EC320: Intermediate Macroeconomics - The Monetary System

The Monetary System

Overview of Money

• Definition: Money is the stock of assets that can be readily used to make transactions. It broadly includes currency (bills and coins) and bank deposits held by the public.

• Three Main Functions of Money:

  1. Medium of Exchange: Money is used to buy goods and services, facilitating complex transactions that would be impossible with barter alone. Barter requires a "double coincidence of wants," where both parties desire what the other has. Money eliminates this need.
  2. Store of Value: Money transfers purchasing power from the present to the future. It allows individuals to save and spend later.
  3. Unit of Account: Money serves as the common unit by which everyone measures prices and values of goods, services, and assets.

• Liquidity: An asset is considered liquid if it can be easily converted into money. Money itself is the most liquid asset.

  • Financial assets (e.g., bank deposits, U.S. government bonds, publicly traded stocks) are generally more liquid than real assets (e.g., houses, cars, art).

Types of Money

• Commodity Money: Currency that possesses intrinsic value, meaning it has value even if not used as money.
  • Examples: Gold coins, silver coins.
  • Silver/Gold Standard: A monetary system where the unit of account is defined based on a fixed quantity of silver or gold.
• Fiat Money: Paper currency that is legal tender but has no intrinsic value.
  • Example: Federal Reserve Notes (U.S. dollar).
  • Implication: Societies using fiat money are more susceptible to inflation, which reduces the purchasing power of money.

Money Supply and Monetary Policy

• Money Supply: The total quantity of money available in an economy.
• Monetary Policy: The control over the money supply, typically conducted by a country's central bank.
• The Federal Reserve System (The Fed): The central bank of the United States.
  • It is organized into 12 Federal Reserve Districts across the U.S.
  • Federal Open Market Committee (FOMC): The primary decision-making body for monetary policy, meeting 8 times a year.
    • Composition: Seven members of the Federal Reserve Board, the president of the New York Fed, and four of the other eleven regional Federal Reserve Bank presidents.
  • Main Tool: The Fed controls the money supply primarily through open market operations.
    • Open Market Purchase: The central bank buys government bonds from the public or banks to increase the money supply (and thus the monetary base).
    • Open Market Sale: The central bank sells government bonds to the public or banks to decrease the money supply (and thus the monetary base).

Measurements of Money Supply

• The most commonly used measures are M1 and M2.
• Key Change: Since May 2020, saving deposits have been included in M1, rather than exclusively M2.
• General Formula: We write money supply as $M = C + D$, where $C$ is currency and $D$ is bank deposits.
• Specific Measures (November 2024 data):
  • C (Currency): $2,359.3$ billion dollars (coins and Federal Reserve Notes outside banks).
  • M1: $18,340.8$ billion dollars. Includes:
    • Currency
    • Checkable deposits (demand deposits, traveler's checks)
    • Saving deposits (including money market deposit accounts)
  • M2: $21,391.7$ billion dollars. Includes:
    • M1
    • Small time deposits
    • Retail money market mutual funds
• Narrower definitions of money supply (like M1) include more liquid forms of deposits.

The Role of Banking in Money Supply

• The banking system is crucial for the overall money supply because bank lending activities effectively create money.
• Banks as Financial Intermediaries: Banks transfer funds from depositors (savers) to borrowers (investors).
• Bank Balance Sheet Preliminaries:
  • Liabilities (Sources of Funds):
    • Deposits (checking, saving, certificates of deposit (CDs/time deposits), money market deposit accounts (MMDAs)). Some are demandable, meaning depositors have immediate access.
  • Assets (Uses of Funds):
    • Reserves ($R$)
    • Bonds
    • Loans
• Reserves ($R$):
  • Bank holdings of cash and cash equivalents, primarily deposited at the Fed, with some held as vault cash.
  • Banks hold reserves for day-to-day business, urgent liquidity needs, and to meet regulatory requirements.
  • Reserve-Deposit Ratio ($rr$): The fraction of deposits banks hold as reserves: $rr = R/D$.
  • Banks typically do not keep a high $rr$ (unless required) because it hurts profitability, as not all depositors withdraw funds simultaneously.
  • Reserve Requirement: The minimum $rr$ that banks are legally mandated to maintain by the Federal Reserve.

