued Keynes assumption that all assets can be grouped into money or bonds. Friedmans money

demand function was:

Md = L(P,Y,rB, rE , rD), (7.22)

where P is price level, Y is output, rB is the nominal interest rate on bonds, rE is the nominal interest rate

on equities, and rD is the nominal return on durable goods. Friedman assumed individuals have a choice

between stocks, bonds, and durable goods (housing) and this assets offer different rates of return.

Friedman views money demand as being stable whereas Keynes view the demand for money was

unstable. Friedman does not sperate his view into the speculative, transactions, or precautionary motives

as Last, Friedman allows for more than one money substitute. Keynes assumed households had a choice

between money and bonds, Friedman assumes households choose between money, equities, bonds, and real

assets. Combining this idea with the Cambridge equation for money demand Friedmans money demand

schedule is:

Md = k(rB, rE, rD)PY, (7.23)

where instead of a constant k we now have k expressed as a function of the rates of return on the assets

that are alternatives to holding money. A rise in the rate of return on any one of these assets would cause

k to fall, reflecting the increased desirability of the alternative asset. Friedman has reinstated the quantity

theory of money demand that includes Keynesian analysis of moneys role as an asset.

The modern quantity theorist differs from Keynes as they believe:

1. The money demand function is stable.

2. This money demand function plays an important role in determining the level of economic activity.

3. The quantity of money is strongly affected by money supply factors.

With a stable money demand function, an exogenous increase in the money supply must either lead to a

rise in PY of cause declines in rB, rE , and rD. Effects to the real interest rate for alternative assets will

affect k and indirectly change PY.

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Early Keynesians believed money demand was unstable; the interest elasticity of money demand was

very high; and as a consequence changes in the quantity of money did not have important predictable

effects on the level of economic activity. Friedman viewed money demand as stable; the interest elasticity

of money demand was very low; and that the quantity of money is an important determinant of economic

activity.

The monetarist believe money was active in determine income, although complete determination was

an exaggeration. Money was a strong determinant of national income and real income in the short-run.

Further, changes in the rate of growth of money are a necessary and sufficient condition for changes in the

rate of growth of money income. We can graph the monetarist view in figure 7.25

r

Y

Figure 7.25: A Monetarist Version of IS-LM

The IS schedule is interest elastic, large changes in the interest rate were needed to increase

investment. The LM schedule is interest inelastic, small changes in the money supply result in large

changes in the interest rate.

Early Keynesians and monetarists differed drastically in their policy views. Friedman took the view

that fiscal policy was ineffective, any changes in output Keynesians contributed to fiscal policy could

ultimately be traced to changes in the quantity of money. Suppose there is an increase in government

spending, holding all else constant, the government must finance the spending through issuing new bonds

or print money. As the government issues bonds, the bond rate will increase, causing money demand to

decrease. Either way, government spending directly influenced the money supply. We can see the effects of

fiscal policy, under the monetarist assumptions, in figure 7.26.

As we can see, an increase in government spending will ultimately result in an increase in interest

rates and little change in output. The increase in government spending will initially cause income to

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r

Y

Figure 7.26: An Increase in Government Spending - Monetarist Assumptions

increase. An increase in income will increase the demand for money (through the transactions motive).

Because of a low interest elasticity of money demand, an increase in money demand will result in a large

increase in the interest rate to equate money supply and money demand. The higher interest rate will then

crowd out private investment, investment is highly elastic in regards to changes in the interest rate.

In the end, monetarists showed money does have an active role in determining real output in the

short-run. Friedman was a staunch advocate of rule based monetary policy (which is what most central

banks do today). Finally Friedman argued against fine tuning the economy. We do not know enough about

monetary policy to use it in response to minor disturbances.

7.9 Practice Questions

1. Define the LM curve. Define the IS curve. Is the LM curve positively or negatively sloped? Is the IS

curve positively or negatively sloped? When is the LM curve relatively steep? When is the IS curve

relatively flat?

