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Investment & Saving (IS) / Liquidity and Money (LM) Model

 Is a short run model of the Economy

 Assume prices are constant, output (GDP) is demand determined

(C + I + G + (X – M))

 The multiplier model is used to derive the IS curve

 Money demand, money supply, and the money market are used to derive
the LM curve

IS Curve (Refer to Exhibit 8 – 7)

 Illustrates all possible combinations of real interest rates and
output

 Has a negative slope (i.e. there is an inverse relationship between
interest rates and Aggregate Output)

At lower interest rates, investment increases, and output increases

At higher interest rates, investment decreases, and output decreases

Shifts in the IS Curve (Refer to Exhibit 8 – 9)

 Changes in autonomous expenditures (C0, I0, G0, (X0 – M0), T0)

 Increase in autonomous expenditures result in a rightward shift in
the IS curve, at all interest rates there is a greater quantity of
output due to the multiplier concept

Multiplier – a change in autonomous expenditures results in a more
than proportional increase to output

 Decrease in autonomous expenditures result in a leftward shift in
the IS curve, at all interest rates there is a lower quantity of output
due to the multiplier concept

Multiplier – a change in autonomous expenditures results in a more
than proportional reduction to output (contraction is multiplied)

Recall from the lecture on the multiplier:



Where:

 mpc is the marginal propensity to consume

Autonomous Expenditures is any change in AE = C 0,T0, I0, G0, X0,
M0

(Note: Taxes and Imports are inversely related to Output:

Decreased Imports and Taxes increase domestic GDP,

Increased Imports and Taxes decrease domestic GDP



 Y equals the change in national income

A given change in any of the following autonomous spending component of
AE will yield a more than proportional change in national income (AE).

Shape of the IS Curve

Determined by slope of Investment Demand Schedule

Investment Demand Schedule – Inverse relationship interest rates and
Investment by business (See Chapter 4 Notes)

The less responsive the Investment demand is to interest rates, the
steeper the Investment demand schedule , the steeper the IS curve .

A steep investment demand schedule indicates that a change in interest
rates yields a small change in autonomous business investment (Note:
investment a function of interest rate not income, therefore
autonomous).

A small change in autonomous business investment times the multiplier
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 The more responsive the Investment demand is to interest rates, the
flatter the Investment demand schedule, the flatter the IS curve

A flat investment demand schedule indicates that a change in interest
rates yields a large change in autonomous business investment (Note:
investment a function of interest rate not income, therefore
autonomous).

A large change in autonomous business investment times the multiplier
yields a larger change in output than if the Investment demand schedule
were steeper.

LM Curve

 Illustrates all possible combinations of real interest rates and
output where the money market is in equilibrium

 LM Curve has a positive slope – increase in income, result in
increased demand for money. Increased demand for money cause increase
interest in the Money market to maintain equilibrium (i.e. Money Supply
(MS) = Money Demand (MD)

 Demand for Money – impacted by income and nominal interest rates

 MD = f (Y, r) (Y = GDP, r = interest rate)

Income and Demand for Money

Spending increase as income increase

Money demanded (for transactions purposes) increases when spending
increases

Therefore, money demand rises when income rises

Interest rates1 and the Demand for Money

The opportunity cost of holding money is the interest rate

As the interest rate rises, the cost of holding money rises, and thus,
demands for money decreases

Changes in interest rates affect quantity of money demanded (a movement
along the Money Demand Schedule), where changes in income result in
shifts of the Money demand schedule

1 The basic model that can be used to explain interest rates is defined
as k = k RF + 

Where

 k = the quoted or nominal rate of interest. Nominal economic
variables are adjusted to include the impact of inflation.

 k RF = the risk free rate of return that is approximated by the
yield on the twenty year U.S. Treasury bond. k RF = k* + IP, where k*
= the real rate of interest (unadjusted for inflation), and IP = the
inflation premium. When the Federal Reserve raises interest the IP
(inflation premium) is higher and k RF increases with resultant
increases in levels of all U.S. interest rates.

 sigma the lower case Greek letter) represents the risk
premium. Risk premiums reflect the additional returns required by
lenders to compensate for higher levels of risk. Various risk premium
elements include default risk, liquidity premiums, and maturity risk
premium.

 This model can be used to explain why interest rates vary between
investment alternatives and different types of loans.

