Chapter 6
The Keynesian System(II)
The IS—LM curves
The Keynesian money demand function
Remember that interest rates were determined in the classical model in the loanable funds
market. This market not only determined the interest rate but household savings and by
implication household consumption. This clearly will not do in the Keynesian view
where income chiefly determined consumption and then savings. First consider Keynes
view of the demand for money.
In the classical model people only held money because it was useful to have in making
purchases(as opposed to barter or selling bonds every time you wanted something). If
one held more money than needed for those purchases one lost interest payments. Hence
households would not hold any money in excess of that needed for typical payments.
Remember the relationship between bond prices and interest rates? If interest rates
increase then bond prices decrease. Suppose bond prices were very high at the moment.
Might it not make sense to sell the bonds, hold on to the proceeds and wait for the prices
to fall again. In other words buy low and sell high. In the simple Keynesian model of
money demand people will hold onto the money for selling the bonds because Keynes
does not allow them any alternative –it’s bonds or money. So if you sell a bond you hold
on to the money until bond prices fall. Then you buy bonds anew when the prices fall.
Bond prices high
Interest rates low
Sell bonds
Bond prices low
Interest rates high
Buy bond
Take capital gain,
hold money, wait for
bond prices to fall
Get rid of money,
buy bonds
Money demand
high
Money demand
low
The Keynesian money demand function is
M d  M 0  M yY  M r r
where
M yY is called the transactions demand for money
M r r is called the speculative demand for money
M 0 is autonomous money demand (precautionary demand is part of this)
Note that the transaction demand for money term is similar to the Cambridge equation
M d  kPy  M yY  M y Py
and has the same meaning—this is the amount of money that households keep on hand to
facilitate regularly occurring purchases. The speculative demand for money represents
the amount of money household keep on hand waiting for bond prices to fall (Keynes got
rich do this and thought it to be fairly common practice). The precautionary demand for
money represents money kept on hand for emergencies.
The coefficients of the money demand function should have the following signs: (a) M y
will be positive so that an increase in Y will cause household to hold more money for
transactions (they buy more things as Y goes up) and (b) M r is negative (if interest rates
go up, bond prices go down and people will want to buy bonds).
Another way of looking at this is to say the classical economists believe people used
money mostly as a medium of exchange (the use it to facilitate regularly occurring
purchases). Keynes believed they used is both as a medium of exchange and as a store of
wealth (holding the wealth in the form of money until bond prices fall).
Figure 6—1 shows the Keynesian money demand function for a fixed level of income. In
this figure the amount of money households decide to hold will be represented by the
Money axis. Interest rates are on the vertical axis. At interest rate r1 households decide
to hold M 1 of their assets as money. As the interest rate falls to r2 bond prices rise, so
some households will decide to sell their bonds and hold on to that money until bond
prices fall. M 2 is the new, larger amount of money they desire to hold. To show the
effect of an increase in is the new, larger amount of money they desire to hold. To show
the effect of an increase in Y we use the same graph but hold interest rates fixed. Such an
increase is shown in Figure 6—2. As income increases households desired money
holdings increase from M1 to M 2 .
We will assume that the central bank (the Federal Reserve Bank in the U.S.) can control
the money supply completely. This is shown as the vertical line in Figure 6—3 labeled
M s . The equilibrium rate of interest is determined in the money market by the supply
and demand for money. Suppose the money market was not in equilibrium but that
somehow interest rates were at r2 in Figure 6—3. In that case M d  M s at that interest
rate. Household want more money. They sell bonds. This decreases bond prices and
raises interest rates until M d  M s . At an interest rate higher than the equilibrium rate
money supply would exceed money demand (household have more money than they
want, so they buy bonds reducing interest rates).
Figure 6—1. They Keynesian demand for money funtion
Figure 6—2. An increase in household income shifts the money demand function to the
right.
Figure 6—3 Equilibrium in the money market.
So we can now determine how interest rates are changed in the Keynesian model.
Suppose that the money market is in equilibrium at interest rate r1 when the money
supply is at M 1s as shown in Figure 6—4. Suppose that the central bank increases the
money supply to M 2s as shown in Figure 6—4. The central bank increases the money
supply by buying bonds  P B  r   . So the effect of the money supply increase is to
lower the interest rate. If the central bank sell bonds, bond supply increases, bond prices
decrease and interest rates increase. So interest rates are controlled in the Keynesian
model by the central bank not by the loanable funds market.
Figure 6—4. An increase in the money supply
The LM curve.
The LM curve is a set of points  ri , Yi  where the money market is in equilibrium. We
can generate an LM curve by taking the graph in Figure 6—4 and letting the income level
vary and noting how the interest rate changes. This situation is depicted in Figure 6—5.
Figure 6—5. The derivation of the LM curve.
Suppose the money market is initially in equilibrium at  r1 , Y1  as shown on each of the
panels in Figure 6—5. Suppose that the income level rises to income level Y2 . At this
higher level of income households will purchase more things and having money makes it
easy to purchase these things. So households attempt to get money by selling bonds.
