Money and Price Level Determination - Ibmec Rio de Janeiro

							Monetary Economics

   Tue-Thu, 9:15-10:55
        Room 404

      Marcelo Mello
   Faculdades Ibmec-RJ
         2011.1          1
• The material below draws heavely from chapter
  4 of Greg Mankiw’s Macroeconomics Textbook.

• See also D. Romer, Advanced Macroeconomics,
  chapter 10.
 Lecture 1: Introduction to Monetary
              Economics

• What is money?
  – Money is defined as anything that is generally
    accepted in payment for goods or services, or in
    the repayment of debts




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• Monetary Theory: The theory relates changes
  in the quantity of money to changes in
  aggregate economic activity and the price
  level.

• Price level: The average price of goods and
  services in an economy

• Inflation: a continuous increase in the price
  level.

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        1. Money and Prices – Review

• In this first lecture we discuss the role of money
  in the economy and how it relates to other
  economic variables, in particular to prices and
  inflation.

• This lecture draws heavily from Mankiw’s
  Macroeconomics text, 5th edition.


                                                   5
 Results that are true for the economy’s
          long-run equilibrium
– the economy’s price level is determined by the money
  supply
– the rate of inflation is determined by the growth rate of
  the money supply
– there is a long-run one-for-one relationship between the
  inflation rate and the nominal interest rate (the Fisher
  effect)
– real variables only affect real variables, and nominal
  variables only affect nominal variables (the Classical
  Dichotomy)
– As a consequence of the Classical Dichotomy, we
  conclude that money is neutral in the long-run, that is,
  increases in the money supply do not affect real
  variables.
                                                          6
   2. Money and the Quantity Theory
• The price of a good or a service is defined as the rate at
  which money is exchanged for the good or the service.
• Thus, in order to understand the behavior of prices and
  inflation, we have to understand what money is.
• As defined above, money is defined as the stock of
  assets that can be readily used to make transactions.
• Money has three functions:
   – it can be used as a store of value (i.e., money can be used to
     transfer wealth intertemporally)
   – as a unit of account (i.e., money is used to quote prices and
     record debts)
   – as a medium of exchange (i.e., money is used to buy goods
     and services).
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• The type of money that modern economies use is
  the so-called fiat money, i.e., money that has no
  intrinsic value.

• In the past, most economies used commodity
  money, e.g., gold coins, or silver coins.

• The quantity of money available is called the
  money supply, and is controlled by the central
  bank, which has a monopoly on the printing of
  money.


                                                      8
• The Fed controls the money supply through open-
  market operations - by buying and selling bonds
  to the public the Fed can alter the money supply.


• When the Fed buys bonds from the public the
  money supply increases, when the Fed sells bonds
  to the public the money supply decreases.
• How does money relate to other economic
  variables?

• Let’s denote by T the total number of
  transactions that take place in the economy
  during a certain period of time, and let P be
  the average price of the a typical transaction.
• Therefore, the total value of all the
  transactions in the economy is given by PxT.
• This quantity is proportional to the amount of
  money circulating in the economy.
                                                10
• Denoting by M the amount of money in
  circulation, we can write the previous
  statement more concisely as follows: MV=PT,
  where V is the velocity of money.



• The above equation says that the total value of
  the transactions in the economy is
  proportional to the amount of money.



                                                11
• Example 1: Consider a one-good economy for
  which in a given year 50 books were sold at a
  price of $10 each. Assume that the money
  supply is $100.
• Thus, we have that T=50 books/year, P=10
  $/book, and M=$100. Using the above
  equation we have that:
• PT=(50 books/year)(10$/book)=500$/year
• That is, the total value of the transactions in
  the economy is 500 dollars.

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• The variable V is then given by: V=PT/M, or
  (500$/year)/$500=>>5/year
• How can we interpret the variable V?
• It can be interpreted as the velocity of money,
  that is, the number of times a dollar bill
  changes hands in the economy.

