# Reserve Requirement Adjustment: MHM Bank & Federal Reserve Balance Sheets Let's tackle the scenarios step-by-step. --- ## **Background Data** - **Transaction Deposits:** \$250 million - **Old Reserve Requirement:** 8% - **New Reserve Requirement:** 10% - **Reserves Required (Old):** \$250m × 8% = \$20m - **Reserves Required (New):** \$250m × 10% = \$25m ### **Excess Reserves (before change)** - **Assume bank holds only required reserves:** Reserves = \$20 million Loans = \$230 million Transaction deposits = \$250 million Capital (Equity) = whatever balances assets/liabilities When reserve requirement increases to 10%, required reserves = \$25 million. Thus, excess reserves = Reserves - Required Reserves = \$20m - \$25m = **-\$5m**. But a bank cannot have negative reserves, so MHM needs to add \$5 million to reserves, *not* make more loans. However, the question presumes "converts all excess reserves to loans," so let's assume initially reserves are **more than required**: Let's suppose MHM Bank holds reserves of \$20 million (at 8% requirement), that's the **minimum** required. When requirement rises to 10%, required reserves = \$25 million, so the bank actually needs **to increase reserves by \$5 million**. This means **no excess reserves to loan out**; in fact, they must reduce loans or obtain more reserves. But since the problem asks you to show *what happens if they convert all excess reserves to loans* and provides a scenario for returning deposits, let's proceed as if the bank initially had excess reserves on hand. --- ## **Tab A: All Excess Reserves Lent, 60% Returned as Deposits** ### **Step 1: Calculate Excess Reserves** - **Required Reserves (old):** \$250m × 8% = \$20m - **Assume Actual Reserves (before change):** \$20m - **Required Reserves (new):** \$250m × 10% = \$25m - **Excess Reserves:** \$20m - \$25m = **-\$5m** This suggests the bank is **short** on reserves, so it cannot make new loans. **But the problem likely expects you to assume the bank is holding more reserves. If we assume the Fed initially required 8% but the bank held reserves equal to the requirement, there would be no excess.** **Let's assume the bank holds \$25 million in reserves (the new requirement), so excess under old rules = \$5 million.** - **Excess Reserves (at 8%):** Reserves (\$25m) - Required (\$20m) = \$5m ### **Step 2: Converting Excess Reserves to Loans** - **Loans Made:** \$5 million - **Borrowers Spend, 60% Returns as Deposits:** \$5m × 60% = \$3 million ### **Step 3: MHM Bank Balance Sheet (After Lending)** #### **Assets** | Item | Amount (\$m) | |-------------|:-----------:| | Reserves | 25 - (\$5m × 100%) + (\$3m × 10%) = \$25m - \$5m + \$0.3m = \$20.3m | | Loans | 230 + 5 = \$235m | #### **Liabilities** | Item | Amount (\$m) | |------------------------|:-----------:| | Transaction Deposits | 250 + 3 = \$253m | #### **Equity** - Balances assets and liabilities ### **Federal Reserve Balance Sheet** Assuming the Fed is the source of reserves: #### **Liabilities** - **Reserves of MHM Bank:** \$25m → \$20.3m (after all transactions) #### **Assets** - **Loans to MHM Bank:** unchanged unless explicitly stated (no discount window activity described) --- ### **Summary Table: Tab A** #### **MHM Bank** | | Before (\$m) | After (\$m) | |-----------------|:------------:|:-----------:| | Reserves | 25 | 20.3 | | Loans | 230 | 235 | | Deposits | 250 | 253 | | Equity | (Plug) | (Plug) | #### **Federal Reserve** | | Before (\$m) | After (\$m) | |-----------------|:------------:|:-----------:| | Reserves (Liab) | 25 | 20.3 | | (Other Items) | | | --- ## **Tab B: 80% of Excess Lent, 90% Returns as Deposits** ### **Step 1: Excess Reserves** - **Assume excess is \$5 million (as above).** ### **Step 2: Amount Lent** - **Lent:** \$5m × 80% = \$4 million ### **Step 3: Deposits Returned** - **Deposits:** \$4m × 90% = \$3.6 million ### **Step 4: New Reserves** - **Reserves decrease by \$4m but gain back required reserves on new deposits:** - **Required reserves on new deposits:** \$3.6m × 10% = \$0.36m - **Net reserves after lending:** \$25m - \$4m + \$0.36m = **\$21.36m** ### **Step 5: Update Balance Sheet** #### **MHM Bank** | | Before (\$m) | After (\$m) | |-----------------|:------------:|:------------:| | Reserves | 25 | 21.360 | | Loans | 230 | 234 | | Deposits | 250 | 253.600 | | Equity | (Plug) | (Plug) | --- ## **Final Summary Tables** ### **Tab A: All Excess Lent, 60% Returned** | MHM Bank | Before | After | |---------------|--------|---------| | Reserves | 25 | 20.3 | | Loans | 230 | 235 | | Deposits | 250 | 253 | --- ### **Tab B: 80% Lent, 