Banking Scenarios: Money Creation

To understand banks' role, consider two scenarios, assuming an initial currency of C = $1,000 deposited into a bank.

• Scenario 1: 100%-Reserve Banking

  • Definition: A system where banks hold all deposits as reserves, meaning $rr = 100\%$.
  • Initial State: C = $1,000, D = $0, M = C + D = $1,000.
  • After Deposit: Households deposit the $1,000$ into Bank 1.
    • Bank 1 Balance Sheet:
      • Assets: Reserves $1,000
      • Liabilities: Deposits $1,000
    • New State: C = $0, D = $1,000, M = C + D = $1,000.
  • Lesson: Under 100%-reserve banking, banks do not impact the total money supply.

• Scenario 2: Fractional-Reserve Banking (Most Common)

  • Definition: A system where banks hold only a fraction of their deposits ($D$) as reserves, meaning rr < 100\%.
  • Initial State: C = $1,000, D = $0, M = C + D = $1,000.
  • Step 1: Bank 1 Deposit and Loan (Assume $rr = 20\%$, or $0.2$):
    • Households deposit the $1,000 into Bank 1.
    • Bank 1 holds $20\%$ ( $200) in reserves and loans out the remaining $800. The borrower holds this as currency.
    • Bank 1 Balance Sheet:
      • Assets: Reserves $200, Loans $800
      • Liabilities: Deposits $1,000
    • New State: C = $800 (borrower's currency), D = $1,000 (at Bank 1). M = C + D = $800 + $1,000 = $1,800.
    • Observation: Bank 1 has created $800 in new money.
  • Step 2: Bank 2 Deposit and Loan:
    • The borrower from Bank 1 deposits the $800 into Bank 2.
    • Bank 2 holds $20\%$ ( $160) in reserves and loans out the remaining $640. The new borrower holds this as currency.
    • Bank 2 Balance Sheet:
      • Assets: Reserves $160, Loans $640
      • Liabilities: Deposits $800
    • New State: C = $640 (new borrower's currency), D = $1,000 (Bank 1) + $800 (Bank 2) = $1,800. M = C + D = $640 + $1,800 = $2,440.
    • Observation: Bank 2 has created an additional $640 in money.
  • Step 3: Bank 3 Deposit and Loan:
    • The $640 is deposited into Bank 3.
    • Bank 3 holds $20\%$ ( $128) in reserves and loans out $512.
    • Bank 3 Balance Sheet:
      • Assets: Reserves $128, Loans $512
      • Liabilities: Deposits $640
    • New State: C = $512, D = $1,000 + $800 + $640 = $2,440. M = C + D = $512 + $2,440 = $2,952.
  • Final Effect on Money Supply (Deposit Creation Model):
    • The process continues as each new loan is redeposited.
    • Total money supply generated from an initial deposit is the sum of the original deposit and all subsequent lendings:
      Total Money Supply = $1,000 + (1-rr) imes $1,000 + (1-rr)^2 imes $1,000 + (1-rr)^3 imes $1,000 + ext{…}
      This is a geometric series sum: Total Money Supply = rac{$1,000}{rr} imes 1 = rac{$1,000}{rr}
    • In our example (with $rr = 0.2$): M = rac{$1,000}{0.2} = $5,000.
  • Lessons from Fractional-Reserve Banking:
    • A fractional-reserve banking system creates money.
    • However, it does not create wealth. Bank loans create new money but also an equal amount of new debt.
    • The amount of money created depends on:
      • The fraction of deposits banks are willing to lend (related to $rr$).
      • The amount of currency held by the public (influences how much money is redeposited).