Autonomous Influences on the Money Supply

 Influences other than Income (Y) and interest rates (r)

 Financial services innovations (debit cards, and internet banking)
that permit transfers from savings and investment accounts (i.e. broker
money market accounts) to checking account for a miniscule fee have
effectively reduced the demand for money. Recall that a reduction in
demand is illustrated by a leftward shift in the demand schedule

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rates

There exists an inverse relationship between interest rates and bond
prices. When interest rates rise, bond prices fall and vice-a-versa
(When interest rates fall, bond prices rise).

If expectations are that interest rate will rise, the demand for money
increases as investors do not want to purchase bonds and incur a capital
loss, and therefore prefer to hold cash balances.

On the other hand, expectations are that interest rate will fall, the
demand for money decreases as investors want to purchase bonds and reap
potential capital gains

Refer to Exhibit 8-10. Notice that a Δ in the interest rate (r) results
in a movement along the M D Schedule, whereas a Δ in Income (Y) results
in a shift of the M D Schedule

The Supply of Money

 Determined by the Federal Reserve

 M s Schedule is independent of the interest rate (see vertical shape
illustrated in Exhibit 8 – 11

Determination of the Interest Rate

 Equilibrium interest rate where M s Schedule = M D Schedule

(Refer to Exhibit 8 – 11)

 Changes in the M s are the basis for Federal Reserve Monetary
Policy.

 Increasing the M s Schedule results in a rightward shift of the M s
resulting in a decrease in interest rates

 Decreasing the M s Schedule results in a leftward shift of the M s
resulting in an increase in interest rates

Derivation of LM Curve

 Refer to Exhibit 8 – 12

 Using the money market graph, when income rises, M D shifts to the
right. The equilibrium interest rate must increase to maintain money
market equilibrium. When income decreases the opposite occurs (M D
shifts leftward, interest rates fall to maintain equilibrium)

 Plotting all possible money market combinations of income (Y = GDP)
and interest rates yields the LM curve

Shifts in the LM Curve

Refer to Exhibit 8 – 14

 Decrease in the M s Schedule shifts the LM curve to the left

 Increase in the M s Schedule shifts the LM curve to the right

 Changes in autonomous influences on money supply

Expectations regarding higher future interest rates will cause
individuals to hold less money; results in leftward shift in LM schedule

Monetary Policy and the LM Curve

 When the Fed implements expansionary monetary policy, it purchases
U.S. Federal Government Bonds (i.e. the Treasury “writes” checks to
bondholders) increasing the M s (decreasing the federal funds rate) and
causing the LM curve to shift to the right.

 The federal funds rate is the rate that banks charge one another for
overnight loans.

 When the Fed implements contractionary, it sells Federal Government
Bonds decreasing the M s (increasing the federal funds rate) and causing
the LM curve to shift to the left

Short Run Equilibrium

 Refer to Exhibit 8 – 16

 Equilibrium in the short run occurs where IS = LM

 At that point the Goods and Services market is in equilibrium with
the Money market.

 At point IS = LN, equilibrium interest rate (r) and equilibrium
income level (Y) is determined

By specifying the investment and money demand functions, we can derive
the IS and LM equations, which will allow for calculating equilibrium
interest rate and output levels.

C = C0 + mpc (Y – T)

T = T0 + t (Y)

I = b0 + b1 (Y) – b2 (r)

G = G0

X = X0

M = M0 + m(Y)

MD = c1 (Y) – c2 (r)

MS = MS0

The IS equation:

Y = C + I + G + (X – M)

Y = [C0 + mpc (Y – T)] + [b0 + b1 (Y) + b2 (r)] + G0 + [X0 – M0 –
m(Y)]

The LM equation:

MD = MS

c1 (Y) – c2 (r) = MS0

Numerical Example

For simplicity assume that b0 = t = m = 0

C = 100 + 0.5(Y – T)

I = 0.25 Y – 500(r)

G0 = 200

T0 = 100

X0 = 200

M0 = 200

MD = 10Y – 20,000(r)

MS0 = 200

The IS Equation

Y = C + I + G + (X – M)

Y = [100 + 0.5(Y – 100)] + [0.25 Y – 500(r)] + [200] + [(200 –
200)]

Y = 250 + 0.75Y – 500(r)

0.25Y = 250 – 500(r)

Y = 1,000 – 2,000(r)

The LM Equation

MD = MS

10Y – 20,000(r) = 200

Y = 20 + 2,000(r)

Equilibrium IS = LM

1,000 – 2,000(r) = 20 + 2,000(r)

980 = 4,000(r)

.245 = r

Y = 20 + 2,000(r)

Y = 20 + 2,000(.245) = 510

Y = 1,000 – 2,000(r)

Y = 1,000 – 2,000(.245) = 510