Worked Problem: Multiplying Money

As part of the Economic Stimulus Act of 2008, the U.S. government issued tax rebate checks to eligible households. On average, rebate checks totaled $950.00.

Economists have estimated that each household initially spent about $450.00 of the rebate. Since the public holds about 50% of M1 in the form of currency, the average household deposited about $250.00 of the remaining $500.00 and held the other $250.00 in cash. In light of this data, approximately how much will the money supply increase in response to the average household’s deposit? (Hint: Create a table that shows the change in the money supply for ten rounds.) Assume that banks lend out the full amount of any excess reserves.

Find the required reserve ratio in the United States.

In order to find and understand the U.S. required reserve ratio, read the section “The Monetary Role of Banks,” beginning on page 488. Pay close attention to the subsections, “What Banks Do,” beginning on page 488, and “Bank Regulation,” beginning on page 490.

The required reserve ratio in the United States is 10%.

Make a table that shows on line 1 the initial deposit, the required reserves, the excess reserves, the loans that a bank makes, and the amount held in currency from the initial loans made by the bank.

Read the subsection, “Bank Regulation,” beginning on page 490, and the section, “Reserves, Bank Deposits, and the Money Multiplier,” beginning on page 494, to help determine the required reserves, excess reserves, and the loans made. The amount held in currency from the initial loans made by the bank is the amount in the loan that “leaks” out of the banking system, which is also discussed in the section, “Reserves, Bank Deposits, and the Money Multiplier.”

The first line of this table is shown here.

Round Deposits Required reserves Excess reserves Loans Held as currency
1 $250.00 $25.00 $225.00 $225.00 $112.50

The deposit amount is $250.00. As determined in Step 1, the required reserves are 10% of this deposit amount: 10% × $250.00 = $25.00. The excess reserves are therefore $250.00 − $25.00 = $225.00. We have assumed that banks loan out all of their excess reserves, so they loan out $225.00. Of this amount, the public will hold 50% in currency: 50% × $225.00 = $112.50.

Extend this table for 10 rounds.

If, after the first round, the public has held $112.50 of $225.00 in loans as currency, then the second round will begin with a deposit of $112.50 = $225.00$112.50. Each round begins with the difference between the loan amount and the amount held in currency from the previous round.

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The extended table is shown below.

Round Deposits Required reserves Excess reserves Loans Held as currency
1 $250.00 $25.00 $225.00 $225.00 $112.50
2  112.50  11.25  101.50  101.25  50.63
3   50.63   5.06   45.56   45.56   22.78
4   22.78   2.28   20.50   20.50   10.25
5   10.25   1.03   9.23   9.23   4.61
6   4.61   0.46   4.15   4.15   2.08
7   2.08   0.21   1.87   1.87   0.93
8   0.93   0.09   0.84   0.84   0.42
9   0.42   0.04   0.38   0.38   0.19
10   0.19   0.02   0.17   0.17   0.09
Total after 10 rounds $454.39 $45.44 $408.95 $408.95 $204.48

Round 2 is constructed in the same manner as Round 1 above. The round begins with a deposit of $112.50. The bank holds $11.25 of this as reserves, and so the excess reserves and the amount loaned out is $112.50 − $11.25 = $101.25. Of this, the public keeps $50.63 in currency.

Determine the increase in the money supply that results from the average household deposit.

Read the section “How Banks Create Money” beginning on page 492. The amount of the increase in the money supply is the total amount that banks have been able to loan out in response to the first deposit.

The approximate increase in the money supply from the average household deposit is $408.95.