Bank Capital and Leverage

• Bank Capital (Bank Equity/Owner's Equity/Net Worth): The resources a bank's owners have invested in the bank.
  • Formula: $Capital = Value of Assets - Value of Liabilities$
  • Example Balance Sheet:
    • Assets: Reserves $200, Loans $550, Securities $250 (Total Assets = $1,000)
    • Liabilities & Owner's Equity: Deposits $750, Debt $150, Capital (owner's equity) $100 (Total Liabilities & Equity = $1,000)
• Leverage: The use of borrowed money to supplement existing funds for investment.
  • Leverage Ratio: $Leverage Ratio = Assets / Capital$
  • Using the example above: Leverage Ratio = $1,000 / $100 = 10 (meaning for every $1 of capital, the bank has $10 in assets).
• Bank Capital Requirement: Financial regulators impose capital requirements on banks due to the fragility caused by high leverage.
  • Vulnerability: High leverage makes banks vulnerable to insolvency (liabilities exceeding assets) if asset values decline.
    • Example: If the example bank's assets lose $150 in value (e.g., $100 from loan defaults, $50 from bond value drops), total assets become $850. With liabilities of $900 ($ $750$deposits +$ $150$debt), the bank becomes insolvent.</li></ul></li> <li><strong>Regulation</strong>: Banks with capital levels at least 8</ul> <h4 id="amodelofmoneysupply">A Model of Money Supply</h4> <p>This model explains how the central bank influences the money supply, expanding upon the deposit creation concept.</p> <ul> <li><strong>Exogenous Variables</strong>:<ul> <li><strong>Reserve-Deposit Ratio ($rr$)</strong>:$rr = R/D$(Reserves / Deposits). Influenced by regulations (reserve requirements) and bank policies (e.g., holding excess reserves).</li> <li><strong>Currency-Deposit Ratio ($cr$)</strong>:$cr = C/D$(Currency / Deposits). Reflects the public's preference for holding cash versus depositing it in banks.</li> <li><strong>Monetary Base ($B$) / High-Powered Money</strong>:$B = C + R$(Currency in circulation + Bank Reserves). Directly controlled by the central bank.</li></ul></li> <li><strong>Endogenous Variable</strong>:<ul> <li><strong>Money Supply ($M$)</strong>:$M = C + D$(Currency in circulation + Bank Deposits). The central bank primarily influences this variable.</li></ul></li> </ul> <h4 id="solvingforthemoneysupplymoneymultiplier">Solving for the Money Supply (Money Multiplier)</h4> <p>The money supply ($M$) relates to the monetary base ($B$) through the money multiplier ($m$).</p> <ul> <li><p>Given:$M = C + D$and$B = C + R$(where$C$is currency,$D$is deposits,$R$is reserves).</p></li> <li><p>Dividing$M$by$B$:<br />$ rac{M}{B} = rac{C + D}{C + R} $</p></li> <li><p>Dividing the numerator and denominator by$D$:<br />$ rac{M}{B} = rac{(C/D) + (D/D)}{(C/D) + (R/D)} = rac{cr + 1}{cr + rr} $</p></li> <li><p>This ratio is defined as the <strong>money multiplier ($m$)</strong>:<br />$ m = rac{cr + 1}{cr + rr} $</p></li> <li><p>Therefore, the money supply is:$M = m imes B$</p></li> <li><p><strong>Money Multiplier ($m$)</strong>:</p> <ul> <li>Measures the increase in$M$when$B$changes by one dollar.</li> <li>$m$is greater than 1 ($m > 1$) as long as$rr < 1$(i.e., fractional-reserve banking exists).</li> <li>A value of$m > 1$indicates that changes in$B$(central bank actions) have a multiplicative effect on$M$. This is why the monetary base ($B$) is also called "high-powered money."</li></ul></li> <li><p><strong>Determinants of the Money Multiplier</strong>:</p> <ul> <li><strong>$m$decreases when$rr$increases</strong>:<ul> <li>A higher$rr$means banks hold more reserves and are willing to lend out a smaller fraction of deposits, leading to less money creation through the lending process.