The LM Curve
The LM curve, named because it shows positions at
which the demand for money (L for liquidity
preference) equals money supply (M), completes the
model. In the quantity theory of money we have already met a
model of the market for money balances. The quantity theory
asserted that velocity was constant, or
(1) MV = Y
which can be rewritten as:
(2) M= (1/V)Y = kY.
Equation 2 says that the amount of money that people hold
is a fraction of income. This equation is always true; k
will take whatever value needed to make it true. In England
in the early 19th century, this equation was altered and
made into a demand-for-money equation. The average amount of
money people want to hold depends on the amount of spending
they expect to do. Thus people who expect to spend a great
deal will, on the average, want to hold larger cash balances
than those who expect to spend only a little. The "on the
average" in the last sentence is important. If a person
holds $1400 on Monday and nothing the rest of the week, he
has an average weekly holding of $200.
Making these alterations in equation 2 gives:
(3) Money demand = k(expected income)
The k in this equation should not move much or
else the equation does not tell us much about how people
act. This equation is unlike equation 2 because it makes a
statement about how people want to act, while
equation 2 tells us how they do act.
The writings of John
Maynard Keynes made economists reconsider the
traditional demand-for-money function. Keynes argued that
there were three reasons why people hold money. They hold
cash for transactions purposes, which is what the quantity
theory had always said. They also hold money for
precautionary reasons, so that in an emergency they would
have a ready source of funds. Finally, they hold money for
speculative purposes. The speculative motive arose from the
effects of interest rates on the price of bonds. When
interest rates rise, the price of bonds falls. Thus when
people think interest rates are unusually low, they would
prefer to hold their assets in the form of money. If they
invested in bonds and the interest rate rose, they would
suffer a loss. Hence the amount of money people would want
to hold should be inversely related to the rate of interest.
People will want to hold more money (liquidity) when
interest rates are low than when they are higher.
Keynes' introduction of the interest rate into the demand
for money has survived, but not for the reasons he gave.
Keynes was thinking in terms of a two-asset world: money,
which earned no interest but which was liquid and had no
danger of a capital loss, and bonds, which earned interest
but which were not as liquid and which could yield a capital
loss. If one thinks not in terms of a two-asset world, but
in terms of the range of assets that actually exist in the
world, there is no reason to hold cash balances for either
precautionary or speculative purposes. There are assets that
are both very liquid and that earn interest, such as savings
accounts and Treasury bills, and these are a better form in
which to hold assets for these purposes.
Though Keynes' explanation of why interest rates
influence the demand for money is flawed, other explanations
are sound. Money held for transactions purposes is much like
inventory that businesses hold. Holding inventories either
ties up funds on which a business could earn interest, or
uses borrowed funds on which it must pay interest. Thus if a
firm can sell $100,000 of its inventory, it has $100,000 in
cash that it can either invest to earn interest or pay off
debt on which it must pay interest. The cost of inventories
increases as interest rates rise or as the size of
inventories increases.
However, there are also costs to holding inventories that
are too low. If inventories are too small, a business may
run out of items and lose sales. Further, if inventories are
held at low levels, the business will need to reorder often,
and there are usually costs to reordering. Thus the business
must balance these costs that rise as inventories increase
with the other costs that fall as inventories increase. The
problem can be solved elegantly using calculus, but you
should be able to see intuitively that a rise in interest
rates will decrease the optimal size of inventories, and a
rise in the cost of reordering will increase the optimal
size.
When people hold cash balances, they hold their assets in
a form that earns either no interest (coin and currency and
some deposits on which checks can be written) or less
interest than is possible in accounts on which no checks can
be written.1 If interest rates rise on non-money
assets relative to money, the cost of holding money in terms
of interest foregone rises, and one would expect people to
try to economize on cash. A business, for example, could
shift money from checking accounts into t-bills. It would be
worthwhile to make more transactions into and out of
interest-bearing assets to take advantage of the higher
interest rates. When interest rates are very low, these
transactions may not be worthwhile, and the business may be
willing to let money lie idle for short periods in checking
accounts.
In a nutshell, the argument boils down to the
store-of-value function of money. Money becomes a less
desirable way to hold wealth when interest rates on other
assets rises, and as a result people will hold smaller cash
balances. These considerations lead us to a revised demand
for money function. Instead of equation 3, the demand for
money should be:
(4) Md = kYe + wi.
The demand for money, or the average amount of money
people want to hold, depends positively on expected
transactions and negatively on the interest rate. The
coefficient w should be a negative number because
with higher interest rates people should want to hold
smaller cash balances.
To complete this part of the model, we need a
money-supply equation and an equilibrium condition. A simple
money-supply equation is that money stock is determined
outside the system by policy. The logical equilibrium
condition is that the market for money balances is in
equilibrium when money supply equals money demand.
To see how this part of the model functions, imagine that
interest rates are very low. When interest rates are very
low, people have no special reason to avoid holding idle
cash, and will hold considerable amounts. If they hold lots
of cash idle, the fixed amount of money cannot support very
much spending. Lots of idle cash means that the
representative dollar is not being spent very
frequently.
On the other hand, if interest rates are very high,
holding idle cash is costly, and people will try to keep
their holdings low. This means that they will spend money
rapidly, or that the velocity of money will be high. With
higher interest rates the same fixed quantity of money will
support more spending than it did when interest rates were
low and people were holding idle cash balances.
The LM curve illustrated below shows the relationship
discussed in the last two paragraphs. The curve tells how
much spending some fixed amount of money will support. When
interest rates are high, as at i*, money is spent rapidly
and supports a lot of spending, y*. When interest rates are
low, at i#, the money stock supports less spending or y#.
Connecting these two points to represent what happens at
other interest rates generates the LM curve.
The addition of interest rates to the quantity theory
allows fiscal policy to have effects within the logic of the
quantity theory. If, for example, the government reduces
taxes, thereby raising its deficit, it must borrow more.
This added borrowing increases the demand for loanable funds
and the price of these funds, which is the interest rate,
should rise. The higher interest rate makes holding idle
funds more expensive, and should result in an increased
velocity of money.
Next we will combine the LM curve
with the IS curve.
1 Between 1933 and the early
1970s U.S. law prohibited interest payments on any account
on which checks could be drawn. With the advent of checking
accounts that earn interest, the importance of interest
rates in determining the size of cash balances may diminish,
though it still should be important in determining in what
form--currency or checking account--money is held.
Copyright
Robert Schenk
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