The Keynesian

The Keynesian Cross Model, The Money Market, and

IS/LM

Planned expenditure and actual

expenditure.

Constructing the Keynesian Cross

• Actual expenditure is Y and planned expenditure is

E = C + I + G.

• I, G, and T are assumed exogenous and fixed.

• Our consumption function is C = c(Y–T), where c is the

marginal propensity to consume (mpc).

• Mapping out

E = c(Y–T) + I + G gives us…

_Y

E

E=C+I+G Y=E

£1

mpc

Y*

E*

• The slope of E is the mpc.

• In equilibrium planned

expenditure equals total

expenditure or Y=E.

Constructing the Keynesian Cross

Y E

E=C+I+G Y=E

• Equilibrium is at the point where Y = C + I + G.

mpc

Y*

E*

Y₂ Y₁

Inventory accumulates.

Inventory drops.

£1

• Because actual expenditure exceeds planned

expenditure, inventory

accumulates, stimulating a reduction in production.

• Similarly at Y

_2,

Y < E

• Because planned expenditure exceeds actual expenditure, inventory drops, stimulating an increase in production.

• If firms were producing at Y

₁

then Y > E

Government expenditure and tax multipliers

•

An increase of G by ΔG causes an upward shift of planned expenditure by ΔG.

Y E

ΔG Y=E

Y₁ E₁

E₂

•

Notice that ΔY > ΔG. This is because although ΔG causes an initial change in Y of ΔG, the increased Y leads to an increase in consumption and triggers a multiplier effect.

•

Now suppose a decrease of T by ΔT that causes an upward shift of

planned expenditure by mpc*ΔT.

Y₂

•

Notice again that ΔY > ΔT but that ΔY is less than in the case with ΔG. This is because ΔT causes no initial

change in Y as ΔG did, the decrease in T simply leads to an increase in consumption and triggers the

multiplier effect.

Y₃ E₃

mpc*ΔT

Building the IS curve

•

The IS curve maps the

relationship between r and Y for the goods market.

IS

Y E

Y₂ Y₁

r

I

I(r)

ΔI

Y₂ Y₁

r₂ r₁ r₂

r₁

I(r₁) I(r₂)

E=Y

E=C+I(r₁)+G E=C+I(r₂)+G

Let the interest rate increase from r

₁

to r

₂

reduce planned investment from I(r

₁

) to I(r

₂

).

This decrease in investment causes the

planned expenditure function to shift down.

So Y decreases from Y

₁

to Y

₂

.

Y r

The IS curve maps out this relationship between the interest rate, r, and output

(or income) Y.

Shifting the IS curve

•

While changing r allows us to map out the IS curve, changes in G, T, or mpc cause Y to change for any level of r. This causes a shift in the IS curve.

IS

Y E

Y₁ Y₂

ΔG

Y₁ Y₂

r₁

E=Y

E=C+I+G₂ E=C+I+G₁

Suppose an increase in G causes planned

expenditure to shift up by ΔG.

Y

For any r the increase in G

r

causes an increase in Y of ΔG times the government

expenditure multiplier.

Therefore, the IS curve shifts to the right by this

amount.

IS´

A loanable funds market interpretation

•

The IS curve maps the

relationship between r and Y for the loanable funds market in equilibrium.

IS

r

I(r) I

Y₂ Y₁

r₂ r₁ r₁

r₂

S(Y₂)

Y

r

S(Y₁)

•

Suppose Y increases from Y₁ to Y₂. This raises savings from S(Y₁) to S(Y₂) resulting in a lower

equilibrium interest rate.

•

The IS curve maps out this relationship between the lower interest rate and increased income.

A loanable funds market interpretation of fiscal policy

•

While changing r allows us to map out the IS curve, changes in G, T, or mpc cause Y to change for any level of r. This causes a shift in the IS curve.

IS

r

I

I(r)

Y₁

r₂ r₁ r₁

S(G₁)

Y

r

r₂

S(G₂)

IS´

•

Suppose again an increase in G.

In the loanable funds market this results in a decrease in S and an increase in the interest rate.

•

Therefore, for a given Y there is a higher level of r. So, the IS curve shifts up by this amount.

Building the LM curve

•

The LM curve maps the

relationship between r and Y for the money market.

LM

r

Real Money Balances

L(r,Y₂)

Y₁

r₂ r₁ r₁

Given money supply and money demand suppose an increase in

income raises money demand.

Y

r

r₂

(M/P)^s

L(r,Y₁)

The LM curve maps out this relationship

between r and Y.

Y₂

Shifting the LM curve

•

While changing money demand allows us to map out the LM curve, changes in M or P cause r to

change for any level of Y. This causes a shift in the LM curve.

r

Real Money Balances

r₂ r₁

Given money supply and money demand suppose a decrease in the money stock

shifts real money supply to the left resulting in a higher

equilibrium interest rate.

(M₁/P)^s

L(r,Y)

Now there is a higher real interest rate for the current

level of output.

(M₂/P)^s

The LM curve shifts up so that at the same

level of output the interest rate is higher.

LM

Y

r₂ r₁

Y

r

LM´

IS=LM: The Short Run Equilibrium

•

Given our IS and LM equation we can now determine the short run equilibrium interest rate and

output

LM

Y*

r*

Y

r

IS

•

By mapping out the relationship between Y and r when the goods market (or loanable funds market) is in equilibrium we get the IS

curve.

•

By mapping out the relationship between Y and r when the money market is in equilibrium we get the LM curve.

•

When we set IS=LM we can solve for the equilibrium levels of r and Y. This represents simultaneous equilibrium in the goods market (or loanable funds market) and the money market.

Conclusion

• We constructed the IS curve from the goods market and from the loanable funds market.

We discussed shifting factors for IS.

• We constructed the LM curve from the money market and discussed shifting factors for LM.

• Finally, we set IS=LM to achieve equilibrium in all markets giving us short run

equilibrium r and Y.