2. Graphically show and analyze the effects of an increase in taxes in the IS-LM model. Utilize the

IS-LM model and analyze the effects of a decrease in the quantity of money.

3. Using an IS-LM graph, illustrate how the central bank could target interest rates in response to

expansionary fiscal policy.

4. You are given the following two situations

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(a) Investment is very interest elastic (interest sensitive) while the demand for money is very interest

inelastic

(b) Investment is very interest inelastic while the demand is very interest inelastic

In which situation would monetary policy be most effective in changing the level of income? In which

situation would fiscal policy be most effective? Explain completely.

5. Assume the following equations describe the goods market of an economy C= 250 + .8(Y T),

I= 100 50r and T = G = 100. Calculate the IS curve for this economy. If G rises to 120, calculate

the new IS curve for this economy. How much and in what direction has the IS curve shifted?

6. Assume that following equations describe the money market of an economy Ms = 1, 000 and

Md = .2Y 100r. Calculate the LM curve for this economy. Now assume that the money supply

rises to 1,200. How much and in what direction has the LM curve shifted?

7. Given the following information: G = 100, T = 0, S= 50 + 0.25Y, I= 150 10r,

Md = 80 20r + 0.2Y, and Ms = 188

(a) Find the equilibrium values of Y and r.

(b) IfMs is increased to 210, find the new equilibrium values of Y and r

8. Consider the following economy: C= .6(Y T), I= 1, 000 20r, G = 180, T = 180, Ms = 1, 500,

and Md = Y 50r

(a) Calculate the IS and LM curves. Use these curves to determine equilibrium interest rates and

output.

(b) Explain in detail the intuition behind why the IS and LM curves are sloped as they are. Provide

graphs to aid your explanation.

(c) Suppose that both G and T rise by 40 to G = T = 220. Calculate what will happen to Y and

r? Can you explain the intuition behind what is going on here? Provide a graph to support

your explanation.

9. Derive the IS curve graphically assuming taxes are lump sum. Now suppose rather than a fixed level

of taxes (T), we have taxes depending on income T = t0 + t1Y where t1 is the marginal income tax

rate. Will the IS schedule for this case be steeper or flatter than when the level of taxes is fixed?

10. Suppose the interest elasticity of investment demand is zero. What will be the resulting slope of the

IS schedule? Explain.

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11. Suppose we had a case in which the interest elasticity of money demand and investment were quite

low. Would either monetary or fiscal policy be very effective? How would you interpret such a

situation? When has such a situation arisen?

12. Why do the Keynesians prefer a policy mix of tight fiscal policy and easy monetary policy?

Explain this preference. Since the Keynesians prefer a policy mix of relatively tight fiscal policy

and easy monetary policy, how would they respond to an income tax cut in order to expand the

economy?

13. What do Keynesians believe caused the Great Depression?

14. What do Monetarists believe about the slope of the IS and LM curves and why? What do these

beliefs imply about the effectiveness of monetary policy.

15. What do early Keynesians believe about the slope of the money demand curve and why? What do

these beliefs imply about the effectiveness of monetary policy.

16. Show how the IS and LM schedules look in the monetarist view. Use these schedules to illustrate the

monetarists conclusions about the relative effectiveness of monetary and fiscal policy.

17. In what sense is a vertical LM schedule a special case of the classical model?

18. Consider the case in which the LM schedule is vertical. Suppose there is a shock that increases the

demand for money for given levels of income and the interest rate. Illustrate the effect of the shock

graphically and explain how income and the interest rate are affected.

19. Why might Keynesians be pessimistic about the ability of monetary policy to stimulate output in

situations such as the 1930s Depression in the United States, the recessions in Japan during the

1990s, or the Great Recession in the United States during the 2000s. What type of policy would

Keynesian economists expect to be effective in such situations?

20. What is meant by a liquidity trap?

21. If the central bank of an economy follows a policy of interest rate targeting, or maintaining a fixed

interest rate, then what will happen to the slope of the LM curve? Draw a graph to illustrate.