Download Suggested Solutions to Assignment 2 (Optional)

EC 223
Economics of the Canadian Banking and Financial System
Instructor: Sharif F. Khan
Department of Economics
Wilfrid Laurier University
Winter 2014
Suggested Solutions to Assignment 2 (Optional)
Total Marks: 42
Read each part of the question very carefully. Show all the steps of your calculations to
get full marks.
B1. [6 marks]
The demand curve and supply curve for one-year T-bills (with a face value of $1000)
were estimated using the following equations:
2 d
B
5
P = 100 + B S
P = 940 −
where P is the price of bonds, B d is the quantity demanded of bonds and B s is the
quantity supplied of bonds.
Following a dramatic decline in the value of the stock market, the demand for bonds
increased and this resulted in a parallel shift in the demand curve for bonds, such as
the price of bonds at all quantities increased $100. Assuming no change in the
supply function for bonds, what is the new equilibrium price and quantity? What is
the new market interest rate?
2 d
B
5
The supply curve for bonds: P = 100 + B S
The demand curve for bonds: P = 940 −
The new demand curve for bonds: P = 1040 −
(1)
(2)
2 d
B
5
(3)
At the bond market equilibrium, B d = B s . To find the new equilibrium quantity of
bonds we have to set B d = B s = B * and solve the new demand function, equation (2),
and the supply function, equation (3), simultaneously for B * :
Page 1 of 5 Pages
1040 −
2 *
B = 100 + B *
5
⇒ B* +
2 *
B = 1040 − 100
5
7 *
B = 940
5
940 * 5
⇒ B* =
7
*
∴ B = 671.43
⇒
So, the new equilibrium quantity of bonds, B * , is 671.43.
We can find the new equilibrium price of bonds by substituting the value of new
equilibrium quantity of bonds into the new demand function, equation (3), or into the
supply function, equation (2):
2 *
2
B = 1040 − × 671.43 = 1040 − 268.57 = $771.43
5
5
*
*
P = 100 + B = 100 + 671.43 = $771.43
P * = 1040 −
So, the new equilibrium price of bonds, P * , is $771.43.
The yield to maturity or the interest rate on any one-year discount bond can be written as
i=
where
F−P
P
P = current price of the discount bond = $771.43
F = face value of the bond= $1000
Thus
$1000 − $771.43
$771.43
⇒ i = 0.29629
i=
∴ i = 29.629%
Thus, the new market interest rate is 29.629%.
Page 2 of 5 Pages
B2. [6 marks]
Using the theory of asset demand, explain why you would be more or less willing to
buy long-term Air Canada bonds under the following circumstances:
a. Trading in these bonds increases, making them easier to sell.
b. You expect a bear market in stocks (stock prices are expected to decline).
c. Brokerage commissions on stocks fall.
d. You expect interest rates to rise.
e. Brokerage commissions on bonds fall.
a) More, because the bonds have become more liquid.
b) More, because their expected return has risen relative to stocks.
c) Less, because they have become less liquid relative to stocks.
d) Less, because their expected return has fallen.
e) More, because they have become more liquid.
B3. [6 marks]
Using both the liquidity preference framework and the supply and demand for
bonds framework, explain why interest rates are pro-cyclical (rising when the
economy is expanding and falling during recessions).
In the loanable funds (the supply and demand for bonds) framework, when the economy
booms, the demand for bonds increases. The public’s income and wealth rises while the
supply of bonds also increases, because firms have more attractive investment
opportunities. Both the supply and demand curves ( B d and B s ) shift to the right. In
Figure 5-6 of the textbook (5th or 4th edition), it is shown as a rightward shift from B1d to
B2d and from B1s to B2s . Depending on whether the supply curve shifts more than
demand curve or vice versa, the new equilibrium interest can either rise or fall. The
supply and demand for bonds framework gives us an ambiguous answer to the question
of what will happen to interest rate in a business cycle expansion. But as it is indicated in
the textbook, based on the empirical observations we can argue that the demand curve
probably shifts less than the supply curve, as it is shown in Figure 5-6 of the textbook (5th
or 4th edition), causing an excess supply of bonds at the initial equilibrium bond price P1 ,
leading to a decrease in the bond price to P2 , resulting into a rise in the equilibrium
interest rate in a business cycle expansion. Similarly, when the economy enters a
recession, both the supply and demand curves shift to the left, but the demand curve
shifts less than the supply curve, so that the interest rate falls. The conclusion is that
interest rates rise during booms and fall during recessions: that is, interest rates are
procyclical.
