IS AND LM MODEL

IS and LM Curve

Qazi Muhammad Adnan Hye

IS-LM Model IS Curve LM Curve Keynesian cross Government-purchases Government-purchases multiplier Tax multiplier mult iplier

 Long

run

prices

flexible output determined by factors of production & technology unemployment equals its natural rate  Short

run

prices

fixed output determined by aggregate demand unemployment negatively related to output

chapter develops the IS -LM  model, the basis of the aggregate demand curve.  We focus on the short run and assume the price level is fixed (so, SRAS curve is  This

horizontal).

The Keynesian model - shows what causes the aggregate demand curve to shift. In the short run, when the price level is fixed, shifts in the aggregate demand curve lead to changes in national income, Y. The IS-LM model = the leading interpretation of Keynes‟ work. The goal of the model: to show what determines national income for any given price level. Price Level, P

SRAS AD'' AD' AD

Y* Y*'Y*''

Income, Output, Y

1. The goods market and the IS curve 2. The money market and the LM curve 3. The short-run equilibrium

The basic textbook Keynesian model: an elaboration and extension of the „classical theory‟.

The model of aggregate demand (AD) can be split into two parts: - IS (“investment” and “saving”)model of the „goods market‟ - LM (“liquidity” and “money”) model of the „money market‟.

The IS curve (which stands for investment and saving) plots the relationship between the interest rate and the level of income that arises in the market for goods and services.

The LM curve (which stands for liquidity and money) plots the relationship between the interest rate and the level of income that arises in the money market. The variable that links the two parts of the IS-LM model: the interest rate (it influences both investment and money demand).

In the General Theory of Money, Interest and Employment  (1936), Keynes proposed: an economy‟s total income was, in the short run, determined largely by the desire to spend  by households, firms and the government. Thus, the problem during recessions and according to Keynes, was inadequate spending .

depressions ,

How to model this insight? - The Keynesian Cross

Planned expenditure is the amount households, firms and government plan to spend on goods and services.  Actual expenditure differs from planned expenditure when firms are forced to make inventory- that is when firms unexpectedly rise or lower their stock of inventories in response to unexpectedly low or high sales. 

The Keynesian Cross A

simple closed economy model in which income is determined by expenditure. (due to J.M. Keynes)

 Notation: I

= planned investment

= C + I + G = planned expenditure  Y  = actual expenditure=GNP PE

 Difference

between actual & planned expenditure = unplanned inventory investment

Graphing planned expenditure PE

planned expenditure

 E   C (Y   T  )   I   G

1

MPC 

income, output, Y 

Graphing the equilibrium condition PE

planned expenditure

PE = Y 

45º income, output, Y 

The equilibrium value of income PE

planned expenditure

PE = Y   E   C (Y   T  )   I   G

A

income, output, Y 

Equilibrium income

An increase in government purchases PE

At Y 1, there is now an unplanned drop in inventory…

 E   C (Y   T  )   I   G1

B  E   C (Y   T  )   I   G

A

G

…so firms increase output, and income rises toward a new equilibrium.

 Y  PE1 = Y 1

 Y  

PE2 = Y 2

If government spending were to increase by $1, then you might expect equilibrium output (Y) to also rise by $1. But it doesn’t! The multiplier shows that the change in demand for  output (Y) will be larger than the initial change in spending. Here’s why: When there is an increase in government spending ( G), income rises by G as well. The increase in income will raise consumption by MPC  G, where MPC is the marginal propensity to consume. The increase in consumption raises expenditure and income again. The second increase in income of MPC  G again raises consumption, this time by MPC  (MPC  G), which again raises income and so on. So, the multiplier process helps explain fluctuations in the demand for output. For example, if something in the economy decreases investment spending, then people whose incomes have decreased will spend less, thereby driving equilibrium demand down even further.

An increase in taxes PE

Initially, the tax increase reduces consumption, and therefore PE : C =

 E   C 1 (Y   T  )   I   G

 E   C 2 (Y   T 

)   I  

At Y 1, there is now an unplanned inventory buildup…

MPC T

…so firms reduce output, and income falls toward a new equilibrium

*

 Y  PE2 = Y 2

 Y  

PE1 = Y 1

The tax multiplier

…is negative :  A tax increase reduces C , which reduces income. …is greater than one  (in absolute value ): A change in taxes has a multiplier effect on income. …is smaller than the govt spending  multiplier :  Consumers save the fraction (1  – MPC ) of a tax cut, so the initial boost in spending from a tax cut is smaller than from an equal increase in G .