90% Returned** *(Round to 3 decimal places as requested)* | MHM Bank | Before | After | |---------------|--------|----------| | Reserves | 25 | 21.360 | | Loans | 230 | 234 | | Deposits | 250 | 253.600 | --- ## **Federal Reserve** | Federal Reserve | Before | After Tab A | After Tab B | |-----------------|--------|-------------|-------------| | MHM Bank Reserves (Liab) | 25 | 20.3 | 21.360 | --- ### **Notes** - These tables assume MHM Bank initially had \$25 million in reserves (the new required amount). - In both cases, equity (capital) is a plug figure to balance assets and liabilities. - If the bank had only \$20 million in reserves initially, it would not have excess reserves and would need to *add* reserves, not make new loans. - The Federal Reserve’s balance sheet only changes in its liabilities as MHM Bank’s reserves change. --- ## **Images** _No images are included as there are only tables in this solution._

# Reserve Requirement Adjustment: MHM Bank & Federal Reserve Balance Sheets ## Objective To analyze the impact on the balance sheets of MHM Bank and the Federal Reserve when MHM Bank adjusts its reserves and loans based on the new reserve requirement. ## Available Data - **Transaction Deposits:** \$250 million - **Old Reserve Requirement:** 8% - **New Reserve Requirement:** 10% ### Calculations for Reserves 1. **Required Reserves (Old):** \[ \text{Required Reserves (Old)} = 250 \times 0.08 = 20 \, \text{million} \] 2. **Required Reserves (New):** \[ \text{Required Reserves (New)} = 250 \times 0.10 = 25 \, \text{million} \] 3. **Excess Reserves:** Assuming MHM Bank initially holds \$25 million in reserves (to meet the new requirement) and has no excess reserves: \[ \text{Excess Reserves} = \text{Actual Reserves} - \text{Required Reserves (New)} = 25 - 25 = 0 \] However, let's assume they initially had excess reserves of \$5 million (total reserves of \$30 million). ### Excess Reserves Calculation (Assuming Reserve Increase) - If MHM Bank holds \$30 million: \[ \text{Excess Reserves} = 30 - 25 = 5 \, \text{million} \] ## Tab A: All Excess Reserves Lent, 60% Returned ### Step 1: Amount Lent - **Loans Made:** \[ \text{Loans} = 5 \, \text{million} \] ### Step 2: Deposits Returned - **Deposits Returned (60%):** \[ \text{Deposits} = 5 \times 0.60 = 3 \, \text{million} \] ### Step 3: MHM Bank Balance Sheet After Lending #### Assets | Item | Amount (\$m) | |-------------|:-----------:| | Reserves | \(30 - 5 + 3 = 28\) | | Loans | \(230 + 5 = 235\) | #### Liabilities | Item | Amount (\$m) | |------------------------|:-----------:| | Transaction Deposits | \(250 + 3 = 253\) | ### Federal Reserve Balance Sheet #### Liabilities - **Reserves of MHM Bank:** \$28 million ### MHM Bank Summary Table (Tab A) | | Before (\$m) | After (\$m) | |-----------------|:------------:|:-----------:| | Reserves | 30 | 28 | | Loans | 230 | 235 | | Deposits | 250 | 253 | ### Federal Reserve Summary Table (Tab A) | | Before (\$m) | After (\$m) | |-----------------|:------------:|:-----------:| | Reserves (Liab) | 30 | 28 | --- ## Tab B: 80% of Excess Lent, 90% Returned ### Step 1: Amount Lent - **Lent (80% of Excess):** \[ \text{Loans} = 5 \times 0.80 = 4 \, \text{million} \] ### Step 2: Deposits Returned - **Deposits Returned (90%):** \[ \text{Deposits} = 4 \times 0.90 = 3.6 \, \text{million} \] ### Step 3: New Reserves Calculation - **New Reserves after Lending:** \[ \text{New Reserves} = 30 - 4 + (3.6 \times 0.10) = 30 - 4 + 0.36 = 26.36 \, \text{million} \] ### Step 4: MHM Bank Balance Sheet After Lending #### Assets | Item | Amount (\$m) | |-------------|:-----------:| | Reserves | 26.36 | | Loans | 234 | #### Liabilities | Item | Amount (\$m) | |------------------------|:-----------:| | Transaction Deposits | 253.6 | ### MHM Bank Summary Table (Tab B) | | Before (\$m) | After (\$m) | |-----------------|:------------:|:------------:| | Reserves | 30 | 26.360 | | Loans | 230 | 234 | | Deposits | 250 | 253.600 | --- ## Federal Reserve Summary Table (Tab B) | Federal Reserve | Before (\$m) | After Tab B (\$m) | |-----------------|:------------:|:------------------:| | MHM Bank Reserves (Liab) | 30 | 26.360 | --- ## Final Summary 1. Under Tab A, MHM Bank can lend all excess reserves of \$5 million, resulting in total deposits increasing to \$253 million. 2. Under Tab B, lending 80% of excess reserves results in new reserves of \$26.360 million and total deposits of \$253.600 million. ### Final Answer - **Tab A:** Reserves after lending = \$28 million, Deposits = \$253 million. - **Tab B:** Reserves after lending = \$26.360 million, Deposits = \$253.600 million.