Question

	2007	2008
Currency Component of M1	760.6B	816.2B
Demand Deposits	606.5B	780.0B
Excess Reserves	1.785B	767.318B
Required Reserves	41.678B	53.558B

Monetary Base 2007= 847.370B 2008= 1669.269

Calculate the MI money multiplier for December of 2007 and for December of 2008.

Explain why the multiplier has changed the way it did and was this change anticipated by the Federal Reserve, why or why not?

What has happened to the relationship between C/D = c and the money multiplier = m between 12/07 and 12/08?

Using the data on the monetary base for 12/07 and the money multiplier for 12/07 (from above), calculate the money supply for 12/07.

Using the data on the monetary base for 12/08 and the money multiplier for 12/08 (from above), calculate the money supply for 12/08.

What is the percent change in the money supply between 12/07 and 12/08?

Assuming a stable money multiplier as of 12/07 and the same change in the monetary base, what would have been the percent change in the money supply?

Answer 1

Solution:

Given the following data, we can construct a table as follows,

	2007	2008
Currency Component of M1 (C)	760.6B	816.2B
Demand Deposits (D)	606.5B	780.0B
Excess Reserves (ER)	1.785B	767.318B
Required Reserves (rr)	41.678B	53.558B
Monetary Base (MB)	847.370B	1669.269

a) The MI money multiplier for December of 2007 and for December of 2008 ca be calculated using the following equation:

m 1 = 1 + ( C / D ) / [ r r + ( E R / D ) + ( C / D ) ]

where, ER/D =  excess reserves ratio, and

C/D = currency ratio.

Therefore, for 12/2007,

m 1 = 1 + ( 760.6/ 606.5) / [ 41.678 + ( 1.785 / 606.5 ) + ( 760.6/ 606.5) ]

= 1 + 1.2541/ 42.9350

= 1 + 0.02920 = 1.0292

For 12/2008,

m 1 = 1 + ( 816.2/ 780.0) / [ 53.558 + ( 767.318 / 780.0) + ( 816.2/ 780.0) ]

= 1 + 1.0464/ 55.5882

= 1 + 0.01882 = 1.0188

b) The money multiplier value fell from 1.0292 in 12/07 to 1.0188 in 12/08. This happened because the people were holding more currency in 2008 than they did in 2007. Also the excess reserves and the required reserves increased in 2008, this lead to a further decrease in the value of the money multiplier from 2007 to 2008.

Yes, this change was anticipated by the Fed as it is Fed who decides the level of required reserves and excess reserves that thte banks have to maintain. This indicates that the currency was not being transformed into credit via the commercial bank system as increasing amounts of it was being held as currency by the people and as reserves by the banks. So if the banks increased their reserves adhering to Fed's orders then Fed had very much anticipated this fall in the money multiplier.

c) Between 12/07 and 12/08 the value of C/D fell from 1.2541 to 1.0464 while the money multiplier value fell from 1.0292 to 1.0188. It is known that a rise in cash deposit ratio leads to a decrease in money multiplier. An increase in deposit rates will induce depositors to deposit more in the banks and this will lead to a decrease in cash to aggregate deposit ratio. This will in turn lead to a rise in the money multiplier.

d) Using the data on the monetary base for 12/07 and the money multiplier for 12/07 (from above), money supply (MS) for 12/07 is given by

ΔMS = m × ΔMB

Here, we do not know the change in monetary base. so we do not calculate the change in MS, but the MS itself

Therefore, MS₂₀₀₇ = m × MB

= 1.0292 x 847.370B

= 872.113204B

e) Using the data on the monetary base for 12/08 and the money multiplier for 12/08 (from above), money supply (MS) for 12/08 is given by

NOTE: The monetary base value for 2008 is given as 1669.269 and not as 1669.269B, so instead of proceeding with the given value, I have assumed the MB to be in billion$. The following answers a based on the assumed value.

MS₂₀₀₈ = m × MB

= 1.0188 x 1669.269

= 1700.651257B

f) The percent change in the money supply between 12/07 and 12/08

={ (1700.651257B - 872.113204B ) / 872.113204B } x 100

= 95.0035%

The money supply has increased by 95.0035% between 12/07 and 12/08.

g) Assuming a stable money multiplier as of 12/07 and the same change in the monetary base, the percent change in the money supply would have been,

ΔMS = m × ΔMB

= 1.0292 x 95.0035%

= 97.7774%

The money supply would have increased by 97.7774% for a 95.0035% increase in the monetary base in 12/2007.