Download In Class Exercise 3

Econ 212
Prof. Cotton
In Class Exercise #3
Let:
MS = money supply
MD = money demand
i = interest rate
Assume for a given economy:
(i)
Consumers spend $100 billion plus 80% of after-tax income, or
C  100  0.8(Y  Tx) .
(ii)

Investment demand is decreasing in the interest rate, such that
I  250 1000i .
(iii)

Government spending is $100 billion and taxes are $125 billion, or
G  100 and Tx  125 .
(iv)

The total money demand curve for this economy is an inverse function of the rate

of interest and is given by the equation
MD 1200 1000i .
(v)
The required reserve ratio for banks in this economy is 15%. The total of reserves
 in the banks is $150 billion. No bank holds excess reserves. In addition to
reserves, there is $100 billion in cash in the economy.
Econ 212
Prof. Cotton
FOR EACH ANSWER, SHOW ALL YOUR WORK.
I.
(a) What is the total money supply? (Hint: begin with (v) above, and use the
required reserve ratio and total amount of reserves to find your answer.)
(b) Graph the market for money, including the money demand curve and the
money supply curve. (Hint: Remember that the money supply curve is a
vertical line.)
(c) What is the equilibrium interest rate? (Hint: in equilibrium, money supply
equals money demand. This is the equilibrium price in the market for money
from part (b). The answer is 5%, 10%, 15%, 20% or 25%.)
(d) What is the equilibrium level of investment, I, given this interest rate?
(e) What is the equilibrium level of national income, Y?
II.
The central bank wants to achieve national income of $1500 billion through open
market operations.
(a) What must investment be for the equilibrium level of national income to be
$1500 billion?
(b) At what interest rate is this level of investment achieved?
(c) If the central bank pursues this level of national income through open market
operations, should it buy or sell bonds?
(d) Assume that the open market operation increases the money supply through
its affect on deposits (i.e., cash stays constant at $100 billion). Banks hold no
excess reserves. How many dollars in bonds must the central bank buy or sell
to achieve this desired interest rate? (Hint: first determine the money supply
necessary to achieve the desired i, then using the required reserve ratio,
determine the dollars in bonds bought or sold.)
(e) If instead of open market operations the central bank pursues this equilibrium
level of national income by changing the required reserve ratio, should it
increase or decrease the ratio?