</li></ul></li> <li><strong>$m$decreases when$cr$increases</strong>:<ul> <li>When the public holds more currency relative to deposits, less money is redeposited into the banking system. Banks, therefore, have fewer deposits available to lend, which reduces the money creation potential.</li></ul></li></ul></li> </ul> <h4 id="howthefedconductsmonetarypolicy">How the Fed Conducts Monetary Policy</h4> <p>The Fed influences the money supply ($M$) in two primary ways:</p> <ol> <li><strong>Changing the Monetary Base ($B$)</strong></li> <li><strong>Changing the Reserve-Deposit Ratio ($rr$)</strong></li> </ol> <h5 id="toolsforchangingthemonetarybaseddbdd">Tools for Changing the Monetary Base ($B$)</h5> <ol> <li><strong>Open Market Operations (OMOs)</strong>: The Fed's buying and selling of government bonds.<ul> <li><strong>Preferred Method</strong>: This is the Fed's most frequent and preferred monetary control tool.</li> <li><strong>Effect on$B$</strong>: OMOs directly affect the monetary base by an equal amount.<ul> <li><strong>Open Market Purchase</strong>: The Fed buys government securities (bonds) from nonbank public or banks.<ul> <li>If the Fed buys from the public: The public holds the proceeds as currency or deposits checks in banks. Currency in circulation increases, or bank reserves increase. Both lead to an increase in$B$. The diagram shows: purchasing government securities$
      ightarrow $nonbank public receives currency$
      ightarrow $holds as currency (C increases) or deposits in banking system$
      ightarrow $reserves increase.</li> <li>If the Fed buys from banks: Bank reserves increase.$B$increases.</li></ul></li> <li><strong>Open Market Sale</strong>: The Fed sells government bonds, which decreases currency in circulation or bank reserves, thus decreasing$B$.</li></ul></li></ul></li> <li><strong>Discount Lending</strong>: The Fed's lending of reserves to banks via the "discount window."<ul> <li><strong>Discount Rate</strong>: The interest rate at which banks can borrow from the Fed.</li> <li><strong>Mechanism</strong>: To increase the monetary base, the Fed can lower the discount rate, encouraging banks to borrow more reserves.</li> <li><strong>Control Limitation</strong>: The Fed sets the discount rate, but banks ultimately decide whether to borrow. The Fed's control over$B$through discount lending is less precise than through OMOs.</li></ul></li> </ol> <h5 id="toolsforchangingthereservedepositratioddrrdd">Tools for Changing the Reserve-Deposit Ratio ($rr$)</h5> <ol> <li><strong>Reserve Requirements</strong>: Fed regulations mandating a minimum reserve-deposit ratio.<ul> <li><strong>Mechanism</strong>: By lowering the minimum$rr$, the Fed can reduce the required reserves banks must hold, potentially allowing them to lend more, which increases$m$and$M$.</li> <li><strong>Effectiveness Post-2008</strong>: This tool became less effective after the 2008-2009 financial crisis, as banks began holding significantly large amounts of <strong>excess reserves</strong> (reserves above the minimum required amount). The chart shows a dramatic increase in excess reserves from around 2008 onwards.</li></ul></li> <li><strong>Interest on Reserves (IOR)</strong>: A new tool introduced in October 2008, where the Fed pays interest on bank reserves deposited with the Fed.<ul> <li><strong>Mechanism</strong>: To reduce excess reserves (and thus potentially lower$rr$if banks choose to lend more), the Fed could pay a lower interest rate on reserves. Conversely, to increase$rr$, the Fed could increase IOR, incentivizing banks to hold more reserves rather than lend them out.