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Econ 116 Spring 2009 Problem Set 3 Solutions
1. Assume that a bank has on its asset side reserves of 500 and
loans of 3000 and
on its liability side deposits of 3500. Assume that the required
reserve ratio is 10
percent.
(a) How much is the bank required to hold as reserves given its
deposits of 3500?
(b) How much are its excess reserves?
Since the bank is holding $500, 500-350=$150 is the amount of
excess reserves.
(c) By how much can the bank increase its loans?
The bank can increase its loans by the amount of total excess
reserves, which is $150.
So they can make additional loans worth of $150.
(d) Suppose a depositor comes to the bank and withdraws 200 in
cash. Show the
banks new balance sheet, assuming the bank obtains the cash by
drawing down its
reserves. Does the bank now hold excess reserves? Is it meeting
the required reserve
ratio? If not, what can it do?
2. The T-account analysis in class showed that the Fed can
increase the money
supply by buying government securities. Why does this action
lower the interest rate?
What assumptions are you making about the demand for money in
your answer?
Explain carefully.
M
r
M*
r*
MS
MD
MS
M**
r**
To increase money supply, Fed, through open
market operations, purchases bonds from public.
This will drive up the price of the bonds in the
open market. Since we know that bond prices are
negatively related to interest rates, interest rates
will decrease.
Since rrr (required reserve ratio or reserve to deposit
ratio)=0.10, then minimum amount of reserves the bank
should hold is R*/D=0.10 => R*/3500=0.10=>R*=350.
Bank is reuired to hold b law at least $350.
Balance Sheet of Bank
Assets Liabilities
R0500 D03500
L03000
Now the bank has $300 in reserves which is $50 less thanthe
required reserve amount. In this case, at the end of the
day, when the bank closes its balances, it can either borrow
from the Fed (using the discount rate) or from other
commercial banks (using the federal funds rate) to achieve
reuired reserve ratio.
Balance Sheet of Bank (afterthe withdrawal) Assets
Liabilities R0300
D03200
L03000
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3. Since the U.S. Treasury must sell government securities to
finance any deficit
that it may run, is it ever possible for a deficit to be
financed by printing money?
Explain carefully. (Hint: the answer is yes.) How is the
interest rate affected, if at all,
when deficits are financed without printing money?
Yes, The Fed could buy newly issued government bonds directly
from the government
(the Treasury).As Fed buys these bonds from the Treasury, and as
Treasury spends
the money, money supply in the economy will increase through the
money multiplier,
which will reduce interest rates.
If government finances its deficit by borrowing from public
(through bonds), there
won't be any change in the money supply. (Think of this as a
transaction between 2parties one borrowing from the other). Since
there is no change in the money supply,
interest rates will stay the same.
4. As recently as last year when Professor Fair went to an ATM
machine to
withdraw money from his interest bearing money market account he
withdrew $300.
Now he withdraws $500. Is this rational on his part? Why or why
not? (Professor Fair
will not feel bad if you say he is not rational as long as this
is the correct answer.)
In this question, we have to understand Professor Fairs demand
for money. Assuming
Professor Fair lives in a Keynesian world, then his money demand
will depend on threevariables, price level, interest rates, and his
income level. MD= f(P,r,Y). In this
equation, as Interest rate increases, your money demand will
decrease (Since you can
earn more by depositing your money to the bank and youll have
less money in your
hand). As your income increases your money demand will increase
(As your income
increases youll engage in more transactions.) Finally, as prices
increase your money
demand will increase (Youll need more money for your
transactions.) Assuming price
level and Professor Fairs income level didnt change over the
last year, and knowing
that Fed decreased the interest rates, we can claim that his
average money holdings
increased over the last year due to the decrease in interest
rates. So he is perfectly
rational.
5. Say you bought a 10-year government bond last year that
yielded 4.5 percent
per year. Assume that since that time the 10-year government
bond rate has dropped
to 3.0 percent. Are you better off or worse off after this drop?
Explain carefully. How is
this related to Professor Serebryakov?
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To make our answer simple, suppose we have a console bond (a
bond that pays a fixed
amount forever). Then, Pb=(1/r), where Pb is the price of the
bond, and r is the
interest rate. In this equation, if the interest rate drops, you
are obviously better off,
since the price of the bond will increase (note, since you
already own the bond when
the interest rates decrease, you will still earn the same coupon
from the bond and
receive a higher price should you wish to sell).
