Show the changes to the T-accounts for the Federal Reserve and

for commercial banks when the Federal Reserve buys $50
million in U.S. Treasury bills. If the public holds a fixed amount
of currency (so that all loans create an equal amount of deposits
in the banking system), the minimum reserve ratio is 10%, and
banks hold no excess reserves, by how much will deposits in the
commercial banks change? By how much will the money supply
change? Show the final changes to the T-account for commercial
banks when the money supply changes by this amount.

To understand the changes to the T-accounts and the impact on deposits in commercial banks, we need to go through the process step by step. Here's how the process plays out:

1. Federal Reserve Buys Treasury Bills:
When the Federal Reserve buys $50 million in U.S. Treasury bills, it typically does so through an open market operation. This means the Federal Reserve purchases the Treasury bills from the public or from commercial banks. In this case, let's assume it buys the Treasury bills from the public.

The T-account for the Federal Reserve would change as follows:
Federal Reserve
Assets: +$50 million (Treasury bills)
Liabilities: No change

2. Impact on Commercial Banks:
When the Federal Reserve buys Treasury bills, it pays the sellers. Let's assume the sellers deposit the payment in their commercial bank. Here's how the T-account for commercial banks would change:

Commercial Banks
Assets: +$50 million (Reserves)
Liabilities: No change

3. Impact on Deposits:
Given the assumption that the public holds a fixed amount of currency and all loans create an equal amount of deposits, we can infer that the amount deposited in commercial banks (reserves) will also become the amount available for lending. However, to calculate the change in deposits, we need to consider the minimum reserve ratio.

The minimum reserve ratio is given as 10%. This means banks must hold at least 10% of their deposits as reserves, and the remaining 90% can be lent out. Banks in this scenario have no excess reserves, so they must maintain the minimum required reserves based on the new deposit amount.

To calculate the change in deposits, we can use the reserve requirement and the reserve ratio.

Change in Deposits = Reserves / Reserve Ratio
Change in Deposits = $50 million / 0.10 (10% expressed as a decimal)
Change in Deposits = $500 million

Therefore, deposits in commercial banks would increase by $500 million.

4. Impact on the Money Supply:
The money supply is affected by changes in deposits and the reserve requirement. In this case, the change in deposits is $500 million, but we also need to consider the money multiplier effect. The money multiplier represents the increase in the money supply resulting from each dollar deposited in banks.

The money multiplier is calculated as:
Money Multiplier = 1 / Reserve Ratio

In this scenario, with a reserve ratio of 0.10 (or 10%), the money multiplier is:
Money Multiplier = 1 / 0.10
Money Multiplier = 10

To calculate the change in the money supply, we multiply the change in deposits by the money multiplier:

Change in Money Supply = Change in Deposits * Money Multiplier
Change in Money Supply = $500 million * 10
Change in Money Supply = $5 billion

Therefore, the money supply would increase by $5 billion.

Overall, the changes to the T-account for commercial banks when the money supply changes by $5 billion would be as follows:

Commercial Banks
Assets: +$50 million (Reserves)
Liabilities: +$500 million (Deposits)