# Step-by-Step Solution ## Given Data - **Required reserve ratio (RRR):** 0.25 (25%) - **No excess reserves** - **No change in public cash holdings** - **Fed wants to reduce money supply by $800 million** - **Tool:** Open market operations --- ## a) What open-market operation will the Fed engage in? **To reduce the money supply,** the Fed will **sell government securities** (bonds) in the open market. - **Reason:** When the Fed sells securities, buyers pay with deposits from their bank accounts. This reduces bank reserves, leading to a contraction of the money supply via the money multiplier process. --- ## b) Initial Effect on a Single Bank's Balance Sheet **Suppose Bank A purchases $X$ million worth of securities from the Fed.** ### Balance Sheet Changes for Bank A | Assets | Liabilities | |----------------|-----------------| | - Reserves ↓ $X$ | | | + Securities ↑ $X$| | | | | - **Assets:** - Reserves decrease by $X$ (used to buy securities) - Securities increase by $X$ (newly acquired asset) - **Liabilities:** - No immediate change **Explanation:** Bank A pays for the securities with its reserves, reducing its reserve holdings at the Fed. --- ## c) Money Contraction Process Through Two More Banks ### Step 1: Bank A - **After purchase:** Bank A's reserves drop by $X$. - **If this makes Bank A’s reserves fall below the required reserve ratio,** it must reduce deposits by a multiple of the reserve deficiency. #### Change in Deposits (Money Multiplier) The **money multiplier** is: \[ \text{Money Multiplier} = \frac{1}{\text{RRR}} = \frac{1}{0.25} = 4 \] Thus, **a reserve loss of $X$ means deposits must fall by $4X$**. Assuming the Fed wants to contract the money supply by $800$ million: \[ \Delta \text{Money Supply} = \text{Money Multiplier} \times \Delta \text{Reserves} \] \[ 800 = 4 \times X \implies X = 200 \text{ million} \] #### Step 1: Bank A - **Reserves decrease:** $200$ million - **To meet reserve requirements, Bank A must decrease deposits:** Required reserves = $0.25 \times (\text{deposits})$ Reserve deficiency = $200$ million So, deposits must decrease by $800$ million. #### Step 2: Bank B - Bank A calls in loans or sells securities, transferring $200$ million of reserves to Bank B as deposits are withdrawn. - **Bank B now faces a $200$ million reserve loss.** - **Bank B must also reduce deposits by $800$ million (in aggregate, across all banks, until total contraction is $800$ million).** #### Step 3: Bank C - The process repeats, with each bank losing reserves and reducing its deposits, until the total contraction of the money supply reaches $800$ million. **At each step:** - Bank loses reserves. - To meet required reserves, it must reduce deposits by a multiple of the reserve loss. --- ## d) Eventual Consolidated Balance Sheet of the Banking System After the full process: ### Assets - **Reserves:** Decrease by $200$ million - **Securities:** Decrease by $200$ million (sold to the public by the Fed) ### Liabilities - **Deposits:** Decrease by $800$ million | Assets | Liabilities | |--------------------|-----------------| | Reserves ↓ $200$M | Deposits ↓ $800$M | | Securities ↓ $200$M| | This reflects the total contraction in the money supply and the corresponding decrease in reserves and securities. --- ## e) Effect of Changing Cash Holdings ### If people hold **less cash as the money supply falls**: - **More funds remain in the banking system as deposits**, enabling banks to lend out more and contract less. - **The reduction in the money supply will be LESS than $800$ million.** **Why?** - The initial calculation assumes a constant currency-deposit ratio. - If people move cash into banks, the effective money multiplier increases (more base money supports more deposits), so the same reserve loss leads to a smaller overall contraction in the money supply. --- ## **Final Answers (Summarized)** ### a) The Fed will **sell $200$ million of government securities** in the open market. ### b) A single bank's reserves decrease by the amount it pays for the securities; securities increase by the same amount. ### c) Each bank losing reserves will reduce its deposits by a multiple of the reserve loss, with the process continuing through the system until the total contraction reaches $800$ million. ### d) **Consolidated balance sheet:** - Reserves ↓ $200$M - Securities ↓ $200$M - Deposits ↓ $800$M ### e) If people hold less cash as the money supply falls, **the reduction in the money supply will be less than $800$ million** because more funds stay in bank deposits, increasing the money multiplier.