4. Money and Inflation

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4. Money and Inflation

• Agenda
• What is money?
• The quantity equation and money demand function
• Quantity theory of Money
• Fisher equation
• Cost of holding money and money demand function
• Seigniorage
• Social costs of inflation
• hyperinflation
• Classical dichotomy

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What is Money?

• The stock of assets used for transactions
• The Functions of Money
• Store of value
• Unit of account
• Medium of exchange --- moneys liquidity
• ? Without money, trade requires the double
  coincidence of wants.
• The types 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  been replaced by fiat money because fiat money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.

3
Money Supply

• 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
• Various measures of money
• Currency, M1, M2, M3
• M2 and M1 are popular, but there is no consensus
  about which measure is the best.

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The Quantity Equation

• The quantity equation is an identity
• Money ? Velocity Price ? Output or
  Transactions
• MV PY
• The number of transactions of goods and services
  is difficult to measure, thus output is used.
  Roughly speaking, output is proportion to
  transactions.
• Y real GDP
• P GDP deflator (Thus, PY is nominal GDP)
• M money supply
• V income transactions velocity of money
• In a sense, the quantity equation is an identity
  that defines V.

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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.
• (M/P)d L(macroeconomic
  variables)
• Here, 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 L(Y) k Y

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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 dollar 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 quantity theory of money.

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

• Recall that output (real GDP) is decided by
  production function, thus Y can be treated as
  exogenous (fixed).

• Price level is only decided by Money supply.
• ? Central banks can control price level, so
  inflation.

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Money Supply Growth and Inflation Rate

• 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
M currencydemand deposits
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Real Interest Rate

• 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.
  Therefore, the nominal interest rate and the
  inflation rate have an one for one relation (the
  Fisher effect).

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Ex Ante and Ex Post Real Interest Rate

• 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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Extension of the Money Demand Function

• 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 instead of bonds
• 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)
• The current price level (P) depends not only
  on the current money supply (M) but also on the
  expected inflation rate (pe), i.e., the expected
  future price level, so the expected future money
  supply.

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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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Seigniorage

• Why does the government (including the central
  bank) increase the money supply even though it
  causes inflation? One answer could be seigniorage
  (the revenue from printing money)
• When the government prints money to finance
  expenditure,
• ? Increases of the money supply
• ? Inflation
• ? Decrease of the real value of the old money in
  the hand of public
• Seigniorage is like imposing an inflation tax on
  holding money.

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The Social Costs/Benefits of Inflation (1)

• According to the classical theory, inflation
  is just a change in price level, there are no
  effects on economy. However
• (1) The cost of expected inflation
• Shoe-leather cost
• The inconvenience of reducing money holding.
• Menu cost
• The cost of showing new pricing information
• Tax laws often do not take into account the
  effects of inflation (e.g., taxation on capital
  gains)

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The Social Costs/Benefits of Inflation (2)

• (2) The cost of unexpected inflation --- more
  unfavorable
• Arbitrary redistributions of wealth between
  creditors and debtors (e.g., fixed-pension,
  mortgage loans)
• Ex ante and ex post real interest rate are often
  different.
• Note that high inflation is variable inflation.
• (3) The benefits of moderate inflation
• Inflation greases the wheels of labor markets.
• Some economists argue that automatic
  reductions in real wage by 2-3 inflation may
  make labor markets work better (because nominal
  wages rarely fall).

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Hyperinflation

• Hyperinflation is often defined as inflation
  that exceeds 50 percent per month, which is just
  over 1 a day.
• Shoe-leather and menu costs are much worse
• Tax systems are distorted
• There is a delay between the time a tax is
  levied and the time the tax is paid. During
  hyperinflation, this short delay greatly reduces
  the real tax revenue
• Eventually the money loses its role, then
  bartering or using commodity money becomes
  prevalent.
• Hyperinflation has a self-reinforcing mechanism
  
• Budget deficit
• ? lots of seigniorage ? hyperinflation
• ? decline of real tax revenue ? larger budget
  deficit

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Hyperinflation in interwar Germany
P
M
p
M/P
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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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Summary

• The Classical theory of money says
• According to the quantity theory of money, price
  level depends on the current money supply. MV
  PY V, Y is fixed.
• 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
  current price level depends on both the current
  and future money supply.M/P L(rpe, Y)
• The money supply does not affect real variables
  (Classical dichotomy)
• Some topics
• Cost/Benefit of inflation
• Expected shoe-leather cost, menu cost, tax
  distortion, etc.
• Unexpected arbitrary redistribution among
  creditors and debtors.
• Benefit moderate inflation could make labor
  market work better.
• Hyperinflation is often self-reinforcing.
• Budget deficit?Seigniorage?Hyperinflation?Decline
  of real revenue

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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)