IS – LM MODEL

INVESTMENTS

• INVESTMENT IS NO LONGER AUTONOMOUS. IT IS NOW DEPENDENT ON INTEREST RATE. •HIGHER THE INTEREST

RATE, LOWER WILL BETHE INVESTMENT.• I = Ῑ - b i b TELLS THE INTEREST RATE RESPONSIVENESS OF INVESTMENT

AGGREGATE DEMAND

• AD= Ᾱ - bi –c( 1- t)YEquilibrium in the goods market now requires AD = Y Y= Ᾱ - bi = αG (Ᾱ- bi) where αG= 1-c( 1-t) 1-c( 1-t)

IS curve

It is the combination of all those points at which the goods market is in equilibrium. EQUATION OF IS CURVE i = Ᾱ - Y b αG bReason why it is downward sloping: It tells as the interest rate falls, investment will increase and thus output.

Slope of the IS curve

• It depends on αG , b•Higher the αG, flatter the IS curve, higher the

change in output with a given change in interest rate.

reason: higher αG means higher MPC , higher MPC implies higher output.•Higher b, flatter the IS curve, higher the change

in output with a given change in interest rate. reason: Higher b means that investment is highly sensitive to the interest rate, so small reduction can increase investment by a large amount and thus output.

Disequilibrium points in IS curve• E3 and E4 are disequilibrium points.• At E3, interest rate is lower than the rate i1 i.e.

needed to attain equilibrium. At this point the investment will be higher. Thus, AD is higher than output.• At E4, output is higher than the AD. Thus,

excess supply of good

Wealth constraint

•Wealth is stored either in form of money or in form of assets such as bonds. •Money provide convenience for transactions.

But it doesn’t provide ay interest rate. Thus interest rate is the opportunity cost of holding money. • Bonds provide interest rate but can’t be used

for transaction purposes. • Real wealth= real demand of money balances +

real demand of bonds.

Real demand of money balances.

L= k Y – hiHere k tells the income responsiveness to demand of real balances. h tells the interest rate responsiveness to demand of real balances.High income, allows individual to hold large

amount of money. Thus, demand of real balances is positively related to income.

Higher the interest rate, higher is the opportunity cost of holding money. Thus , demand of real balances is negatively related to income

Real demand of money balances

LM curve

• It is the combination of all those points at which money market is in equilibrium.•With a given money supply, we can derive the

LM curve from the demand of real balances curve.• Reason why it is upward sloping: as the interest rate increase, demand of bonds increase and thus demand of money falls. With the same level of money supply, inorder to achieve equilibrium income should increase.

Derivation of LM curve

LM curve

L = money supply. kY – hi = mC / CpkY – mC / Cp = hii = kY - mC / Cp h h

Slope of LM curve• It depends on k and h•Higher k, steeper the LM curve, smaller will the

increase in the income due to given change in interest rate. Or large change in interest rate with a given change in income.

reason: if the income increase then the demand of money will rise by large amount. Thus, we require a huge increase in interest rate to bring the market into equilibrium. • lower h, steeper the LM curve, smaller will the

increase in the income due to given change in interest rate.

Reason: lower h means that if interest rates falls, the demand of money will rise by small amount. So, only small amount of increase in money ids required to bring the market into equilibrium.

Points off the LM curve

• E1 is ESM• Reason: at higher

interest rates, demand of bonds is high and thus there is excess supply of money.• E3 is EDM• Reason: at same

interest rate i1 income rise to Y2 . Thus, demand of money rise, causing excess demands of money.

E1E2

E3E4

Y1 Y2

i2

i1

How the equilibrium output and interest rate are determined

• They are determined by the intersection of two curves IS and LM.• So that at equilibrium both the goods market

and the asset market is in equilibrium.• IS: Y= αG( Ᾱ- bi) LM :i = kY - mC / Cp h h• Substituting the value of I from LM into Is will

give

What causes changes in equilibrium points

• Shifts in IS or LM curves , will bring changes in equilibrium points.• Shift in LM due to changes in money supply• Shift in IS due to change in autonomous

spending.

Suppose there is increase in autonomous spending

• This will shift IS curve rightwards.• Change in Y is less than the αG • Reason: y L with the same money

supply i I Y• thus, both asset market and goods market clears

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