4' Money market equilibrium: the LM curve

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4. Money market equilibrium the LM curve

• Abel, Bernanke and Croushore
• (chapters 7 and 9.3)

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I. What Is Money? (Sec. 7.1)

• A) The functions of money
• 1. Medium of exchange
• a. Barter is inefficientit 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 dont have to
  produce their own food, clothing, and shelter

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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 dont 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 1930s)

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I. What Is Money? (cont.)

• B) Measuring moneythe monetary aggregates and
  the Money Supply
• 1. Distinguishing what is money from what isnt
  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. Theres no single best measure of the money
  stock
• 2. The M1 monetary aggregate. Narrow definition
  for Money Supply.
• a. Consists of currency and travelers 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.
• M3M2 institucional MMMF large saving
  deposits eurodollars

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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 consumers wage is
  12/hour, then F 3)

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II. The demand for money the Baumol-Tobin model

• N 1

Average PY/ 2
Money holdings with one trip to the bank
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II. The demand for money the Baumol-Tobin model
N 2
PY
PY/ 2
Average PY/ 4
Money holdings with two trips to the bank
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II. The demand for money the Baumol-Tobin model
N 3
PY
Average PY/ 6
PY/ 3
Money holdings with three trips to the bank
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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
• dTC/dN - (iPY/2N²) P F 0

• Solve for the cost-minimizing N

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II. The demand for money the Baumol-Tobin model
Finding the cost-minimizing N
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II. The demand for money the Baumol-Tobin model

• 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.

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II. The demand for money the Baumol-Tobin model

• The Baumol-Tobin real money demand function

• 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

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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

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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 VPY/ 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
  velocitys decline in the early 1980s
• d. M2 velocity is closer to being a constant, but
  not over short periods

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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, rpe)
• 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

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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

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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 isnt 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

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III. The LM curve (cont.)
Positive relationship between output (Y) and the
expected real interest rate (r) to restore the
money market equilibrium
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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

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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
• ?P/P ?M/M ?L/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

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Figure 7.3 The relationship between money
growth and inflation (1995-2001)
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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

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IV. Factors that shift the LM curve (cont.)

• Example 1. An increase in the money supply

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IV. Factors that shift the LM curve (cont.)

• Example 2. An increase in the money demand