</li></ul></li> </ol> <h4 id="limitsofthefedscontrolonmoneysupply">Limits of the Fed's Control on Money Supply</h4> <p>While the Fed has direct control over the monetary base ($B$) through OMOs, its influence on the overall money supply ($M = m imes B$) can be dampened by changes in the money multiplier ($m$).</p> <ul> <li><strong>Factors Muting Fed's Control (during crises)</strong>:<ul> <li><strong>Public Preference (raising$cr$)</strong>: During banking crises, households may lose confidence in banks and prefer to hold more physical cash, increasing$cr$. An increase in$cr$decreases$m$, leading to a fall in$M$even if$B$is constant.</li> <li><strong>Bank Behavior (raising$rr$)</strong>: Similarly, banks may become more cautious during crises and decide to hold a greater proportion of deposits as reserves (beyond requirements), increasing$rr$. An increase in$rr$also decreases$m$, leading to a fall in$M$.</li></ul></li> <li><strong>Historical Examples</strong>:<ul> <li><strong>The Great Depression (1929–1933)</strong>:<ul> <li>Loss of confidence in banks led to a sharp increase in$cr$.</li> <li>Banks became more cautious, significantly increasing$rr$.</li> <li>Both factors caused$m$to fall sharply (from over 6 to below 4).</li> <li>Despite a$20\%$increase in$B$by the Fed, the large decrease in$m$resulted in a substantial <strong>decrease in the M1 money supply</strong>, which worsened the recession.</li></ul></li> <li><strong>The Great Recession (2007–2009)</strong>:<ul> <li>$cr$remained roughly constant.</li> <li>However, banks significantly increased$rr$due to two main reasons:<ol> <li>The Fed began paying interest on reserves.</li> <li>Banks became much more cautious in their lending practices.</li></ol></li> <li>This led to a sharp fall in the money multiplier ($m$) from about 9 to under 5.</li> <li><strong>Fed's Response</strong>: The Fed managed to largely offset the decrease in$m$and maintain$M$by sharply increasing the monetary base ($B$) through <strong>Quantitative Easing (QE)</strong>, which involved large purchases of long-term government bonds.</li></ul></li></ul></li> </ul> <h4 id="exercisesandanswers">Exercises and Answers</h4> <h5 id="exercise1">Exercise 1</h5> <p>If a central bank wants to increase the money supply, it can <strong><em></strong></em> bonds in open-market operations or <strong><em></strong></em> reserve requirements.</p> <ul> <li>a. buy, increase</li> <li>b. buy, decrease</li> <li>c. sell, increase</li> <li>d. sell, decrease</li> </ul> <p><strong>Answer</strong>: <strong>b. buy, decrease</strong></p> <ul> <li>Buying bonds increases the monetary base ($B$).</li> <li>Decreasing reserve requirements lowers$rr$, which increases the money multiplier ($m$).</li> <li>Both actions increase$M = m imes B$.</li> </ul> <h5 id="exercise2">Exercise 2</h5> <p>Consider the following data:</p> <ul> <li>Currency:$ $100$billion</li> <li>Bank reserves:$ $200$billion</li> <li>Bank deposits:$ $800$billion</li> </ul> <p>A. Calculate the values for the currency-deposit ratio, reserve-deposit ratio, the monetary base, the money multiplier, and the M1 money supply.</p> <p>B. Suppose the central bank conducts an open market purchase of bonds held by banks of$ $50$billion. Assuming the same$cr$and$rr$as in (A), predict the effect on the monetary base and money supply.