• We saw above that the total value of the
  transactions is $500, and the amount of
  money in the economy is $100, so that each
  dollar changes hands 5 times.
                                                13
            The Quantity Equation
• The equation -- MV=PT -- is known as the
  quantity equation.
• Note that the quantity equation is an identity, not
  a behavioral equation.
• We need to make an important modification in
  the above equation. Since there is no way to
  measure the total number of transactions in the
  economy, we need to replace the variable T with
  a proxy variable for it.
• The best proxy for T is the real GDP, Y.
• Therefore, the quantity equation can be rewritten
  as follows: MV=PY
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   4. The Quantity Equation and the
       Money Demand Function
• At this point, we haven’t established any
  behavioral relationship between the variables
  M, V, P, and Y.
• In order to get some results out of this model
  we need to make assumptions.

• For now, we assume that V is constant. The
  assumption of a constant velocity of money
  will give interesting results.
                                                   15
• When we study how money affects economic
  variables, we typically look at M/P and not M.
• The variable M/P is called real money balances,
  and it measures the purchasing power of the
  stock of money in the economy.
• The demand for real money balances, (M/P)d,
  henceforth demand for money, gives the
  amount of money individuals wish to hold.
• Based on the quantity equation, a possible
  functional form for the money demand function
  is given by: (M/P)=kY, where k=1/V.
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• Equilibrium in the money market requires that
  the money supply should be equal to the
  money demand:

                 M/P=(M/P)d=kY

• The above equation is the basis of the
  quantity theory of money. First, it is useful to
  rewrite it as follows:
                      MV=PY

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• Real GDP Y is determined by the amount of
  factors of production (i.e, machines and tools
  used in the production of goods and services,
  the amount of labor engaged in production,
  etc.) and the technology of the economy - the
  quantity of money does not affect the real
  GDP.

• V is constant by assumption.

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• Therefore, changes in the money supply affect
  only the economy’s price level. (Long-run vs.
  Short-run)

• This is relatively intuitive. Suppose that the Fed
  announces that tomorrow the denomination
  of all dollar bills in the economy will double.
• Does the U.S. will produce more goods and
  services because of that? No; the only change
  we will have in the economy is that all prices of
  goods and services will double.
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• Conclusion: In the long-run equilibrium in the
  economy when prices are flexible the money
  supply determines the economy’s price level.



• Alternatively, we can state that in the
  economy’s long-run equilibrium with flexible
  prices the money supply determines the
  economy’s nominal GDP, PY.


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      Price Level Determination
• The above theory explains how the economy’s
  price level is determined.
• First, the nominal GDP, PY, is determined by
  the money supply.
• Second, the real GDP is determined by the
  economy’s productive capacity.
• Third, the economy’s price level is determined
  by the ratio of nominal GDP to real GDP.
• That is, P=PY/Y
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             A theory of inflation
• A theory of the price level determination
  naturally gives us a theory of inflation. We can
  rewrite MV=PY in percentage changes as follows
               %ΔM+%ΔV=%ΔP+%ΔY

• Assuming that the velocity is constant, and the
  money supply does not affect output in the long-
  run (assume that %ΔY=0), that is, we have that
                       %ΔM=π
• Where π is the inflation rate.
                                                22
• The above equation establishes that in the
  long-run the inflation rate is determined by
  the growth rate of the money supply.
• Since the central bank controls the money
  supply, the inflation rate is ultimately under
  the control of the central bank.

• The above equation gives the story behind the
  famous quote by Milton Friedman: “Inflation
  is always and everywhere a monetary
  phenomenon”.
                                                   23
 5. Inflation, Interest, and the Fisher Effect
• In the presence of inflation we need to
  distinguish between the nominal interest rate
  (that is, rates of return measured in monetary
  terms) and the real interest rate (that is, rates
  of return measured in terms of physical
  quantities, e.g., units of output).

• The real interest rate, r, is equal to the nominal
  interest rate, i, minus the inflation rate, π, that
  is, r=i-π.
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• Rearranging the above equation, we obtain the
  so-called Fisher equation, which states that the
  nominal interest rate is equal to the real interest
  rate plus the inflation rate.
                          i=r+π
• We know that the real interest rate is determined
  by the flows of saving and investment, and that
  the quantity theory of money establishes that the
  rate of inflation is determined by the rate of
  money growth.
• Thus, we now have a theory of the determination
  of the nominal interest rate: by the Fisher
  equation the nominal interest rate is given by the
  sum of the real interest rate plus the inflation
  rate.
                                                    25
• In spite of its simplicity, the Fisher equation
  entails some interesting results.
• An increase in the rate of money growth
  causes a one-for-one increase in the rate of
  inflation. Increases in the inflation rate causes
  a one-for-one increase in the nominal interest
  rate in the long-run.

