Chapter 4
The classical model(II)
Classical aggregate demand curve
The quantity theory of money and the Cambridge equation
Household allocate assets between bonds and money
Assets = (bonds, money)
The household’s demand for money is how much of it’s assets to hold in the form of
money? Remember a demand curve for a consumer good is not a curve indicating how
much of the good that people want, it is a curve showing how much they will buy given
their income. A demand curve is not a want curve. Likewise the demand for money
curve is not a want curve but a description of how much they will actually hold out of
their current assets. Note that if the household wants more money all it need do is
convert a bond into money.
The classical view was that households would try to have only enough money to be able
to conveniently meet regular monthly payments (rent, utilities, food, etc). If your regular
expenses are about $1000 per month, say, it would be reasonable to have about $1000 of
assets available at the beginning of the month to meet these expenses. If more of your
assets were held in money than the amount the household needed for these expenses, the
household would be sacrificing interest income.
The classical economists believed that money demand could be modeled as
M d  kPy
where M d is money demand, k is a proportionality constand, P, the price level, and y is
real income. Note that Py is nominal income. Suppose that k=0.20 and that (monthly)
nominal income is $6000, then the households would tend to hold (0.20)(6000) = $1200
to meet monthly expenses.
Two things can cause the demand for money to increase. If the real income, y, increases
then households will tend to buy more things because they can afford them and will hold
more money as a means of paying for them. The other thing that could happen is that the
price level increases. In that case the household would be buying the same things but the
things would cost more (if nominal income increases because of price change increases
then households nominal income increases but real income does not).
Suppose that the money supply is controlled completely by the monetary authority (the
Federal Reserve Bank). We will use the symbol M s to stand for the money supply or
money stock. Then we have for the money market
M d  kPy
M s  M d when the money market is in equilibrium
M s  kPy when the money market is in equilibrium.
We can revise this equation to be
Ms
ky
which is the classical aggregate demand function. A graph of the function for
M s  100 and k  0.2 is shown in Figure 4—1. A table of values of  P, y  determined
P
by using these values of M s and y is shown in Table 1—1. This indicates the as the price
level declines household would purchase more goods. (Note that there is a difference
between demand in the macro sense and demand in the micro sense. In microeconomics
consumers responded to relative prices. A decline in the price of one good meant that
consumers usually buy more of that good and less of some other good (unless we are
dealing with a Giffin good). So what consumers were pictured as doing in micro is
comparing prices of different goods –hence the relative price term. In macro we do not
distinguish between goods. The price level is an overall price level. Implicitly we
assume that relative prices don’t change.)
P
50
10
1
Y
10
50
100
Table 1—1. The aggregate supply curve for M s  100 and k  0.2 .
Figure 4—1. The classical aggregate demand function. (using data in Table 1—1.)
Figure 4—2. Aggregate supply and aggregate demand together determine the price level
in the classical model.
Figure 4—3 The effect of an increase in the money supply in the classical model.
The intersection of the aggregate supply curve and the aggregate demand curve determine
the price level in the classical model as shown in Figure 4—2. An increase in the money
supply (from M 1s to M 2s in Figure 4—3) will increase the price level ( P1 to P2 in Figure
4—3).
Now look at the aggregate demand curve again
Ms
P
ky
where now we have written y to indicate that output is fixed in the classical model. This
equation indicates the an increase in the money supply will increase the price level also.
In fact this equation says that doubling the money supply will double the price level.
Now let’s consider why this may be true. Suppose that the central bank decides to
increase the money supply by purchasing bonds in the bond market. Households now
have bonds rather than money. But now they are holding more money than they need to
meet ordinary expenses. How can the household get rid of the money? By (a) buying
bonds or (b) buying things. But they just sold a bond so why buy a new one? If they buy
things that will drive up the price of things (the number of things that are produced are
fixed remember). As you will see in the next section, this purchase of bonds will tend to
raise bond prices and lower market interest rates. This will encourage firms to sell bonds
to finance the purchase of capital equipment. But this will tend to raise the price of
capital equipment. Using this sort of reasoning the classical economists believed that an
increase in the money supply would lead to increases in the price level. Using the
Cambridge equation they would assert that an increase in the money supply will lead to a
proportional increase in the price level.
The loanable funds market.
The previous chapter showed how output was determined in the classical model. The
bulk of this chapter is devoted to showing how that output is distributed.
I suspect in your principles courses you assumed that household consumption was
determined by household income. One might say that the household decides how much
to consume (determined by household income) out of its income and household saving
was whatever was left over.
In the classical model, the household decides how much to save (determined by interest
rates) out of its income and consumption is whatever is left over.


Keynes model –consumption is paramount, determined by income, savings is a
residual
Classical model—savings is paramount, determined by interest rates,
consumption is a residual
The demand for loanable funds
Firms borrow money by selling bonds in a market called the loanable funds market.
Households buy bonds in this market. The government also sells bonds in this market to
finance deficit spending. To keep life simple we will assume that a bond has no maturity
date, but pays interest forever (such an instrument is called a consul).
