BlCh5 1

Goods and Financial Markets1: IS-LM

• Goal: link the goods and the financial markets into a more general model that will determine the equilibrium and the equilibrium in the economy (with prices)

• The goods market will be represented by the curve (standing for investment-savings) • The financial markets (money market) will be

represented by the curve (liquidity-money)

1. The Hicks-Hansen model based on Keynes’ General Theory

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The goods market - IS curve• Equilibrium condition

• will provide the link to the financial markets

• Determinants of investment:– If increase, producers

might want to increase their productive capacity by investing in capital goods.

– If , producers find that borrowing to add new capital becomes more expensive

€

I=

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• Equilibrium in the goods market becomes:Y =

• Basically – When i I and Ye

– When i I and Ye

• The ZZ curve shifts now as the interest rate changes and a multiplier effect takes place– If MPI is the marginal propensity to invest out of new

income, assume that MPC + MPI < 1– The slope of the ZZ curve is now and

the interest rate is included in the intercept

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Construction of the IS curve

Z

Y

Y

i

Y’e Ye

YeY’e

i

i’

When the interest rate increases, I (Y, i) drops and the ZZ curve shifts down. The economy contracts from Ye to Y’e.

E and E’ correspond to 2 combinations of i and Y, such that the good market is in equilibrium.

i

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The IS curve• Y = • Definition: All the combinations

i.e. the above equation is satisfied• Shift of the IS: A change in any of the

in the equation will

cause IS to shift.– Shift variables:

• (confidence variables)• (fiscal policy variables)

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Expansionary fiscal policy: increase in G

Z

Y

Y

i

Ye

Ye

Y=Z

ZZ (G)

i E

IS

When G increases by ∆G, ZZ shifts up and IS shifts to the right.

An increase in T would has the opposite effect as it is contractionary.

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Shifts of IS

i

Y

IS

GTc0

I0

GTc0

I0

Expansionary

Contractionary

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The financial markets - LM curve

• Equilibrium condition1:

supply of money = demand for money

Ms = or Ms/P =

(Ms/P is the real money supply)

• It is clear that both LM and IS are relations between i and Y

1. The bonds market is automatically in equilibrium when the

money market is in equilibrium

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Construction of the LM curve

ii

M/P Y

Ms

Y0 Y1

i0

Md(Y0)

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The LM curve• Ms = • Definition: All the combinations of and

such that the ( and ) are in equilibrium• Shift of the LM curve: a change in the

money or a change in or an exogenous shift in the money demand – An in the money supply ( or a in price) is expansionary– A change in the velocity of money

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Expansionary monetary policy: an increase in Ms

A

ii

M/P Y

Md(Y0)

Y0

i0

Ms

LM

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Shifts of LM

Y

iLM

Ms

PV

Ms

PV

Expansio

nary

Contracti

onary

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The IS-LM model

Y = IS curveM/P = LM curveIS is sloped and LM is sloped, they will intercept in E

determining Y and i in equilibrium.At that point, all three markets : two financial markets and the goods market,

are

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The IS-LM graph

i

Y

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Problem # 4

IS-LM model:

C = 200+ .25YD

I = 150 + .25Y - 1000i

G = 250 and T = 200

(M/P)d = 2Y - 8000i

M/P = 1,600

IS

LM

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a. Derive the IS curve: Y = C + I + G

Y = 200 + .25Y- .25T + 150 + .25Y - 1000i + 250

= 550 + .5Y - 1000i

Y - .5Y = 550 - 1000i

Y (1 - .5) = 550 - 1000i

Y = [1/.5] (550 -1000i) multiplier = 2

IS curve:Y = 1100 - 2000i

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b. Derive the LM curve: YL(i) = M/P

2Y - 8000i = 1600

8000i = 2Y - 1600

LM curve: i = Y/4000 - .2

c. Solve IS-LM for equilibrium Y

Y = 1100 -2000i

= 1100 - 2000(Y/4000 - .2)

= 1100 - .5Y + 400

1.5Y = 1500 so Y = 1000

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d. i = Y/4000 - .2

= 1000/4000 - .2

= .25 - .2 = .05 so i = 5%

e. Replace equilibrium Y and i into C and I

C = 200 + .25*1000 - .25*200 = 400

I = 150 + .25*1000 - 1000*.05 = 350

G = 250

So Y = 400 + 350 + 250 = 1000

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Fiscal Policy• Instruments: • Curve affected: • Effect:

Expansionary: when (G-T) or G or T

IS shifts to the Contractionary: when (G-T)

or G or T IS shifts to the

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A fiscal expansion

i

ie

YYe

LM

IS

A

The economy moves along the LM curve from A to A’

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Mechanics of fiscal expansionGoods market effects

As G Y = too immediatelyThen C= and I = alsoMultiplier effect: at same i, Y reaches a higher level as IS shifts to the right

Financial markets effectsAs Y the demand for money M = and the ward shift in Md results in a i, but this is a movement along the curve to A’.

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Effect on investment

As i increases, investment is . So there are 2 opposite effects on investment

as Y increases I

as i increases I

It means that the overall expansion due to the increase in G will be by the impact of the increase in the interest rate on investment.

There is some of private investment due to the increase in government spending.

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Z

Y

Y

i

Ye Y”

Ye

Y=Z

ZZ (G)

i

∆G

IS

LMi

M/P

Ms

Md

i

i’

Y’e

i’

ExpansionaryFiscalPolicy

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Net effect of increase in G on investment

1. Using investmt functas Y increases I

as i increases I Net effect is ambiguous

2. Using equil condition

as Y increases Sp as G increases (T - G)

Net effect is ambiguous

€

I =

€

I =

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Problem # 5 cont.

g. A fiscal expansion: G increases to 400

New IS curve: Y = 700 + .5Y - 1000i

Y = [1/.5] (700 - 1000i)

= 1400 - 2000i

Same LM curve: i = Y/4000 - .2

Solve: Y = 1400 - 2000(Y/4000 - .2)

1.5Y = 1800 so Y = 1200

Replace in LM and we get i = .10 or 10%

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Calculate the corresponding equilibrium for C & IC = 200 + .25Y - .25T = 200 + 300 - 50 = 450I = 150 + .25Y - 1000i = 150 + 300 - 100 = 350Y = C + I + G = 450 + 350 + 400 = 1200Impact of fiscal expansion:

both Y and i increase.C (a function of Y) increases too.I increases when Y increases and decreases when

i increases (ambiguous results overall). With these data, I does not change as the two

effects neutralize each other.

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Monetary policy• Instrument:

• Curve affected:

• Effect:

Expansionary when Ms increases

LM shifts to the

Contractionary when Ms is cut

LM shifts to the

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A monetary contraction

LM

IS

i

Y

A

Ye

ie

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Mechanics of a monetary contraction

• Open market of bonds

• Suppose P=1 constant - so monetary contraction in terms is equivalent to a terms one.

Financial market effects

As Ms drops, i - money market effect.

Goods market effects

As i increases, investment I = I(Y,i) is affected and Y = .

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Effect on investment

Unambiguous: as Y drops and

i increases,

investment can only .

Note that the money demand will shift to the left as Y drops dampening the extent of the increase in the interest rate on the fall of I and subsequently on the fall of Y.

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i

M/PY

iMsM’s

IS

LM

Mdi

Ye

A monetary contraction

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Problem #5 cont.g. Monetary expansion: M/P increases to 1840Same IS curve: Y = 1100 - 2000iNew LM curve: 2Y - 8000i = 1840i = Y/4000 - 1840/8000i = Y/4000 - .23Solve the IS-LM system:Y = 1100 - 2000(Y/4000 - .23)Y = 1100 - .5Y - 4601.5 Y = 1560 so Y = 1040

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Replace in LM:i = 1040/4000 - .23 so i = .03 or 3% Solve for C and IC = 410 and I = 380A monetary expansion reduces i

and increases YThus C (function of Y) increases and I (function of Y and of i) increases

unambiguously.

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Policy Mix 1• To maximize the

expansionary (or contractionary) impact on the economy, use both expansionary monetary and expansionary fiscal policy (or both contractionary).

i

Y

IS

LM

Rational:

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• To dampen the inflationary impact of an expansionary fiscal policy, use at the same time contractionary monetary policy.

i

Y

IS

LM

Policy Mix 2

Rational: