Question

Suppose that the public wishes to hold 15 percent of its total money balances as cash, the remainder in the form of bank deposits, and banks hold cash reserves equal to 12 percent of the deposits. What total amount of cash will be required, for use both by the banks and the public, for a total money supply of \(\$ 200\) billion?

Short answer

The total amount of cash required for both the banks and the public for a total money supply of \(\$200\) billion is \(\$50.4\) billion.

Step-by-step solution

Calculate the amount of cash held by the public

Since the public wishes to hold 15% of its total money balances as cash, we need to find 15% of the total money supply (which is \(\$200\) billion). To calculate this, we simply multiply the total money supply by 15%: Public cash holdings = Total money supply * 15% = \(\$200\) billion * 0.15 = \(\$30\) billion

Calculate the amount held as bank deposits

Since the remainder of the money balances is held in the form of bank deposits, we subtract the public's cash holdings from the total money supply: Bank deposits = Total money supply - Public cash holdings = \(\$200\) billion - \(\$30\) billion = \(\$170\) billion

Calculate the cash reserves required by the banks

Banks need to hold cash reserves equal to 12% of their deposits. To calculate this, we multiply the bank deposits by 12%: Bank cash reserves = Bank deposits * 12% = \(\$170\) billion * 0.12 = \(\$20.4\) billion

Calculate the total amount of cash required

To find the total amount of cash required, we add the cash holdings of the public and the cash reserves of the banks: Total cash required = Public cash holdings + Bank cash reserves = \(\$30\) billion + \(\$20.4\) billion = \(\$50.4\) billion Therefore, the total amount of cash required for both the banks and the public for a total money supply of \(\$ 200\) billion is \(\$50.4\) billion.

Key concepts

Cash Reserve Ratio

Understanding the cash reserve ratio (CRR) is essential in monetary economics, as it impacts how much money a bank can loan out and thus influences the overall money supply in the economy. CRR refers to the percentage of a bank's total deposits that must be kept in reserve and not used for lending. For instance, a 12% CRR means that for every \(100\) units of currency deposited, \(12\) units must be kept in reserve. The central bank often sets this rate, and it serves as a regulatory tool to ensure that banks have enough liquidity to meet demand for withdrawals and to manage inflation.

In our exercise, the banks' CRR is set at 12%. If banks possess \(\$170\) billion in deposits, they need to reserve \(\$170\) billion * 0.12 = \(\$20.4\) billion in cash. This cash is not available for lending or investment, but it's a safety net for the stability of the banking system.

Bank Deposits

Bank deposits represent the funds that individuals and businesses place in a bank for safety and to earn interest. These deposits can take various forms, including savings accounts, checking accounts, and time deposits. When people choose to hold their money in banks, this money becomes part of the bank's reserves, which the bank can then use to make loans to other customers.

The amount of money held in deposits is critical for calculating the money supply since a portion of these deposits will be held as the bank's reserves (CRR). In the given exercise, the public retains 85% (100% - 15% cash holding preference) of their total money as bank deposits, which equals \(\$170\) billion from a \(\$200\) billion money supply. Thus, bank deposits play a vital role in determining how much money banks can create through loans, significantly influencing the overall economy.

Public Cash Holdings

Public cash holdings are the physical money that people choose to keep on hand instead of depositing into a bank account. This can include currency notes and coins in their wallets, houses, or other secure places. The preference for holding cash varies among individuals and is influenced by factors such as convenience, trust in financial institutions, and accessibility to banking services.

In the context of our exercise, the public decides to hold 15% of their total money balances in cash, meaning that out of a \(\$200\) billion money supply, \(\$30\) billion is held as cash by the public. This portion of money supply does not contribute to the reserves of banks, and consequently, it affects the bank’s capability to create additional money through lending.

Monetary Economics

Monetary economics is a branch of economics that examines the role of money and financial institutions in the overall economy. It explores how the policies of central banks, changes in the money supply, and the regulation of financial markets affect inflation, employment, and economic growth. One of the fundamental concepts in monetary economics is the money creation process, which involves how commercial banks can lend more than the amount of their actual reserves by keeping a fraction of deposits on reserve (the CRR).

The exercise we are discussing illustrates how monetary policy tools, like the cash reserve ratio, influence the total money supply. With a target money supply of \(\$200\) billion, adjustments to the CRR or changes in public cash holding preferences significantly alter the amount of money available in the economy for lending and economic activities.