</p> <p><strong>Answers</strong>:<br /> A. C =$100$, R =$200$, D =$800$</p> <ul> <li><strong>Currency-deposit ratio ($cr$)</strong>:$cr = C/D = 100/800 = 0.125$</li> <li><strong>Reserve-deposit ratio ($rr$)</strong>:$rr = R/D = 200/800 = 0.25$</li> <li><strong>Monetary Base ($B$)</strong>:$B = C + R = 100 + 200 = $300$billion</li> <li><strong>Initial M1 Money Supply</strong>:$M1 = C + D = 100 + 800 = $900$billion</li> <li><strong>Money Multiplier ($m$)</strong>:$m = M1/B = 900/300 = 3$<ul> <li>Alternatively, using the formula:$m = rac{cr + 1}{cr + rr} = rac{0.125 + 1}{0.125 + 0.25} = rac{1.125}{0.375} = 3$</li></ul></li> </ul> <p>B. An open market purchase of$ $50$billion from banks directly increases bank reserves by$ $50$billion.</p> <ul> <li>New Reserves ($R'$):$R' = R + 50 = 200 + 50 = $250$billion</li> <li>Currency ($C$) remains unchanged:$C = $100$billion</li> <li>Deposits ($D$) are assumed unchanged for calculating ratios, as$cr$and$rr$are assumed constant.</li> <li>New Monetary Base ($B'$):$B' = C + R' = 100 + 250 = $350$billion</li> <li>The money multiplier ($m$) remains the same ($m = 3$) because$cr$and$rr$are assumed constant.</li> <li>New M1 Money Supply ($M1'$):$M1' = m imes B' = 3 imes 350 = $1,050$billion</li> </ul> <h5 id="exercise3">Exercise 3</h5> <p>How would each of the following affect the U.S. money supply?</p> <p>A. Banks decide to hold more excess reserves.<br /> B. People withdraw cash from their bank accounts for Christmas shopping.<br /> C. The Fed sells gold to the public.<br /> D. The Fed reduces the interest rate it pays on deposits of depository institutions held at the Fed.<br /> E. A financial crisis leads people to sell many of their stocks and deposit the proceeds in bank accounts, which are federally insured.<br /> F. The federal government sells$ $20$billion of new government bonds to the Fed. The proceeds are used to pay government employees.</p> <p><strong>Answers</strong>:<br /> A. <strong>Banks decide to hold more excess reserves.</strong><br /> * This increases the reserve-deposit ratio ($rr$).<br /> * An increase in$rr$causes the money multiplier ($m$) to fall.<br /> * Therefore, the money supply ($M$) <strong>falls</strong>.<br /> B. <strong>People withdraw cash from their bank accounts for Christmas shopping.</strong><br /> * This increases the currency-deposit ratio ($cr$).<br /> * An increase in$cr$causes the money multiplier ($m$) to fall.<br /> * Therefore, the money supply ($M$) <strong>falls</strong>.<br /> C. <strong>The Fed sells gold to the public.</strong><br /> * When the Fed sells assets (like gold), the payment received from the public effectively withdraws money from circulation or bank reserves.<br /> * This decreases the monetary base ($B$).<br /> * Therefore, the money supply ($M$) <strong>falls</strong>.<br /> D. <strong>The Fed reduces the interest rate it pays on deposits of depository institutions held at the Fed.</strong><br /> * Reducing the interest on reserves makes holding excess reserves less attractive for banks.<br /> * This incentivizes banks to lend more, effectively decreasing the reserve-deposit ratio ($rr$).<br /> * A decrease in$rr$causes the money multiplier ($m$) to increase.<br /> * Therefore, the money supply ($M$) <strong>increases</strong>.<br /> E. <strong>A financial crisis leads people to sell many of their stocks and deposit the proceeds in bank accounts, which are federally insured.</strong><br /> * People prefer bank deposits (insured) over stocks (riskier), so they will move funds from less liquid assets (stocks) into more liquid bank deposits.<br /> * This activity increases bank deposits ($D$) relative to currency ($C$) (assuming the funds were not initially in cash), effectively decreasing the currency-deposit ratio ($cr$).<br /> * A decrease in$cr$causes the money multiplier ($m$) to increase.