4' Money and Inflation

1
4. Money and Inflation

• Agenda
• What is money?
• How much do people want to hold money?
• What kinds of relation do we have between real
  interest rate and nominal interest rate?
• If we assume the cost of holding money, how much
  do people want to hold money?
• What are classical dichotomy and monetary
  neutrality?

2
What is Money?
1. Without money, double coincident of wants is
needed for transactions.
4. Velocity of money Real money balances Output
Y 3 Assume the prices P 1 If M1,
V3 times, M/P1 If M3, V1 times,
M/P3
3
What is Money?

• In economics, money means the stock of assets
  that can be readily used to make transactions
• The Functions of Money
• Store of value
• Unit of account
• Medium of exchange
• Liquidity the ease with which money is converted
  into other things --- goods and services.
• Without money, trade requires the double
  coincidence of wants
• It is unlikely that two people, each having a
  good that the other wants, make an exchange at
  right time and place.

4
The Type of Money

• Fiat money
• No intrinsic value
• It is established as money by government
  declaration
• Commodity money
• Intrinsic value
• Gold is the most widespread example (gold
  standard)
• Historically speaking, commodity money had
  been replaced by fiat money because fiat money
  reduces transaction costs.

5
How the Quantity of Money Is Controlled

• Money supply
• The quantity of money available in an economy
• Monetary policy
• The money supply is controlled by central banks
• Central banks usually keep independence of the
  governments.
• Open market operation
• The central banks buys sells the government
  bonds in order to increase decrease the money
  supply

6
The Measures of Money

• M2 and M1 are popular, but there is no
  consensus about which measure is the best.

7
The Quantity Equation

• The quantity equation is an identity
• Money ? Velocity Price ? Output
• MV PY
• Y Output (real GDP)
• P Price level (GDP deflator, PY is nominal GDP)
• M money supply
• V income velocity of money
• V shows how many times the money (M) is used for
  transactions in a year. The number of
  transactions of goods and services is difficult
  to measure. Roughly speaking, output is
  proportion to transactions. Thus, output is used
  instead of the number of transactions.
• The quantity equation is an identity that defines
  V.

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The Money Demand Function

• Real money balances (M/P)
• The purchasing power of the stock of money in
  an economy.
• Money demand function
• What determines the quantity of real money
  balances people wish to hold?
• Let us focus on its role as a medium of
  exchange.
• It is plausible that the demand for real
  money balances depends on the output. Simply
  suppose that the demand is proportionate to the
  output, then
• (M/P)d kY
• (k is a constant that tells how much money
  people want to hold for each unit of income)

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Interpretation of the Quantity Equation

• The money demand function is like the demand
  function for a particular good. Here the good
  is the convenience of holding real money
  balances.
• At the equilibrium of the money market, the
  supply of the real money balance (M/P) equals the
  demand (M/P)d
• M/P (M/P)d kY
• This gives another way of view the quantity
  equation. Simply rearrange this equation, we get
• M(1/k) PY
• MV PY (where V 1/k)
• So, when people want to hold a lot of money
  for each unit of income (k is large), money
  changes hands infrequently (V is small)

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Quantity Theory of Money

• The quantity equation is an identity, but if we
  add the assumption of constant velocity, it
  becomes the quantity theory of money.

• If the velocity is constant, then the nominal GDP
  (PY) is proportionate to the money supply (M).
  Note that this assumption implies that we assume
  the simplest money demand function M/P kY (k
  is constant)

• Recall that the output is decided by the
  production function and the amount of labor and
  capital.

• The price level is only decided by the money
  supply.
• ? Central banks can control the price level, so
  inflation.

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Inflation and Money Growth

• Mathematics tells that if MV PY, then
• change in M change in V change in P
  change in Y
• Money supply growth (assume zero) Inflation
  rate (assume zero)

International data on Inflation and Money Growth
during 1990s
Positive correlation
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Inflation and Interest Rates

• (1) If we borrow 100 oranges this year, then we
  have to pay 100 oranges as principal and r
  oranges as interest next year.

(2) The orange price changes p 1 ? (1p/100).

