Lecture outline: The Keynesian cross and the IS curve

ContextThis chapter develops the IS-LM model,

the theory that yields the aggregate demand curve. We focus on the short run and assume the price level is

fixed. This chapter focus on the closed-economy case.

*The IS-LM model translates the General Theory of Keynes into neoclassical terms (often called the neoclassic synthesis )* It was proposed by John Hicks in 1937 in a paper called “Mr

Keynes and the "Classics": A Suggested Interpretation” and enhanced by Alvin Hansen (hence it is also called the Hicks-Hansen model). *The model examines the combined equilibrium of two markets :* The goods market, which is at equilibrium when investments

equal savings, hence IS.* The money market, which is at equilibrium when the demand

for liquidity equals money supply, hence LM. * Examining the joint equilibrium in these two markets allows us

to determine two variables : output Y and the interest rate i.

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

Notation: I = planned investment

E = C + I + G = planned expenditureY = real GDP = actual expenditure

Difference between actual & planned expenditure: unplanned inventory investment

consumption function:government policy

variables:planned investment is

exogenous:planned expenditure:Actual expenditure Planned expenditure

Y E

( )C C Y T

,G G T T

I I( )E C Y T I G

Equilibrium condition:

C = C0 + MPC(Y-T)Where Co is a constant and 0 < MPC < 1

Assume that the government expenditure, Taxes and the Investment are not fixed.

The planned expenditure equation becomes : E = Co + MPC(Y-T)+G+I

Equilibrium Y = E, so we can write : Y = Co + MPC(Y-T)+G+IHOW TOTAL INCOME CHANGES IF WE CHANGE ALL VARIABLES ON

THE RIGHT SIDE?(∆C, ∆T, ∆I, ∆G)

From equation C = C0 + MPC(Y-T) we have that ∆C = MPC∆Y- MPC∆T

(Co is a constant so its change is zero by definition).Total change in income is equal to the sum of the changes

in the variables on the right side: ∆Y= MPC∆Y- MPC∆T+∆G+∆I

Definition: the increase in income resulting from a one-unit increase in G.

In this model, the government purchases multiplier equals:

Example: If MPC = 0.8, then

11 MPC

YG

1 51 0.8YG

An increase in G causes income to increase by 5 times as much!

Initially, the increase in G causes an equal increase in Y: Y = G.

But Y C further Y further C further Y

So the final impact on income is much bigger than the initial G.

Definition: the change in income resulting from a one-unit increase in T :

If MPC = 0.8, then the tax multiplier equals

MPC1 MPC

YT

0 8 0 8 41 0 8 0 2. .. .

YT

…is negative: A tax hike reduces

consumer spending, 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.

IS curvea graph of all combinations of r and Y that result

in goods market equilibrium,i.e. actual expenditure (output) = planned

expenditureThe equation for the IS curve is:

( ) ( )Y C Y T I r G

*A fall in the interest rate motivates firms to increase investment spending, which drives up total planned spending (E ). *To restore equilibrium in the goods market, output (a.k.a. actual expenditure, Y ) must increase.

( ) ( , )dM P L i Y(M/P)d = real money balances, the purchasing power of the money supply

(M/P) depends : positively on Y ( )

higher Y more spending need more money money demand increases

negatively on r ( )r is the opp. cost of holding money

We are assuming a fixed supply of real money balances because P is fixed by assumption (short run), and M is an exogenous policy variable. sM P M P

The real income (Y) is fixed and the interest rate the main determinant of the money demand.

The interest rate adjusts to equate the supply and demand for money:

( )M P L r

To increase r, central bank reduces M

LM curve is a graph of all combinations of r and Y that equate the supply and demand for real money

balances.The equation for the LM curve is:

( , )M P L r Y

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

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 supply5. IS-LM model

Intersection of IS and LM curves shows the unique point (Y, r ) that satisfies equilibrium in both the goods and money markets.