This reduces bond prices and forces interest rates up. Of course with higher bond prices
some households will sell bonds to take capital gains. This will continue until the money
market is back in equilibrium at  r2 , Y2  . Both of these equilibrium points are shown in
the rightmost panel of Figure 6—5.
Shifts in the LM curve
A change in the money supply will shift the LM curve as shown in Figure 6—6. Suppose
the money market is in equilibrium at  r1 , Y1  as shown in the leftmost panel in Figure
6—6. Because this is an equilibrium point it is a point on an LM curve, in this case LM1
on the rightmost panel of Figure 6—6. Let the central bank increase the money supply
As shown in Figure 6—4 this will lower the rate of interest in the money market.. But
note that there has been no change in the income level. Now we have a new equilibrium
point at  r2 , Y1  . But this must have meant that the LM curve has shifted, and has shifted
down in this case. So an increase in the money supply will shift the LM down. A
decrease in the money supply would shift it up.
Figure 6—6. A change in the money supply shifts the LM curve.
An autonomous change in money demand will also shift the LM curve. This is shown in
Figure 6—7. Recall that the money demand equation is
M d  M 0  M yY  M r r
Figure 6—7. The effects of an increase in autonomous money demand
where M 0 represents autonomous money demand. If autonomous money demand
increased, households will want to hold more money even though interest rates and
income have not changed. Suppose that the money market is initially in equilibrium with
money demand represented by M d  r , Y1  and the equilibrium values given by  r, Y1  . If
the households experience an endogenous increase in money demand they want to hold
more money. This shifts the money demand curve to M d  r , Y1  . Households will sell
bonds to increase their money holdings. This lowers bond prices and raises interest rates.
Now we have, in the money market, a case where interest rates have increased but
income has remained constant. This is represented by an upward shift in the LM curve.
Note: and increase in the money supply shifts the LM curve down but an increase in
money demand shifts the LM curve up.
Investment spending in the Keynesian model.
Business investment spending in the Keynesian model is similar to that in the classical
model (there will be certain differences in emphasis). We will write the investment
spending function as
I  I0  Ir r
Ir  0
where r is the interest rate. The negative sign on I r means that investment spending will
decline if interest rates increase. We have a different graphical representation in the
Keynesian scheme – here Y rather than r is the critical variable.
Figure 6—8. The investment spending function in the Keynesian model
The Keynesian view of the investment spending function is shown in Figure 6—8. At
interest rate r1 firms spend I1 . Suppose that interest rates rise to r2 . In that case firms
will decrease spending to, say, I 2 . Because investment spending does not depend on Y
the curve is a horizontal line. Increases or decreases in investment spending are
represented by shifting the I+G curve up or down.
The IS curve.
The IS curve is a set of combinations of values Yi , ri  where the product market is in
equilibrium. The product is the market where goods and services are bought and sold.
This is distinct from the money market where financial instruments are bought and sold.
We will derive the IS curve using the I+G=S+T relationship. Suppose the product
market is initially in equilibrium at  r1 , Y1  . This is shown in the leftmost panel where
I  r1   G  S Y1   T . Suppose that interest rates increase to r2 . If so, investment
spending will decline I  r2   I  r  . This shift the I+G curve down so that a new
equilibrium is determined where I  r2   G  S Y2   T . Both equilibrium points are
shown on the rightmost panel of Figure 6—9. The curve in the right most panel is called
an IS curve.
Figure 6—9. The IS curve
Another way to look at the IS curve is by considering the Another way to look at the IS
curve is by considering the Y=AE relationship
Y1  C Y1   I  r1   G
r  I  r  
I  r2   I  r1 
Y1  C Y1   I  r2   G (more output being produced than being sold)
Y  ? C Y    I  r2   G (income and consumption both fall)
Y2  C Y2   I  r2   G (until a new equilibrium is established with higher r and lower Y)
The IS curve is a set of combinations of r and Y where the product market in in
equilibrium.
Things that shift the IS curve.
Anyhing that changes a spending component (other than r or Y) will shift the IS curve. r
and Y don’t shift the curve—they are the curve.
Figure 6—10. An increase in autonomous savings shifts the IS curve.
Consider the situation in Figure 6—10. The product market is in equilibrium with the
combination  r1 , Y1  . Suppose now that households decide to save more (an autonomous
savings increase). The autonomous increase in savings shifts the S+T curve up
( S Y1   S Y1  ). Because of the increase in savings less is now being consumed and
more is being produced than is being bought. This, as usual, will decrease employment
and household income until a new equilibrium exists at  r1 , Y2  . Because the interest rate
has no changed but income has decreased we must have a leftward shift in the IS curve.
It is interesting to note what has finally happened to savings. Households tried to save
more but have they succeeded?
S Y2   T  S Y1   T  I  r1   G
The attempt to increase savings created a decrease in income. The decrease in income
reduces savings. But in any case since S+T=I+G and since I+G haven’t changed, then S
won’t either. Autonomous savings increased but endogenous savings decreased.