Question

2. a. With appropriate equations and notations, derive the money multiplier (M1).

b) AMALAND is a country with a required reserve ratio of 10%. Assume that the banking system has an excess reserves equal to 4 billion. Further, the currency in circulation equals 450 billion, and the total amount of checkable deposits equals 900 billion. Based on these numbers, calculate (i) required reserves held by the banking system (ii) total reserves held by the banking system, (iii) monetary base (iv) total money supply (M1) l (v) the money multiplier

Answer 1

In economics, the money multiplier shows how an initial deposit brings forth to a greater final increase in the total money supply in the economy. It refers to the highest degree to which the money supply is influenced by changes in the quantity of deposits.

Let us consider a model of the money supply under fractional-reserve banking with three exogenous variables.

1. The monetary base (B) is the total number of dollars held by the public as currency (C) and by the banks as reserves (R). It is directly controlled by the Central Bank.

2. The reserve–deposit ratio (rr) is the fraction of deposits that banks hold in reserve. It is determined by the business policies of banks and the laws regulating banks.

3. The currency–deposit ratio (cr) is the amount of currency (C) people hold as a fraction of their holdings of demand deposits (D). It reflects the preferences of households about the form of money they wish to hold.

The model shows how the money supply depends on the monetary base, the reserve–deposit ratio, and the currency–deposit ratio. It allows us to examine how Central Bank policy and the choices of banks and households influence the money supply.

Let us begin with the definitions of the money supply and the monetary base:

M = C + D,

B = C + R.

The first equation states that the money supply is the sum of currency and demand deposits. The second equation states that the monetary base is the sum of currency and bank reserves. To solve for the money supply as a function of the three exogenous variables (B, rr, and cr), we first divide the first equation by the second to obtain

M/B = (C + D)/(C + R)

Then divide both the top and bottom of the expression on the right by D.

M/B = (C/D + 1) / (C/D + R/D)

Note that C/D is the currency–deposit ratio cr, and that R/D is the reserve–deposit ratio rr. Making these substitutions, and bringing the B from the left to the right side of the equation, we obtain

M = {(cr + 1) / (cr + rr)} x B

This equation shows how the money supply depends on the three exogenous variables. We can now see that the money supply is proportional to the monetary base. The factor of proportionality, (cr + 1)/(cr + rr), is denoted m and is called the money multiplier. We can write

M = m × B

Each dollar of the monetary base produces m dollars of money. Because the monetary base has a multiplied effect on the money supply, the monetary base is sometimes called high-powered money.

With appropriate equations and notations, derive the money multiplier (M1). (5 marks)

b) AMALAND is a country with a required reserve ratio of 10%. Assume that the banking system has an excess reserves equal to 4 billion. Further, the currency in circulation equals 450 billion, and the total amount of checkable deposits equals 900 billion. Based on these numbers, calculate (i) required reserves held by the banking system (ii) total reserves held by the banking system, (iii) monetary base (iv) total money supply (M1) l (v) the money multiplier

It is given that,

Required reserve ratio (R) = 10% = 0.1

Excess reserves (ER) = 4 billion.

Currency in circulation (C) = 450 billion,

Total amount of checkable deposits (D) = 900 billion

i. Required reserves held by the banking system (RR) = Required reserve ratio x Total amount of checkable deposits

Required reserves held by the banking system (RR) = 0.1 x 900 = 90 billion

ii. Total reserves held by the banking system (R) = Required reserves held by the bank (RR) + Excess reserves (ER)

Total reserves held by the banking system (R) = 90 + 4 = 94 billion

iii. Monetary base (B) = Currency in circulation (C) + Total reserves held by the bank (R)

Monetary base (B) = 450 + 94 = 544 billion

iv. Total money supply (M) = Currency in circulation (C) + Total amount of checkable deposits (D)

Total money supply (M) = 450 + 900 = 1350 billion

v. The money multiplier (m) = Total money supply (M) / Monetary base (B)

The money multiplier (m) = 1350 / 544 = 2.4816 billion