(3) Then, how many dollars we have to pay next
year?
100i (1p/100)(100r) 100prpr/100
pr/100 is negligible. 100pr
? i rp

1 oranges1
1 oranges(1p/100)

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Inflation and Interest Rates

• Nominal interest rate the interest rate that the
  bank pays
• Real interest rate the interest rate measured in
  terms of the purchasing power ( adjusted by
  inflation rate)
• r i - p
• Alternatively,
• i r p
  (Fisher equation)
• r real interest rate
• i nominal interest rate
• rate of inflation (the percentage change of the
  price level P)
• The real interest rate is pre-determined so
  that it can equalize the saving and investment.
  Thus, the nominal interest rate and the inflation
  rate have an one for one relation.

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Ex Ante and Ex Post

• Ex ante the real interest rate the borrower and
  lender expect when a loan is made
• r i - pe (pe
  expected inflation rate)
• Ex post the real interest rate that is actually
  realized
• r i - p (p
  actual inflation rate)
• Because actual inflation is not known when
  the nominal interest rate is set, the nominal
  interest rate can adjust only to expected
  inflation. Thus, the Fisher effect is more
  precisely written as
• i r pe

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The Nominal Interest Rate and the Demand for Money

• Money is the asset most easily used to make
  transactions, but money does not bring returns.
• The cost of holding money
• The nominal interest rate is the opportunity
  cost of holding money it is what you give up by
  holding money rather than bonds which earn
  interest.
• The demand for real money balance decreases if
  nominal interest rate ( the cost of holding
  money) increases

(M/P)d L( i, Y)
L(rpe, Y)

• In summary, the money demand depends
• negatively on the nominal interest rate (irpe)
• positively on the output (Y)

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The Linkages Among Money, Prices and Inflation
Rates
M is given by central bank
Inflation rate change in price level
Fisher equation i r pe
Money demand function (M/P)d L(i, Y)
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The Classical Dichotomy

• Two kinds of variables
• Real variables (measured by physical units Ch.3)
• Quantities real GDP (Y), capital stock (K)
• Relative price real wage (w), real interest rate
  (r)
• Nominal variables (expressed in terms of money
  Ch.4)
• Price level (P), inflation rate (p)
• Classical dichotomy
• In the classical theory, the real variables and
  nominal variables are determined separately.
• This irrelevance of money for real variables is
  called monetary neutrality. For the purpose of
  studying long-run issues, monetary neutrality is
  approximately correct.

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Monetary Neutrality
If the zoom (money supply) changes, ? oranges
(real variables) do not change. ? Photos (nominal
variables) change. Note that if oranges change,
photos also change.
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Seigniorage

• Why does the government increase the money supply
  even though it causes inflation? One possible
  answer is
• Seigniorage the revenue from printing money
• If the government prints money to finance its
  expenditure,
• ? Increase in the money supply
• ? Inflation
• ? Decrease in the real value of the old money
  in the hand of public
• This is like imposing an inflation tax on holding
  money.
• Hyperinflation (50 per month) is often caused by
  serious budget deficit, and it has a
  self-reinforcing mechanism.
• Budget deficit ? lots of seigniorage ?
  hyperinflation ? decline of real tax
  revenue ? larger budget deficit

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Summary

• The Classical theory of money says
• According to the quantity theory of money, the
  price level depends on the money supply. MV
  PY
• The nominal interest rate is the sum of the real
  interest rate and expected inflation rate. i
  r pe
• If we assumed the cost of holding money, the
  money demand depends on both the output and the
  nominal interest rate. M/P L(rpe, Y)
• The money supply does not affect real variables.

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(Optional) Mathematical Notes

• (1) If C AB, change in C change in A
  change in B
• (2) If C A/B, change in C change in A -
  change in B
• Proof Let A and B increase at a and b, then C
  increase as follows
• (1)
• (2)
• If a and b are relatively small number,
  ab/10000 can be ignored, and (a-b)/100b is
  nearly equal to (a-b)/100.
• (For example, if a3, b2 then
  (ab)/1000.05, (a-b)/100 0.01
• and ab/100000.0006, (a-b)/(100b) 0.009803.
• Thus, in the case of (1) C changed at (ab)
• in the case of (2), C changed at (a-b)