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How the Fed controls the money supply? Recall: money supply = currency plus deposits at banks Decisions are made by FOMC –FOMC meets next Tuesday –markets will be speculating about what the Fed will do to the short-term interest rate (Federal funds rate) –we will see that the decisions about the money supply are directly linked to this interest rate

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Simplest Case: currency is whole money supply Then the Fed simply prints all the money and the total amount of money is easily determined But this is not the real world: deposits are a major part of the money supply –At the end of last year, for example, currency = $426 billion M1 = $1,069 billion M2 = $4,019 billion

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More relevant case: deposits at banks are part of the money supply. First observe where deposits fit in to banks business

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In order to control the money supply, the Fed must have a link to deposits at banks. Why? –Because deposits are part of money supply In symbols, the money supply is: M = CU + D –where M = money supply CU = currency D = deposits at banks

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First key idea in the story: people want to hold a fixed mix of deposits and currency. This is a reasonable simplifying assumption An equation to describe this assumption is CU = kD where k is a constant called the currency to deposit ratio –example: k = 0.2, so that people hold currency equal to 20 percent of their deposits –k depends on custom, crime enforcement, etc. –it is possible for k to change over time (banking panics), but we assume k is fixed for now

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Second key idea in the story: banks are required to hold bank reserves equal to a certain fraction of their deposits Bank reserves are deposits a (commercial) bank holds at the central bank (Fed) An equation describing this requirement is BR = rD where r is a constant called the required reserve ratio –example: r =.1, so that banks are required to hold bank reserves equal to 10 percent of deposits The above equation is a link for the Fed to control the money supply

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Third key idea in the story: The Fed can control the amount of bank reserves in the economy How? (Recall that bank reserves are simply deposits that banks have at the Fed) By buying and selling things and paying or getting paid with the reserves, the Fed can determine the total amount of reserves –what are the things? Ketchup? No, there is not enough of it. Government bonds? Yes, there are plenty of them.

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The monetary base Defined as currency plus bank reserves In symbols, MB = CU + BR where MB = monetary base CU = currency BR = bank reserves Because the Fed can control bank reserves, it can control the monetary base

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Look at what we have so far: M = CU + D CU = kD BR = rD MB = CU + BR

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Logical implication of what we have so far: M = CU + D = kD + D = (k+1)D MB = CU + BR = kD + rD = (k+r)D Thus: M = [(k+1)/(k+r)]MB Example: k =.2 and r =.1 implies [(k+1)/(k+r)] = (1.2)/(0.3) = 4 The blue term is the money multiplier

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The money multiplier The end of the story. We (and the Fed) now know how much the money supply will increase as a result of an increase in the monetary base. The term multiplier is used because the number is greater than one, e.g. 4. Since the Fed can control the monetary base it can control the money supply. example: say the money multiplier is 4 Fed increases the monetary base (MB) by $1 money supply (M) will increase by $4 billion.

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The Gory Detail I

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The Gory Detail II

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The Gory Detail III

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The Gory Detail…. Set k = 0 to focus on deposits at banks

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If you sum up the numbers in the first column of the previous table you get: 10(1 +.9 +.9 2 +.9 3 …) = 10/(1 -.9) = 100 So the money multiplier is 10 just what we get from the earlier analysis if k = 0 and r =.1

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Wrap up of Long Run Analysis Factors affecting long-run real GDP growth Growth rate of aggregate hours (working age population, employment to population ratio, hours per worker) Growth rate of productivity (capital, technology-- use SAM and the growth accounting formula) Factors affecting long-run rate of inflation Money growth (Fed and the money multiplier) Velocity growth Use quantity equation of money Now on to economic fluctuations next week

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Finally, use quantity equation of money to determine the appropriate growth rate of the money supply Potential GDP growth rate ( 2.3) + inflation rate (2.3) - velocity growth rate (0.0) = money growth rate (4.6)

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END OF LECTURE

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Money Multiplier Objectives: 1.Determine the maximum potential extent to which the money supply will change following a Federal Reserve purchase or sale.

Money Multiplier Objectives: 1.Determine the maximum potential extent to which the money supply will change following a Federal Reserve purchase or sale.

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