This is “The M2 Money Multiplier”, section 15.2 from the book Finance, Banking, and Money (v. 1.1).
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Note that m_{1} is the M1 money multiplier. With a little bit more work, one can also calculate the M2 money multiplier (m_{2}). Recall from Chapter 3 "Money" that M2 = C + D + T + MMF, where T = time and savings deposits and MMF = money market funds, money market deposit accounts, and overnight loans. We account for the extra types of deposits in the same way as we accounted for currency and excess reserves, by expressing them as ratios against checkable deposits:
(T/D) = time deposit ratio
(MMF/D) = money market ratio
which leads to the following equation:
$${m}_{2}=1+(C/D)+(T/D)+(MMF/D)/[rr+(ER/D)+(C/D)]$$Once you calculate M2, multiply it by the change in MB to calculate the change in the MS, specifically in M2, just as you did in Exercise 2. Notice that the denominator of the m_{2} equation is the same as the m_{1} equation but that we have added the time and money market ratios to the numerator. So M2 is alwaysM2 would equal m_{1} iff T = 0 and MMF = 0, which is highly unlikely. Note: iff means if and only if. > m_{1}, ceteris paribus, which makes sense when you recall that M2 is composed of M1 plus other forms of money. To verify this, recall that we calculated m_{1} as 2.6316 when
Required reserves (rr) = .2
Currency in circulation = $100 million
Deposits = $400 million
Excess reserves = $10 million
We’ll now add time deposits of $900 million and money market funds of $800 million and calculate M2:
$${m}_{2}=1+(C/D)+(T/D)+(MMF/D)/[rr+(ER/D)+(C/D)]$$ $${m}_{2}=1+(100/400)+(900/400)+(800/400)/[.2+(10/400)+(100/400)]$$ $${m}_{2}=1+.25+2.25+2/(.2+.005+.25)$$ $${m}_{2}=5.5/.455=12.0879$$This is quite a bit higher than m_{1} because time deposits and money market funds are not subject to reserve requirements, so they can expand more than checkable deposits because there is less drag on them during the multiple expansion process.
Practice calculating the M2 money multiplier on your own in the exercise.
Calculate the M2 money multiplier using the following formula: M2 = 1 + (C/D) + (T/D) + (MMF/D)/[rr + (ER/D) + (C/D)].
Currency | Deposits | Excess Reserves | Required Reserve Ratio | Time Deposits | Money Market Funds | Answer: M2 |
---|---|---|---|---|---|---|
100 | 100 | 10 | 0.1 | 1,000 | 1,000 | 18.33 |
100 | 100 | 10 | 0.2 | 1,000 | 100 | 10 |
100 | 100 | 10 | 0.2 | 100 | 1,000 | 10 |
1,000 | 100 | 10 | 0.2 | 1,000 | 1,000 | 3.01 |
1,000 | 100 | 50 | 0.2 | 1,000 | 1,000 | 2.90 |
100 | 1,000 | 50 | 0.2 | 1,000 | 1,000 | 8.86 |
100 | 1,000 | 0 | 1 | 1,000 | 1,000 | 2.82 |
100 | 1 | 10 | 0.1 | 1,000 | 1,000 | 19.08 |