Page 3 of 5 Pages
The same answer is found with the liquidity preference framework. When the economy
booms, the demand for money increases; people need more money to carry out an
increased amount of transactions and also because their wealth has risen. The money
demand curve, M d , shifts to the right for any given level of the interest rates. In Figure
5-9 of the textbook (5th ed.) or Figure 5-10 of the textbook (4th edition), it is shown as a
rightward shift from M 1d to M 2d , causing an excess demand for money at the initial
equilibrium interest rate i1 . The excess demand for money implies an excess supply of
bonds. This excess supply of bonds will lead to a decrease in the price of bonds. As the
price of bonds falls, the interest rate will rise toward the new equilibrium interest rate i2 .
When the economy enters a recession, the demand for money falls and the demand curve
shifts to the left, lowering the equilibrium interest rate. The liquidity preference
framework thus generates an unambiguous conclusion that interest rates are procyclical.
B4. [6 marks]
Using the supply and demand for bonds framework, explain why interest rates rise
when expected inflation rises.
See “Application - Changes in the Interest Rate Due to Expected Inflation: The Fisher
Effect” and Figure 5-4 on pages 95-96 of the textbook (5th ed.).
Or,
See “Application - Changes in the Interest Rate Due to Expected Inflation: The Fisher
Effect” and Figure 5-4 on pages 94-95 of the textbook (4th ed.).
B5. [6 marks]
If the next governor of the Bank of Canada announces has a reputation for
advocating an even slower rate of money growth than the current governor, what
will happen to interest rates? Discuss the possible resulting situations.
The slower rate of money growth will lead to a liquidity effect, which raises interest
rates, while the lower price level, income, and inflation rates in the future will tend to
lower interest rates. There are three possible scenarios for what will happen: (a) if the
liquidity effect is larger than the other effects, then interest rates will rise; (b) if the
liquidity effect is smaller than the other effects and expected inflation adjusts slowly, then
interest rates will rise at first but will eventually fall below their initial level; and (c) if the
liquidity effect is smaller than the expected inflation effect and there is rapid adjustment
of expected inflation, then interest rates will immediately fall.
Page 4 of 5 Pages
B6. [6 marks]
There are three goods produced in an economy by three individuals:
Good
Apples
Bananas
Chocolate
Producer
Orchard owner
Banana grower
Chocolatier
If the orchard owner likes only bananas, the banana grower likes only chocolate,
and the chocolatier likes only apples, will any trade among these three persons take
place in a barter economy? How will introducing money into the economy benefit
these producers?
Because the orchard owner likes only bananas but the banana grower doesn’t like apples,
the banana grower will not want apples in exchange for his bananas, and they will not
trade. Similarly, the chocolatier will not be willing to trade with the banana grower
because she does not like bananas. The orchard owner will not trade with the chocolatier
because he doesn’t like chocolate. Hence, in a barter economy, trade among these three
people may well not take place, because in no case is there a double coincidence of
wants. However, if money is introduced into the economy, the orchard owner can sell his
apples to the chocolatier and then use the money to buy bananas from the banana grower.
Similarly, the banana grower can use the money she receives from the orchard owner to
buy chocolate from the chocolatier, and the chocolatier can use the money to buy apples
from the orchard owner. The result is that the need for a double coincidence of wants is
eliminated, and everyone is better off because all three producers are now able to eat
what they like best.
B7. [6 marks]
How can the adverse selection problem explain why you are more likely to make a
loan to a family member than to a stranger?
Because you know your family member better than a stranger, you know more about the
borrower’s honesty, propensity for risk taking, and other traits. There is less asymmetric
information than with a stranger and less likelihood of an adverse selection problem, with
the result that you are more likely to lend to the family member.
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