# Money Demand and the LM Curve This lecture will

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```							                              Money Demand and the LM Curve

This lecture will develop the money demand and LM curves. Students should read Chapter 7
in Froyen.

Factors that Affect Money Demand

Money is not an interest bearing asset (though some checking accounts do pay a low level of
interest). Interest bearing (which I deﬁne to include any asset that is expected to yield a positive
nominal return) assets include stocks, bonds, derivatives, options, etc. Households must decide
how much of their assets to hold in money, and how much to hold as interest bearing assets.

We also need to make an important distinction between nominal and real money balances. Nominal
money balances, M, refers to the face value of all currency and checkable deposits in the economy.
If there is 10 billion dollars in currency, and 90 billion dollars in checkable deposits, M= 100
billion dollars. Real money balances equal M/P. Dividing by the price level gives us a measure of
the purchasing power of the money stock.

Suppose that inﬂation causes the price level to double. If a household holds 10 dollars in currency,
the nominal value of its money stock does not change. The purchasing power of its money stock,
captured by its real value, is cut in half. Dividing by the price level is a common method of
converting a nominal variable into a real variable. This course will use this technique many times.

The model considers three factors that affect money demand:

1. The Transactional Demand for Money: Recall that money acts as a medium of exchange that
makes it more convenient to conduct transactions. If a household were to hold all of its wealth
in interest bearing assets, it would have to endure transactional costs (both ﬁnancial and time)
to liquidate an asset every time it wanted to make a simple purchase. The more transactions a
household needs to conduct, the greater its demand for money.

As national income (Y) increases, so does the number of transactions that the average household
conducts. Aggregate money demand is therefore an increasing function of Y.

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2. The Speculative Demand for Money: Money demand also depends on the nominal interest rate.
The nominal interest rate represents the opportunity cost of holding money instead of an interest
bearing asset. As the nominal interest rate rises, households will demand less money. Because
money only has an opportunity cost, r appears on the vertical axis in the graph of the supply and
demand for money.
Suppose that a household can either hold 100 dollars in money for a year, or can invest it for a
year. If the interest rate is 5 percent, the household would receive 105 dollars at the end of the year,
a return of 5 dollars. Now suppose that the interest rate is 10 percent instead. The household would
forgo 10 dollars instead of 5 dollars if it chooses to hold money. When the interest rate increases,
fewer households will choose to hold money and money demand will decrease.

Graph (nominal interest rate on vertical axis, money demand on horizontal, constant Y)

- If Y increases, then households will demand more money for any interest rate. The money
demand curve therefore shifts to the right when Y increases.

3. The Precautionary Demand for Money: Households do not know in advance exactly how many
transactions they will conduct each period. The model therefore assumes that they hold some extra
money in case their actual transactions exceeds their expectations. Like the transactional demand

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for money, the precautionary demand for money is an increasing function of Y.

To summarize:

M d = L(Y, r)    where     ∂L/∂Y > 0      and    ∂L/∂r < 0

The LM Relationship/Curve

Recall that the IS curve represents all combinations of Y and r where the goods market is in equi-
librium. The LM curve is all combinations of Y and r where the money market is in equilibrium.
The equilibrium condition is that money demand equals the real money supply, the latter being
chosen (exogenously) by the Fed:

L(Y, r) = M/P

To obtain the LM curve, change r and plot the change in Y. As an exogenous variable, the real
money supply (M/P) is held constant.

Graph 1: Supply and Demand for Real Money (graph on right)
Graph 2: Interest Rate/ Output Space (graph on left)

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-Initially, the interest rate is r0 , and output is Y0 . We can plot this point in interest rate/output space.

-Now suppose that output increases to Y1 > Y0 . This will increase the transactional demand for
money and shift money demand to the right. The new equilibrium in the money market has a
higher value of r, and a higher value of Y. We can also plot this point in interest rate/output space.

-If we continue to change Y, we will trace out an upward sloping relationship between interest rates
and output. This is the LM curve. The LM curve represents all the possible combinations of Y and
r where money supply equals money demand.

-Intuition: Real money supply is ﬁxed. Money demand must equal money supply in equilibrium,
so money demand must stay the same as well. An increase in output increases money demand. The
only way to offset this increase this increase in money demand is for interest rates to rise, reducing
money demand.

Shifting the LM curve:

Suppose that the real money supply, M/P, increases (either M rises or P falls). Lets Consider what
must happen to Y if we hold r constant.

Graph 1: Supply and Demand for Real Money (graph on right)
Graph 2: Interest Rate/ Output Space (graph on left)

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-When money supply increases, money demand must increase as well. One way for this to happen
is for Y to increase. For each value of r, it takes a higher level of output for money supply to equal
money demand. The LM curve shifts to the right.

-Alternatively, r may fall so that money demand rises to meet the increase in money supply. For
each value of Y, it takes a lower interest rate for money supply to equal money demand. The LM
curve shifts down.

-The previous two statements are equivalent.

-Increases in the real money supply shift the LM curve to the right. Changes in output or the
interest rate move the economy along the LM curve.

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