Figure 4-4. A consul.
A representative consul is shown in Figure 4-4. The 5% is called the coupon rate and the $5000
is called the par value. The two of these determine how much you will receive if you purchase
the instrument. If you buy this thing, you will receive coupon rate times the par value or
0.05*$5000 = $250 each year that you own the bond. If you own a bond, you can either hold it or
you can sell it if you choose. You might buy a bond directly from the company (when it issues a
new bond) or you might buy an existing bond from someone else in the household sector. It can
even be the case that the government might own some bonds it wishes to sell. Anyone that owns
existing bonds can sell them in the loanable funds market and anyone that wants to buy one can
do so if he is willing to pay the market price for the bond.
It is usually more convenient to talk in terms of interest rates rather than bond prices. The
problem with talking about bond prices is that the par value statements vary from bond to bond.
Market interest rates do not. Suppose that someone paid $2500 for the bond shown in Figure 4-1.
In that case the interest rate the bond would earn is $250/2500 = 10%. So if the market rate of
interest is 10% that bond will sell for $2500. If the market rate of interest is 20% the bond will
sell for $1250. If the market rate of interest is 5% it will sell for $5000.
Bond prices are inversely related to the market rate of interest. If the
market rate of interest increases then the owners of bonds will receive less
for them if they sell them.
P B  r  and P B  r 
B
where P represents bond prices and r market interest rates.
Household savings.
The classical economists believed that households would save more as interest rates increased.
Households trade off current consumption for future consumption. If the interest rate increases
households will be able to consume more in the future by giving up a certain amount of current
consumption. The greater the interest rate increase the more valuable future consumption
becomes and the greater the reduction in current consumption (or equivalently the greater the
increase in current savings). Figure 4—4 shows the classical savings function.
Figure 4-5. The classical savings function
Business investment spending
From the firm’s point of view, a higher interest rate raises the cost of doing business. Suppose
that the firm considers funding a number of projects such as those shown in Table 4-2..Assume
that each of these projects will return a stream of income given in the table and that this stream
will last forever (this is a simplifying assumption much like the consul–in each case we can
ignore the effects of time). The rate of return of each of the income streams is shown in the last
column. If the value of the income stream exceeds the cost of borrowing the project will be
profitable. The firm will maximize profits if it funds each project that is individually profitable.
If the market rate of interest is 7.5%, the firm will find it profitable to borrow $10000+$2000 and
fund Projects A and B. If the interest rate falls to 6.5% the firm should fund A, B and C by
borrowing $10000+$2000+$5000. We call the firms’ purchase plant and equipment (the Cost in
the table) business investment spending (investment for short) of We conclude from this that
firms will borrow more as interest rates decline, or saying it another way, investment will
increase as interest rates decline. This is represented in Figure 4—6
Project
Cost
Profits per year Rate of return
A
$10000
$1000
0.10
B
2000
$160
0.08
C
5000
$350
0.07
D
20000
$1200
0.06
E
10000
$500
0.05
Table 4-2. A list of projects a firm is considering funding.
Figure 4-6. Investment--the demand for loanable funds
The loanable funds market
Putting the two together give the loanable funds market shown in Figure 4—7. This market
determines the amount borrowed and lent at the market equilibrium interest rate r1 .
Figure 4—7. The loanable funds market.
Figure 4—8. The effects of an exogenous change in household savings.
The effects of a change in household savings is shown in Figure 4—8. Suppose initially the
market is in equilibrium at  r1 , y1  with savings equal to investment at s1  i1 . Now let us
suppose that households decide to save more at interest rate r1 . (This is a exogenous change in
household savings. In other words a change in the amount of savings by household caused by
something other than a change in interest rates. Households do change the amount they decide
to save if interest rates change; we refer to this as an endogenous change. Any change in savings
other than interest rates are exogenous changes) We represent this with a shift in the savings
curve.
We do not ask households might want to save more, the reason is not important—the effects will
be the same regardless of the reason. We represent the increase in savings by shifting the supply
curve from s1  r  to s2  r  . This shift is done initially holding the interest rate r1 fixed
(household decide to save more even though interest rates don’t change). The change here is one
where household try to increase savings from s1 to A. Households increase savings by buying
more bonds. This increases bond prices which is the same as an interest rate decrease (the interest
rate falls to r2 .. At the lover interest rate (higher bond price) saving becomes less attractive and
households save an amount smaller than A ( s2  A ). So an increase in savings will lower interest
rates.
Figure 4—9 The effects of an exogenous change in investment.
Figure 4—9 shows the effects of an exogenous change in investment spending on the loanable
funds market. As usually the initial conditions are that the market is in equilibrium where savings
and investment are equal s1  i1 at r1 . For some reason investors now decide to save more even
though there has been no change in interest rates (perhaps some new profitable projects appear).