Let‟s now relax the assumption that the level of planned investment is fixed. - We write the level of planned investment as: I = I (r).

The investment function - downward-sloping (it shows the inverse relationship between investment and the interest rate) The IS curve summarizes the relationship between the interest rate and the level of income. It is downward-sloping. The IS curve combines: •the interaction between I and r expressed by the investment function •the interaction between E and Y demonstrated by the Keynesian cross.

An increase in the interest rate (in graph a), lowers planned investment, which shifts planned expenditure downward (in graph b) and lowers income (in graph c). (a) r

(b) E

Y=E Planned Expenditure, E=C+I+G

Income, Output, Y

(c) r

I(r) Investment, I

IS Income, Output, Y

An increase in government purchases

How fiscal policy  shifts the IS curve? 

An increase in government purchases or a decrease in taxes - IS curve shifts outward.

A decrease in government purchases or an increase in taxes - IS curve shifts inward.

E

Y=E Planned Expenditure, E=C+I+G

Income, Output, Y r

IS2 IS1 Income, Output, Y

Summary •The IS curve shows the combinations of the interest rate and the level of income that are consistent with equilibrium in the market for goods and services. •The IS curve is drawn for a given fiscal policy. •Changes in fiscal policy that raise the demand for goods and services shift the IS curve to the right. •Changes in fiscal policy that reduce the demand for goods and services shift the IS curve to the left.

LM curve = the relationship between the interest rate and the level of income that arises in the market for money balances  The theory of liquidity preference - how the interest rate is determined in the short run r

The supply of real money balances - vertical Supply The demand for real money balances downward sloping The supply and demand for real money balances determine the equilibrium interest rate. Demand, L (r)

L(r) = M/P

Money Demand

equals

Real Money Balances

A Reduction in the Money Supply: -M/P r

Supply' Supply

Demand, L (r,Y) M/P

M/P

Since the price level is fixed, a reduction in the money supply reduces the supply of real balances. Notice the equilibrium interest rate rose.

(M/P)d = L (r,Y) The quantity of real money balances demanded is negatively related to the interest rate (because r is the opportunity cost of holding money) and positively related to income (because of transactions demand).

r

Supply

r

LM

r2 r1

L (r,Y)' L (r,Y)

M/P M/P Y An increase in income raises money demand, which increases the interest rate; this is called an increase in transactions demand for money. The LM curve summarizes these changes in the money market equilibrium.

r

r

Supply' Supply

r2

r2

r1

r1

LM' LM

L (r,Y) M´ /P M/P

M/P

Y

A contraction in the money supply raises the interest rate that equilibrates the money market. Why? Because a higher interest rate is needed to convince people to hold a smaller quantity of real balances. As a result of the decrease in the money supply, the LM shifts

Summary •The LM curve shows the combinations of the interest rate and the level of income that are consistent with equilibrium in the market for real money balances. •The LM curve is drawn for a given supply of real money balances •Decreases in the supply of real money balances shift the LM curve upward •Increases in the supply of real money balances shift the LM curve downward

r IS

LM(P0)

r0

Y0

Y The IS curve/equation Y= C (Y-T) + I(r) + G The LM curve/equation M/P = L(r, Y) The intersection of the IS and LM curves represents simultaneous equilibrium in the market for goods and services and in the market for real money balances for given values of government spending, taxes, the money supply, and the price level.

The Big Picture Keynesian Cross Theory of Liquidity Preference

IS  curve LM  curve

IS-LM  model

Agg. demand curve Agg. supply curve

Explanation of short-run fluctuations

Model of Agg. Demand and Agg. Supply

Chapter Summary 1. Keynesian cross 

basic model of income determination

takes fiscal policy & investment as exogenous  fiscal policy has a multiplier effect on income 

2. IS  curve 

comes from Keynesian cross when planned investment depends negatively on interest rate



shows all combinations of r  and Y  that equate planned expenditure with actual expenditure on goods & services

Chapter Summary 3. Theory of Liquidity Preference 

basic model of interest rate determination

takes money supply & price level as exogenous  an increase in the money supply lowers the interest rate 

4. LM  curve 

comes from liquidity preference theory when money demand depends positively on income



shows all combinations of r  and Y  that equate demand for real money balances with supply