• The long-run one-for-one relationship
  between the rate of inflation and the nominal
  interest rate is known as the Fisher effect.
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• So far, we have not distinguished between
  expected inflation and actual inflation.
• However, when two parties agree on a
  nominal contract they cannot know for sure
  what the inflation rate will be by the end of
  the contract’s term.

• Clearly, their inflation expectations can differ
  from the realized inflation.
• If this is the case, the expected and actual real
  interest rates will also differ.
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• In this sense, we distinguish between the
  expected real interest rate and the realized
  real interest rate.

• In fact, these two variables receive a special
  name: the former is called the ex-ante real
  interest rate, and the latter is called the ex-
  post real interest rate.



                                                    28
• The distinction between expected and actual
  inflation is important because it affects the
  Fisher effect.

• The nominal interest rate cannot adjust to the
  actual inflation rate because when the nominal
  interest rate is set the actual inflation is
  unknown.

• The nominal interest rate can only adjust to
  expected inflation.
                                              29
• Therefore, the Fisher effect establishes a one-
  for-one relationship between the nominal
  interest rate and the expected inflation rate.



• That is, the Fischer equation is more
  appropriately written as follows: i=r+πe,
  where πe denotes the expected inflation.


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6. Keynesian Money Demand Function
• The quantity theory assumes that the only
  determinant of the money demand is real income.
• However, when we hold money we must give up
  the (nominal) interest rate we could earn by
  purchasing government bonds.
• That is, the nominal interest rate is the
  opportunity cost of holding money. The higher
  the nominal interest rate the higher the
  opportunity cost of holding money.

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• Therefore, the demand for money depends
  negatively on the nominal interest rate.
• A more general specification for the money
  demand function could look like this:
                  (M/P)d=L(i,Y)

• Equilibrium in the money market is
  determined as before, namely, by the equality
  between money demand and money supply.
  Thus, in equilibrium, we must have that:
                    M/P=L(i,Y)
                                              32
• In this case, does the money supply still
  determine the economy’s price level? Yes.

• Let’s see how. Suppose that the central bank
  doubles the money supply. We know that in
  the long-run equilibrium real GDP, Y, is not
  affected by the quantity of money, so that Y is
  unchanged.

• Furthermore, we know that monetary shocks
  cannot affect the real interest rate, r, only
  changes in savings or investment.
                                                33
• The question is then if a one-shot
  increase in the money supply affects the
  expected inflation.


• If there is a one-shot increase in the
  money supply, would you change your
  expectation of the inflation rate?
  Probably not.
• Recall that the inflation rate is characterized by
  an ongoing increase in the price level, not a
  one-shot increase.

• Therefore, given an increase in the money
  supply, the only variable affected in the
  equation M/P=L(i,Y) is the price level.




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• In conclusion, in the long-run, an increase in
  the money supply does not affect the nominal
  interest rate or the real output, only the price
  level.

• Therefore, the money supply determines the
  economy’s price level, even under the more
  general money demand function.
        7. The Classical Dichotomy
• Consider the following thought experiment:
  suppose that tomorrow the government
  announces that every dollar bill in the economy
  will be worth twice its denomination.

• This is equivalent to doubling the economy’s
  money supply.
• Is it going to affect the economy’s real
  variables?
• Does it change the amount of goods and
  services the economy is capable of producing?
                                               37
• The change in the money supply does not affect
  the real GDP since the amount of inputs and the
  technology used in the production of goods and
  services is unchanged.

• In fact, if prices are flexible, real variables are
  not affected by the monetary change, only the
  price level of the economy is affected.
• This is the only effect caused by the increase
  in the money supply.

• The result that real variables are not affected
  by monetary variables in the long-run is
  known as the long-run neutrality of money.




                                                    39
• The long-run neutrality of money is an
  important result. It basically establishes that
  real variables (such as the real GDP, Y, real
  interest rate, r, real wage, W/P, etc.) are
  determined separately from nominal variables
  (such as the price level, P, the inflation rate, ,
  the nominal wage W, etc.).

• The separation between real and nominal
  variables in macroeconomics is known as the
  classical dichotomy, and it is the at the core of
  the so-called classical macroeconomic theory.
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