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IS-LM MODEL

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Equilibrium in product market with I autonomous

In SKM equilibrium in product market implies Y = C+I

where, Y is national income/national product; C is consumption which is a function of Y and I is investment (exogenously given)

o Thus, solving Y= C(Y)+ Io we obtained the equilibrium Y

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Equilibrium in product market with I as a function of Y

Y = C(Y) + I(Y) Solving this we can obtain

equilibrium Y

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Equilibrium in product market with I as a function of interest rate ‘r’

Let I = I (r) where I’ (r) <0 Now AD=C+I. So given C, an

increase in I → AD↑ at each level of income → equilibrium Y

This implies that there will be different equilibrium values of Y at different rates of interest

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The IS curve

The curve that shows the different equilibrium values of Y at different rates

of interest is called IS-curve

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What is an IS-curve?

The IS-curve represents the different pairs of ‘r’ & ‘Y’ at which the product market is in equilibrium. at which

Y = C(Y) + I(r)or, S(Y) = I(r)

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Problem encountered in determining product market equilibrium with I(r)

The equilibrium value of ‘Y’ cannot be determined without knowing the equilibrium value of ‘r’

Qs: How is equilibrium ‘r’ determined?

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Determination of ‘r’

In Keynes’ liquidity preference theory of interest equilibrium ‘r’ is determined by demand for & supply of money

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Supply of & demand for money

Let nominal money supply (M0)& general price level (P) be given. So real money supply is

o The Keynesian demand for money function/liquidity preference function is

M0/P.

Md/P = L1(Y) + L2 (r) = L (Y,r)

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Explanation of terms in demand function

L1(Y)→ demand for active real balances→ L1’(Y) > 0

L2 (r)→ demand for idle (or speculative) cash balances in real terms → L2’(r) < 0 (so long r is higher than a certain minimum rate r min but lower than a certain maximum rate r max

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Explanation of terms in demand function

The minimum rate of interest r min is called the floor rate → at this rate demand for real speculative balances is perfectly interest-elastic

At r max at which demand for real speculative balances is zero

L’(r) < 0 so long as ‘r’ lies between the two extreme rates

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Money market equilibrium

The equilibrium is given by the equality of supply of real money balances to the demand for it M0/P0 = L (Y, r)

= L1(Y) + L2(r)In the equilibrium equation there are two unknowns ‘Y’ & ‘r’. So equilibrium value of ‘r’Will depend on the level of ‘Y’ given the L (Y, r)→ there are different equilibrium values of ‘r’ at different levels of income ‘Y’

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The LM curve

The curve gives the different combinations of ‘r’ & ‘Y’ that keeps the money market in equilibrium

It shows the equilibrium interest rates at different levels of income, given the nominal money supply, the price level & the L (Y, r) function

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Problem at hand

To determine the equilibrium level of income (Y) it is necessary to know equilibrium rate of interest (r)

And to know equilibrium rate of interest (r) it is necessary to the equilibrium level of income (Y)

This necessitates simultaneous determination of equilibrium values of ‘r’ & ‘Y’

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Determination of equilibrium ‘Y’ & ‘r’ simultaneously

Mathematically-assignment Graphically – to be done in class

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Slope of IS-curve

IS –curve is downward sloping, indicating that higher levels of equilibrium income are associated with lower rates of interest

Reasonr falls → I rises→ S (=I) rises

Now S rises implies Y must have risen

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Mathematical derivation of IS slope

I’ (r) = S’ (Y)dr/dy = S’ (Y)/ I’ (r)

< 0

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Slope of LM curve

assignment

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Product mrkt & Money mrkt in equilibrium

At the intersection of IS & LM curves Figure showing ESG, ESG, EDM &

ESM –to be shown in class

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Monetary & Fiscal Policies

Two main macroeconomic policies Monetary Policy-has its initial impact on

money/asset market Fiscal Policy-has its initial impact on goods

market Goods & assets market are closely

interconnected & so both these policies have effects on both output & interest rateThe IS-LM model helps to understand the working of these policies

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Working of Monetary Policy

Let initially goods & asset mkt be in equilibrium

Suppose nominal money supply↑. P being constant M/P increases→ rightward shift of LM curve

New equilibrium shifts to right at a higher income level & lower interest rate

Figure- to be done in class

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Reasons

M↑; excess Ms; people buy financial assets creating excess demand; price of financial assets↑; yields↓; economy immediately moves towards a point to right of original given by the new LM curve at original Y

Here ‘r’ is low & public hold larger quantity of real money

Here there is excess demand for goods→ inventory run down

Output expands→ movement up the LM curve Equilibrium established at higher Y & relatively

higher r

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Transmission Mechanism

Mechanism by which the changes in monetary policy affect aggregate demand

Two stages in this mechanism An increase in real money supply causes a

portfolio disequilibrium at the prevailing interest rate & level of income i.e. people hold more money than they want→ buy more financial assets→ pushes up prices→ causes interest rate↓

Changes in interest rate affects aggregate demand via investment changes

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Fiscal Policy

Example: let government spending ↑- this is expansionary fiscal policy (figure- done in class)

G ↑; AD↑ (at unchanged r); Y↑; IS curve shifts to the right

Goods market reaches equilibrium to the right of initial equilibrium at the same ‘r’ but at higher ‘Y’

Here money market is not in equilibrium Y ↑; demand for money↑; r↑;I falls; AD falls Economy reaches final equilibrium in between

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Crowding Out

In figure explaining fiscal policy as ‘G’ rises IS curve shifts to the right at which product market is in equilibrium raising ‘Y’ at original ‘r’

As ‘r’ is allowed to rise via rise in ‘Y’ the economy reaches equilibrium in between this & original

A comparison of second & final equilibrium shows the dampening effect of interest rate on aggregate demand

‘r’ rise due to ‘G’ rise cause ‘I’ to fall G rise crowds out I spending

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How to prevent crowding out?

By preventing a rise in ‘r’ when ‘G’ rises

For this Ms must increase Figure- to be done in class

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The Aggregate Demand Curve

Shows the combinations of price level & the level of output at which the goods & money market are simultaneously in equilibrium

Figure – to be done in class

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Aggregate Supply Curve

Two related concepts: Short run aggregate supply- upward

rising – to be explained in class Long run aggregate supply-vertical;

referred to as the natural rate of output