Question

suppose that banks use x fraction of their deposits to buy treasuries. Derive the money multiplier as a function of x, currency-deposit ratio cdr, and actual reserve ratio ar. How does an increase in x aﬀect money multiplier, monetary base, and money supply?

Answer #1

Let’s assume “M=money supply”, “C=currency hold by people”, “D=deposits”, “B=monetary base”, “R=reserve” and “T=treasuries”. The money supply and monetary base are given below.

=> “M = C + D”, and “B = C + R + T”.

=> M/B = (C + D) / (C+ R + T), => M/B = (c*D + D) / (c*D+ r*R + x*D), where “c=currency deposit ratio”, “r = reserve deposit ratio” and “x = fraction of deposit to buy treasuries”.

=> M/B = (c + 1) / (c + r + x), => M = m*B, where “m=money multiplier”.

So, as “x” increases implied more of deposit are used to buy treasuries, => “T” increases, => the monetary base also increases. Here “m” is the money multiplier where “x” on the denominator, => as “x” increases the money multiplier decreases. Now, as the money multiplier decreases the money supply also decreases, => “x” and money supply are inversely related to each other.

4.
Money Supply
(a) Express the money multiplier (m) as a function of the
currency-deposit ratio and reserve to deposit ratio. Say, the
reserve-deposit ratio is 20% and the currency-deposit ratio is 40%.
If the monetary base is $18million, what is the total money supply
in the economy?
(b) What fraction of money supply is held as deposits?
(c) If several new ATMs are erected all throughout a country so
that it is now much easier for people to withdraw...

An economy requires banks to keep 10% of deposits as reserves.
Currency is 50 billion dollars and deposits are 2000 billion
dollars.
A) calculate the money supply
B) calculate the monetary base
C) If the central bank sells 20 billion in dollars worth of
securities calculate the resulting money supply assuming the
currency deposit ratio and the reserve deposit ratio stay the
same

Consider an economy where banks keep 25% of deposits as
reserves. Currency is 50 billion pesos, which constitutes 10% of
the monetary base. If the central bank buys 10 billion pesos worth
of securities, calculate the percentage change in the monetary base
and the percentage change in the money supply assuming that the
currency-deposit ratio and the reserve-deposit ratio stay
unchanged.

Suppose that currency in circulation (C) is $50 billion, the
amount of checkable deposits (D) is $500 billion, and excess
reserves (ER) are $20 billion. Also, the required reserve ratio
(rD) on checkable deposits is 5%. Calculate the money supply (M),
the required reserves (RR), the total reserves (R), the monetary
base (MB), the currency-to-deposit ratio (c), the excess
reserve-todeposit ratio (e), and the money multiplier (m)

Answer the questions on the money multiplier based on the
following information: Suppose that the required reserve ratio is
10%, currency in circulation is $600 billion, the amount of
checkable deposits is $950 billion, and excess reserves is $20
billion. a) The money supply is ____________ billion. b) The
currency deposit ratio is _____________. c) The excess reserves
ratio is ____________. d) The money multiplier is ____________. e)
Suppose the central bank conducts a large open market purchase of
bonds...

You are given the following information about the economy of
Nocoin
The banks have deposits of $300 billion. Their reserves are
$15 billion, two thirds of which is in deposits with the central
bank. Households and firms hold $30 billion in bank notes. There
are no coins!
The banks have no excess reserves.
Suppose that the central bank in Nocoin increases bank reserves
by $0.5 billion.
Explain why the change in the quantity of money is not equal to
the...

Suppose that currency in circulation is $800 billion, the amount
of checkable deposits is $1200 billion, the required reserve ratio
is 10% and excess reserves are $12 billion.
a. Calculate the money supply, the currency-to-deposit ratio,
the excess reserve ratio, and the money multiplier.
b. Suppose the central bank conducts an unusually large open
market purchase of bonds held by banks of $2000
billion due to a sharp contraction in the economy. Assuming the
ratios you calculated in part (a)...

Provide a brief explanation or show work
5. The ratio of the money supply to the monetary base is
called:
a. the currency–deposit ratio. b. the reserve–deposit ratio. c.
high-powered money. d. the money multiplier.
6. When the Fed makes an open-market sale,
it:
a. increases the money multiplier (m). b. increases the
currency–deposit ratio (cr). c. increases the monetary base (B). d.
decreases the monetary base (B).
7. Suppose the banking system currently has $400 billion
in reserves, the...

8. The reserve requirement, open market operations, and
the money supply
Assume that banks do not hold excess reserves and that
households do not hold currency, so the only form of money is
demand deposits. To simplify the analysis, suppose the banking
system has total reserves of $500. Determine the money multiplier
and the money supply for each reserve requirement listed in the
following table.
Reserve
Requirement
Simple Money Multiplier
Money
Supply
(Percent)
(Dollars)
25
10
A lower reserve requirement...

15. Under the assumptions of this chapter, the value of the
money multiplier (m) is:
a. Always a positive fraction (0 < m < 1)
b. Always greater than one (m > 1)
c. Not necessarily positive
d. Always less than the reserve-deposit ratio
16. The Federal Reserve, which is the central bank of the United
States, can increase the U.S. monetary base (B) by taking the
following action:
a. Increase the currency held by the public (C) by printing...

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