Download I. What Is Money?

4. Money market
equilibrium: the LM curve
Abel, Bernanke and Croushore
(chapters 7 and 9.3)
I. What Is Money? (Sec. 7.1)
 A) The functions of money
 1. Medium of exchange
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a. Barter is inefficient—it requires a double
coincidence of wants
b. Money allows people to trade their labor for
money, then use the money to buy goods and
services in separate transactions
c. Money thus permits people to trade with less
cost in time and effort
d. Money also allows specialization, since trading
is much easier, so people don’t have to produce
their own food, clothing, and shelter
I. What Is Money? (cont.)
 A)
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The functions of money (cont.)
2. Unit of account
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a. Money is the basic unit for measuring economic value
b. This simplifies comparisons of prices, wages, and incomes
c. The unit-of-account function is closely linked with the medium-ofexchange function
d. But countries with very high inflation may use a different unit of
account, so they don’t have to constantly change prices
3. Store of value
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a. Money can be used to hold wealth
b. Most people use money only as a store of value for a short
period and for small amounts, because it earns less interest than
money in the bank
Discuss what happens in an hyperinflation episode (for example,
Germany in the 1930’s)
I. What Is Money? (cont.)
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B)
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Measuring money—the monetary aggregates and the Money Supply
1.Distinguishing what is money from what isn’t money is sometimes difficult
 a. For example, bank deposits may be transformed into cashed with
some cost , but give a higher return than bank checking accounts: Are
they money?
 b. There’s no single best measure of the money stock
2.The M1 monetary aggregate. Narrow definition for Money Supply.
 a. Consists of currency and traveler’s checks held by the public, and
checking account balances (which pay no interest)
 b. All components of M1 are used in making payments, so M1 is the
closest money measure to our theoretical description of money
3. The M2 monetary aggregate. Broad definition for Money Supply.
 a. M2 = M1 + less moneylike assets
 b. Additional assets in M2 include small savings deposits, and balances
from noninstitutional monetary market funds (MMMF) (MMDA)
 (1) Savings deposits bear interest and have a fixed term
(substantial penalty for early withdrawal). Quasi-money (liguidity
cost and pay interest).
 (2) MMMFs invest in the secondary market for very short-term
securities (for example, government bonds). Quasi-money
(liguidity cost and pay interest).
4. The M3 monetary aggregate.
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M3=M2 + institucional MMMF + large saving deposits+ eurodollars
II. The demand for money: the Baumol-Tobin model
 A transactions theory of money demand
 notation:
PY = total nominal spending, done gradually over
the year
i = nominal interest rate on savings account
N = number of trips consumer makes to the bank
to withdraw money from savings account
F = cost of a trip to the bank
(e.g., if a trip takes 15 minutes and
consumer’s wage is €12/hour, then F = €3)
II. The demand for money: the Baumol-Tobin
model
Money
holdings
PY
N=1
Average
= PY/ 2
1
Money holdings with one trip to the bank
Time
II. The demand for money: the Baumol-Tobin
model
Money
holdings
N=2
PY
PY/ 2
Average
= PY/ 4
1/2
Money holdings with two trips to the bank
1
Time
II. The demand for money: the Baumol-Tobin
model
Money
holdings
N=3
PY
Average
= PY/ 6
PY/ 3
1/3
Money holdings with three trips to the bank
2/3
1
Time
II. The demand for money: the Baumol-Tobin
model
 The cost of holding money
 In general, average money holdings = PY/2N
 Foregone interest = i (PY/2N )
 Cost of N trips to bank = P  F N
 Thus,
Total cost= i (PY/2N ) + P  F N
 Given P,Y, i, and F,
consumer chooses N to minimize total cost
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II. The demand for money: the Baumol-Tobin
model
 Finding the cost-minimizing N:
Total cost= i (PY/2N ) + P  F N
 Take the derivative of total cost with respect to
N, set it equal to zero:
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dTC/dN = - (iPY/2N²) + P F = 0
Solve for the cost-minimizing N*
II. The demand for money: the Baumol-Tobin
model
Cost
Foregone interest =
iPY/2N
Cost of trips = PFN
Total cost
N*
Finding the cost-minimizing N
N
II. The demand for money: the Baumol-Tobin
model
 The money demand function
 The cost-minimizing value of N :
iY
N 
2F
 To obtain the money demand function,
plug N* into the expression for average real
money holdings, M/P =PY/2N
 Average real Money
 M/P= (PY/2N*)/P= Y/2N*
 M/P= Y/(2(iY/2F)^0.5)=(YF/2i)^0.5
*
 Money demand depends positively on P, Y and
F, and negatively on i.
