EC 223 Economics of the Canadian Banking and Financial System Instructor: Sharif F. Khan

Department of Economics Wilfrid Laurier University Fall 2010

Suggested Solutions to Assignment 2 (Optional) Total Marks: 40 Read each part of the question very carefully. Show all the steps of your calculations to get full marks. B1. [5 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 * :

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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 = 940 − × 671.43 = 940 − 268.57 = $771.43 5 5 * * P = 100 + B = 100 + 671.43 = $771.43

P * = 940 −

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%.

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B2. [5 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. [5 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 (page 96 of the 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, 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.

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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 5-10 of the textbook (page 104 of the 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 94-95 of the textbook (4th ed.).

B5. [5 marks] Many commentators, including high officials of the Bank of Canada, have blamed the profligate spending habits of the Canadian public for high interest rates. Using the supply and demand for bonds framework, explain whether they right or wrong. See “Application – Have low Savings Rates in Canada Led to Higher Interest Rates?” and Figure 5-8 on pages 98-99 of the textbook (4th ed.).

B6. [5 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.

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B7. [5 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.

B8. [5 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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