Question

Suppose that the Federal Reserve makes a \$10 million discount loan to First National Bank (FNB) by increasing FNB's account at the Fed. a. Use a T-account to show the effect of this transaction on FNB's balance sheet. Remember that the funds a bank has on deposit at the Fed count as part of its reserves. b. Assume that before receiving the discount loan, FNB has no excess reserves. What is the maximum amount of this \(\$ 10\) million that FNB can lend out? c. What is the maximum total increase in the money supply that can result from the Fed's discount loan? Assume that the required reserve ratio is 10 percent.

Short answer

a. The $10 million discount loan would increase FNB's reserves (assets) and liabilities by $10 million. b. FNB can lend out the entire $10 million received from the Federal Reserve. c. The maximum total increase in the money supply could potentially be $100 million, which is 10 times the initial deposit, based on the 10 percent reserve ratio.

Step-by-step solution

Record the Transaction in T-account

A T-account is used to record the debit and credit of a business's financial transactions. In this case, when FNB receives a $10 million discount loan from the Federal Reserve, this increases its assets in the form of reserves by $10 million. This is recorded on the debit side (left side) of the T-account as it is an increment in assets. Also, as it's a loan, it will increase the liabilities by $10 million as well, which will be recorded on the credit side (right side).\n\nReserves (Debit or Left side):\n+ $10 million\n\nLiabilities (Credit or Right Side):\n+ $10 million

Calculate the Amount FNB can Lend Out

Since FNB had no excess reserves before this loan, all the reserves it has now are from the discount loan. In a fractional reserve banking system, banks are required to keep a certain fraction of their deposits as reserves and can lend out the rest. Since it's mentioned that FNB doesn't have any excess reserves before the loan, the entire $10 million becomes excess reserves because of the loan and FNB can lend this full amount out to borrowers.

Calculate the Potential Increase in Money Supply

Under a system of fractional reserve banking, a bank's lending can lead to a multiplication of deposits and consequently the money supply, depending on the reserve ratio. In this case, with a reserve ratio of 10 percent, each deposit can be lent out and re-deposited, only 10 percent of each deposit getting kept as reserves. Therefore, the total increase in money supply more than the initial loan, often called the money multiplier, could be calculated by: 1 / Reserve Ratio = 1 / 0.1 = 10. So, the maximum total increase in the money supply would be 10 times the initial deposit, i.e., $10 million * 10 = $100 million.

Key concepts

Discount Loan

When it comes to understanding how financial institutions manage liquidity and accessibility to funds, the concept of a discount loan is pivotal. A discount loan is generally provided by a central bank, such as the Federal Reserve, to commercial banks in need of liquidity. The process is simple: the commercial bank receives an amount of money that immediately bolsters its reserves, while simultaneously creating an obligation to repay the amount with interest at a later date.

In our example from the exercise, the First National Bank (FNB) receives a \(10 million discount loan, which is recorded as an asset. This cash infusion increases the bank's reserves, allowing FNB to lend more money to its customers, which is a key activity of banks to support economic activity. The loan impacts the bank's balance sheet by adding to both sides — assets and liabilities — each with \)10 million.

As the loans are repaid over time, the bank's cash flow is affected by not only the principal amounts but also the accrual of interest, which contributes to the bank's revenues. However, if the bank lends out these funds, it needs to maintain a buffer, known as the reserve ratio, to ensure it can meet withdrawal demands. Thus, the discount loan acts as a tool to control liquidity within the banking system and can influence overall economic conditions.

Reserve Ratio

Another fundamental concept of banking operations is the reserve ratio. This ratio dictates the minimum fraction of customer deposits that a bank must retain as reserves rather than lending out. Reserves are held either as currency inside the bank or as deposits at the central bank.

The reserve ratio is established by regulatory institutions to ensure that banks have enough funds available to meet withdrawal demands while still allowing them to lend out a portion of their deposits. This ensures liquidity and banking stability, at the same time preventing banks from running out of cash.

In our case study, the reserve ratio is set at 10%, meaning that for every dollar deposited, the First National Bank must keep 10 cents in reserve, and it is free to loan out the remaining 90 cents. If these requirements are not met, the bank could be subject to penalties or other regulatory actions. The reserve ratio also significantly impacts the total amount of money that banks can create through lending, as it's inversely related to the money multiplier effect.

Money Multiplier

Finally, to fully grasp the ripple effects of banking transactions on the broader economy, you must understand the money multiplier. This concept illustrates the maximum amount by which the money supply can increase based on the central bank's actions, fractional-reserve banking, and the reserve ratio.

The money multiplier formula is simple: it is the reciprocal of the reserve ratio (\frac{1}{reserve \text{ } ratio}). So with a 10% reserve ratio, the multiplier is 10. This multiplier effect arises because banks can lend out a portion of their deposits; these loans become other people's deposits, which in turn can be lent out again, continuing the cycle.

Each round of lending and depositing escalates the amount of money in the system. For the First National Bank's scenario, receiving a \(10 million loan can potentially lead to a \)100 million increase in the overall money supply due to the multiplier effect. However, it is essential to note that the actual increase in money supply also depends on other factors, such as whether borrowers actually take out loans and how much money holders choose to deposit versus hold as cash. The money multiplier is a maximal theoretical increase, assuming the banks lend out as much as possible, and people re-deposit all the funds lent out.