II. The demand for money: the Baumol-Tobin
model
 The Baumol-Tobin real money demand function:
d
(M / P )
=
YF
2i
 L (i ,Y , F )
 B-T nominal money demand implies:
price elasticity =1.0
income elasticity = 0.5,
interest rate elasticity = 0.5
Resembles LM curve, positive relationship
between Y and i to clear money market
II. The demand for money: the Baumol-Tobin
model
Summary of the Baumol-Tobin model
 a transactions theory of money demand,
stresses “medium of exchange” function
 Real money demand (Md/P) depends positively on
spending (Y), negatively on the nominal interest
rate (i),
and positively on the cost of converting
non-monetary assets to money (F)
 Microfoundation for the LM curve
slide 14
II. The demand for money: the Baumol-Tobin
model
 Alternative model. Quantity theory of money: Real money
demand is proportional to real income
 a. Money velocity definition V=PY/ M,
 b. Assuming constant velocity and money market
equilibrium, we obtain this money demand formulation in the
Quantity theory of money:
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where k = 1/V
c. But velocity of M1 is not constant; it rose steadily from
1960 to 1980 and has been erratic since then
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Md/P = kY
(1) Part of the change in velocity is due to changes in interest
rates in the 1980s
(2) Financial innovations also played a role in velocity’s decline
in the early 1980s
d. M2 velocity is closer to being a constant, but not over
short periods
III. The LM curve
 LM curve represents the money market equilibrium
 If the economy is on some point that belongs to the LM curve
the amount of money demanded is equal to the amount of
money supplied, Md = Ms
 Md is decided by the private sector (households) as in the BT
model.
 Md = P L(Y, i) where the L money demand function depends
positively on Y and negatively on i
 Md = P L(Y, r+πe)
 Ms is decided by the central bank
 Open market operations
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Open market purchase to increase Ms (monetary expansion)
Open market sale to decrease Ms (monetary contraction)
Ms as a monetary policy instrument
III. The LM curve (cont.)
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Ms /P = L(Y, r + e) real money supply = real money demand
a. Ms is determined by the central bank
b. e is fixed
c. The labor market determines the level of employment; using
employment in the production function determines Y
d. Given Y, the goods market equilibrium condition determines r
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With all the other variables determined, the money market
equilibrium condition determines the price level
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a. P = M/L(Y, r + e)
b. The price level is the ratio of nominal money supply to real
money demand
c. For example, doubling the money supply would double the
price level
III. The LM curve (cont.)
 3. Equilibrium in the money market requires that the
real money supply equal the real quantity of money
demanded
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 4.
a. Real money supply is determined by the central
bank and isn’t affect by the real interest rate
b. Real money demand falls as the real interest rate
rises
c. Real money demand rises as the level of output
rises
The LM curve (Figure 9.4) is derived by plotting
real money demand for different levels of output and
looking at the resulting equilibrium
III. The LM curve (cont.)
Positive relationship between output (Y) and the expected real interest
rate (r) to restore the money market equilibrium
III. The LM curve (cont.)
 5. The LM curve shows the combinations of
the real interest rate and output that clear the
money market
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a. Intuitively, for any given level of output, the
LM curve shows the real interest rate
necessary to equate real money demand and
supply
b. Thus the LM curve slopes upward from left
to right
Money growth and inflation
 The inflation rate is closely related to the growth rate
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of the money supply. High-inflation countries often
have rapid money growth
Rewrite LM curve as:
ΔP/P = ΔM/M – ΔL/L
If money market is in equilibrium, the inflation rate
equals the growth rate of the nominal money supply
minus the growth rate of real money demand
Discuss inflation targeting as a central-bank strategy
for monetary policy
Figure 7.3 The relationship between money growth
and inflation (1995-2001)
IV. Factors that shift the LM curve
 a. The LM curve shifts to the right because of
 (1) an increase in the nominal money supply
 (2) a decrease in the price level
 (3) an increase in expected inflation
 (4) a decrease in the nominal interest rate on money
 (5) a decrease in wealth
 (6) an increase in the efficiency of payment
technologies (lower F in the BT model)
 b. The LM curve shifts to the left when the opposite
happens to the six factors listed above
IV. Factors that shift the LM curve (cont.)
 Example 1. An increase in the money supply
IV. Factors that shift the LM curve (cont.)
 Example 2. An increase in the money
demand