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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 3 • 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. 4 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). 7 • 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$/year • That is, the total value of the transactions in the economy is 500 dollars. 12 • The variable V is then given by: V=PT/M, or (500$/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 14 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. 16 • 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 17 • 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. 18 • 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. 19 • 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. 20 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 21 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. 24 • 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. 26 • 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. 27 • 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. 30 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. 31 • 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. 35 • 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. 40

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