<br /> * Therefore, the money supply ($M$) <strong>increases</strong>.<br /> F. <strong>The federal government sells$ $20$billion of new government bonds to the Fed. The proceeds are used to pay government employees.</strong><br /> * The Fed's purchase of bonds from the government is similar to an open market purchase, increasing the monetary base ($B$) by$ $20$billion.<br /> * The government then spends this$ $20$billion, putting it into circulation.<br /> * Therefore, the monetary base ($B$) <strong>increases</strong> by$ $20$billion ($M$will increase by$ $20$billion multiplied by$m$).</p> <h5 id="exercise4">Exercise 4</h5> <p>Suppose in an economy:</p> <ul> <li>Monetary base is$ $1,000$billion.</li> <li>People hold a third of their money in the form of currency.</li> <li>Banks hold a third of deposits in reserves.</li> </ul> <p>A. What is the reserve-deposit ratio? What is the currency-deposit ratio?<br /> B. Calculate the money multiplier and the money supply.<br /> C. One day, fear about the banking system strikes the population. People now want half of their money in the form of currency. If the central bank does nothing, what is the new money multiplier and the new money supply?<br /> D. Continue with C. If, in the face of this panic, the central bank wants to conduct an open-market operation to keep the money supply at its original level, it should (buy/sell) government bonds of what amount?</p> <p><strong>Answers</strong>:<br /> A. <strong>Initial Ratios</strong>: Assuming "money" here refers to$M = C+D$<br /> * "People hold a third of their money in the form of currency":$C = (1/3)M$. So$C = (1/3)(C+D)$, which means$(2/3)C = (1/3)D$, so$C/D = 1/2$. Thus, <strong>$cr = 0.5$</strong>.<br /> * "Banks hold a third of deposits in reserves": <strong>$rr = R/D = 1/3 hickapprox 0.333$</strong>.</p> <p>B. <strong>Initial Money Multiplier and Money Supply</strong>:<br /> *$B = $1,000$billion.<br /> *$m = rac{cr + 1}{cr + rr} = rac{0.5 + 1}{0.5 + (1/3)} = rac{1.5}{0.5 + 0.333…} = rac{1.5}{0.833…} = 1.8$<br /> *$M = m imes B = 1.8 imes $1,000$billion = <strong>$ $1,800$billion</strong>.</p> <p>C. <strong>New Money Multiplier and Money Supply (with fear)</strong>:<br /> * "People now want half of their money in the form of currency": New$C = (1/2)M$. So$C = (1/2)(C+D)$, which means$(1/2)C = (1/2)D$, so new$C/D = 1$. Thus, new <strong>$cr' = 1$</strong>.<br /> *$rr$remains unchanged:$rr = 1/3$<br /> * New money multiplier ($m'$):$m' = rac{cr' + 1}{cr' + rr} = rac{1 + 1}{1 + (1/3)} = rac{2}{4/3} = 2 imes 3/4 = 1.5$<br /> * If the central bank does nothing,$B$remains$ $1,000$billion.<br /> * New money supply ($M'$):$M' = m' imes B = 1.5 imes $1,000$billion = <strong>$ $1,500$billion</strong>.<br /> * <strong>Observation</strong>: Increased currency holding (higher$cr$) lowers the money multiplier and thus the money supply.</p> <p>D. <strong>Central Bank Action to Restore Money Supply</strong>:<br /> * The central bank wants to keep the money supply at its original level:$M^* = $1,800$billion.<br /> * The new money multiplier is$m' = 1.5$.<br /> * To achieve$M^$with$m'$, the new monetary base ($B^$) must be:$B^* = M^* / m' = $1,800$billion /$1.5 = $1,200$billion.<br /> * The original monetary base was$ $1,000$billion.<br /> * The Fed needs to increase the monetary base by$ $1,200$billion -$ $1,000$billion =$ $200$billion.<br /> * To increase the monetary base, the Fed must <strong>buy government bonds</strong>.<br /> * <strong>Amount</strong>: The Fed needs to buy <strong>$ $200$$ billion worth of government bonds.

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