Suppose they wish to increase investment spending from i1 to A . To fund this new investment
they must issue new bonds (they supply of bonds increases). The increase in investment spending
is represented by a rightward shift in the investment spending curve from i1  r  to i2  r  . This
drives bonds prices down (interest rates up). This means that firms can’t get as much for bonds
as they had hoped, so some of the new profitable projects are no longer profitable. Firms reduce
they spending plans from A to s2 .
The government sector
The government is also active in the loanable funds market. The government has three ways to
finance a deficit (a) by borrowing in the loanable funds market, (b) by printing money, and (c) by
selling government property. We will deal with (a) here. We will not bother considering (c)
ever.
Let g represent government spending and t the amount of taxes the government collects; then
 g  t  is the size of the deficit. If the government does not wish to print money or sell
something it must borrow the money—and it will borrow the money regardless of the rate of
interest. Suppose that i1  r  represents private borrowing in the loanable funds market. Total
borrowing is i1  r    g  t  . The government sector adds a constant amount  g  t  to
borrowing in the market. The total borrowing curve is shown in Figure 4—10.
Figure 4—10. Government in the loanable funds market.
Figure 4—11. The effects of an increase in government spending in the classical model
( g 2  g1 )
Using the loanable funds market we can see what the classical economists predicted about an
increase in government spending. An increase in government spending ( g increases from g1 to
g 2 ) is shown in Figure 4-11 by a shift in the borrowing curve from i  r    g1  t1  to
i  r    g2  t1  . This suggests that the increase in deficit spending by the government will
increase interest rates. Let’s see if that makes sense. The government finances the deficit by
selling bonds in the loanable funds market. The increase in the supply of bonds will lower bond
prices. Remember lower bond prices means higher interest rates.
Now consider what happens to savings, consumption, and investment in this case. Recall that
household income is fixed at y . Now households receive income, pay taxes, decide how much
to save, and then consume what is left. Stated mathematically (using a level of taxes t1 in Figure
4-11).
c  y  s  t1 .
Household savings will increase because the interest rates have increased. So
consumption must decrease
c  y  s  t1 .
Businesses will purchase less output as well. Interest rates have increased so investment
spending will decrease as well. Looking at the GDP accounting framework from the
spending side
y  c  i   g  .
In other words the government spending increase must just be offset by consumer and
business spending decreases. Remember income and output y is fixed by labor market
conditions, so a spending increase in one sector of the economy must be offset by
spending decreases elsewhere.
Figure 4—12. The effects of an increase in taxes on the loanable funds market
t2  t1  .
Suppose that the government decided to reduce deficit spending by funding government spending
by increasing taxes and reduce borrowing. In this case the supply of bonds decreases (the
government will not be issuing as many of them), bond prices increase and market interest rates
decrease. If interest rates decrease households will want to decrease savings which is probably
just as well because they will have to pay more taxes. However, households will likely reduce
consumption as well. The lower interest rate will increase investment spending and looking at the
spending components of the economy consumption must decrease.
y  c  i   g .
Looking at the income side we note that consumption decreased for the reason stated immediately
above. Also savings will decrease because of the decrease in the interest rate.
y  c   s  t  .
Lump sum taxes vs marginal taxes
We have been talking about lump sum taxes up to now. A lump sum tax is one that is
levied on some unit such as a household. Every household would pay the same amount
of tax regardless of income, wealth or any other consideration. Using lump sum taxes in
economic models generally avoid some messiness caused by marginal taxes. Marginal
taxes probably do have an effect on the economy and in the classical model it plays out in
the supply side. Note that the lump sum tax does not have any effect on the labor supply
decision. Households pay the same amount regardless of how much they work.
Marginal taxes should have an effect on the labor supply decision. Suppose the marginal
tax rate is  , then the tax the worker pays is.
 W
t   income    N 
 P
Note the tax the worker pays depends on how much work he provides. So household
income is
W
N
P

W 
   N   or

P
W 
N 1     
P
This last equation shows that an increase in the marginal tax rate acts just like a decrease
in the real wage rate. What do workers do in the classical model when wages decline?
Supply less labor is what they do.
Figure 4—14. The introduction of a marginal tax rate shifts the labor supply curve to the
left.
The effects of a marginal tax rate is shown in Figure 4—14. If someone works 24 hours
W 
then the income earned is 24 1      . If the marginal tax rate is zero (   0 ) then
P
W 
earnings are 24   . So the budget constraint line rotates down just like a decrease in
P
W 
the real wage would. Note that the wage paid   does not change. So we represent
P
the effects of the increase in the tax rate by shifting the labor supply curve back. Note
that the firms hiring decision is not affected if the real wage rate does not change.
Figure 4—15. A increase in the marginal tax rate.
Figure 4—15 shows that the imposition of a marginal tax should shift the labor supply
curve to the left, reducing the amount of labor supplied by workers, and hence reducing
output in the economy. The final effect of this is to shift the aggregate supply curve to
the left as shown in Figure 4—16.
Figure 4—16. The marginal tax rate shifts the aggregate supply curve to the left.