4. Money market equilibrium: the LM curve

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

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) The functions of money (cont.) 2. Unit of account

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-of-

exchange 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

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)

B) 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. M3=M2 + institucional MMMF + large saving deposits+ eurodollars

I. What Is Money? (cont.)

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 accountF = 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)


N = 1PY

Money holdings

Time1

Average = PY/ 2

Money holdings with one trip to the bank


Money holdings

Time11/2

Average = PY/ 4

PY/ 2

PY

N = 2

Money holdings with two trips to the bank


Average = PY/ 6

1/3 2/3

Money holdings

Time1

PY/ 3

PY

N = 3

Money holdings with three trips to the bank


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


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:

dTC/dN = - (iPY/2N²) + P F = 0

Solve for the cost-minimizing N*


N

Cost

Foregone interest =iPY/2N Cost of trips = PFN

Total cost

N*

Finding the cost-minimizing N


The money demand function The cost-minimizing value of N :

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.


The Baumol-Tobin real money demand function:

B-T nominal money demand implies:price elasticity =1.0income elasticity = 0.5, interest rate elasticity = 0.5Resembles LM curve, positive relationship

between Y and i to clear money market

II. The demand for money: the Baumol-Tobin modelSummary 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:

Md/P = kY 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 (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

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.) 1. 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

2. With all the other variables determined, the money market equilibrium condition determines the price level 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 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 4. 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 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

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

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4. Money market equilibrium: the LM curve