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JOHANNES KEPLER UNIVERSITÄT

DEPARTMENT OF ECONOMICS

IK: Einkommen Inflation and Arbeitslosigkeit WS08/09

Worksheet 4: Financial markets 27 October 2008 Question 1 In the notation used by Blanchard, you have been provided with the following information: R = 50, CU = 250, D = 250. Answer the following questions:

a. Calculate the reserve ratio θ. Θ = D/R = 250/50 = 0.2 b. Calculate what proportion of people’s total money holdings are held in the form

of cash (i.e. calculate the value of c). c = CU/(CU+D) = 250/500 = 0.5 c. Calculate the magnitude of the monetary base (or high-powered base) H. H =

CU+R = 50+250 = 300 d. Calculate the magnitude of the money supply Ms. Ms = CU + D = 250 + 250 =

500 e. Calculate the magnitude of the money multiplier. Multiplier = 1/[c + θ(1-c)] =

1/[0.5 + 0.2(1-0.5)]= 1.667; Alternatively multiplier = M/H = 500/300 = 1.667 Question 2 Imagine that a European country’s government wishes to raise money, and does so by selling bonds. They sell the bonds for 1 million euro on 1 January 2007, and will pay 5% interest on 31 December 2007 and 31 December 2008, when the capital amount will also be redeemed. When the bond was launched on 1 January 2007 the two-year interest rate was 5%. Now it is 1 January 2008. The interest for the previous year has been paid the day before.

a. How much interest did the holder of the bond receive the previous day? 50 000 euro

b. If the holder of the bond wishes to sell the bond and the one-year interest rate on such bonds is 4%, how much can he sell the bond for? (1 000 000 x 1.05)/1.04 = 1 009 615 euro

c. If the one-year interest rate were to be 5%, how much would he be able to sell the bond for? (1 000 000 x 1.05)/1.05 = 1 000 000 euro

d. If the one-year interest rate were to be 6%, how much would he be able to sell the bond for? (1 000 000 x 1.05)/1.06 = 990 566 euro

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e. If someone had bought the bond for 985 000 euro on 1 January 2008 (please note the change), what is the implied one-year return on that bond? (1 000 000 x 1.05)/(1+i) = 985 000, solving for i yields i = 6.599%1

f. If someone had bought the bond for 975 000 euro on 1 January 2008 (please note the change), what is the implied one-year return on that bond? (1 000 000 x 1.05)/(1+i) = 975 000, solving for i yields i = 7.692%

g. If we hear “The bond market has fallen”, does that mean that the interest rate on bonds has decreased? Why or why not? No, it means that the bonds are sold for a lower amount and the implied yield on them has increased.

Question 3 (taken from Blanchard) Suppose the following assumptions hold:

• The public holds no currency; i.e. CU = 0; c = 0 • The ratio of deposits to reserves is 10; i.e. θ = 0.1 • The demand for money is given by Md = $Y (0.8 – 4i) • Initially the monetary base is $100 billion and nominal income is $5000 billion,

i.e. H = 100 and $Y = 5000 a. What is the demand for central bank money? Hd = [c + θ(1-c)] $Y (0.8 – 4i) =

0.1 $Y (0.8 – 4i) = 0.1 Md b. Find the equilibrium interest rate by setting the demand for central bank money equal

to the supply of central bank money. 100 = 0.1 (5000) (0.8 – 4i); solving for i yields i = 0.15 = 15%

c. What is the overall supply of money? Is it equal to the overall demand for money at the interest rate you found in (b)? Ms = (1/0.1) 100 = 100; Md = 5000 [0.8 – 4(0.15)] = 1000

d. What is the impact on the interest rate if central bank money is increased to $300 billion? 300 = 0.1 (5000) (0.8 – 4i); solving for i yields i = 0.05 = 5%

e. If the overall money supply increases to $300 billion, what will be the impact on the interest rate? (Hint: use what you have learnt in (c))? Note that this is a typing error that I copied from Blanchard. How can the money supply increase from 1000 to 300? The answer: 300 = 5000 (0.8-4i); solving for i yields i = 0.18.

Question 4 Consider the financial markets of Randland as defined by the following information: Give your answers to the nearest rand. Md = $Y*L(i) CUd = ? Dd = ? Rd = ? Hd = ? 1 Please note the original typing error. However, if the bond, with a face value of 1 000 000 euro was bought at 985 000 euro on 1 Jan. 2007, then the implied return would be calculated as follows: 985 000 = 50 000/(1+i) + 1 050 000/(1+i)2. Through interpolation (or other means), i = 5.815% (approx.). Similarly, for part f the yield would be approximately 6.37%.

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H = ? Nominal income ($Y) = R20 000 000 Velocity of circulation = 1/(1-4i) The current interest rate on bonds is 7% Reserve ratio = 10% You may assume that people demand 70% of their total money demand in checkable deposits.

a. Show that the equilibrium demand for money is R14 400 000. Md = 20 mill [1-4(0.07)] = 14.4 mill

b. What is the demand for currency? CUd = c Md = 0.3 (14.4 million) = 4.32 million c. What is the demand for checkable deposits? 0.7 (14.4 million) = 10.08 million d. What is the demand for central bank money? Hd = [c + θ(1-c)] Md = [0.3 +

0.1(1-0.7)] 14.4 million = 0.37 x 14.4 million = 5.328 million e. What is the value of the monetary multiplier? 1/0.37 = 2.703 f. If there was on increase in nominal income of R375, by how much would the

SARB have to change the supply of central bank money to prevent the interest rate from changing? Show all workings (round off to the nearest Rand for your final answer). First calculate change in Md = ∆Md = ∆$Y (1-4i) = 375 (0.72) = 270; then ∆Hd = 0.37 ∆Md = 0.37 x 270 = 100.

g. Explain why your answer in (f) makes intuitive sense. Greater level of income increases demand for money. If the supply does not increase, the interest rate would have to increase (but we assume here that the central bank does not want the interest rate to increase). The central bank increases H by an amount. The money supply increases by a multiplied amount, through the money multiplier. The increase in the money supply is exactly enough to meet the increase in the demand for money.

h. Suppose that the central bank of Randland is concerned about credit growth and they believe that an increase in the equilibrium interest rate (here you can assume they are concerned with the interest rate on bonds) of 1% will be enough to curb the credit growth. By how much do they need to decrease the supply of central bank money to achieve this? New Hd = [0.3 + 0.1(0.7)] x 20 million x [1 – 4(0.08)] = 0.37 x 20 million x 0.68 = 5.032; thus reduce Hd by 5.328 – 5.032 = 0.296 million

i. How would they accomplish this increase through changing the supply of central bank money? Open Market Operations; sell bonds to banks and the public.

j. If instead they decided to try and accomplish the same goal altering the amount of money created by the commercial banks how would they do this? What variable would they change and by how much? 5.328 = [0.3 + θ’(0.7)] 20 [1 – 4(0.08)]; solving for θ’ yields θ’ = 0.131

k. How could a change in consumer behaviour alter the multiplier? Through changes in c; if c increases the multiplier decreases. If H remains unchanged, an increase in c will reduce the money supply; similarly, a decrease in c will increase the money supply.

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Question 5 a. Intuitively, explain the concept of the velocity of money. See Blanchard pp 70-71. b. Did the rise of credit cards theoretically cause the function L(i) to increase or

decrease? Does this represent an increase or decrease in the velocity of money? Reduces L(i), since for each level of interest rate, people demand to hold less money. The inverse of L(i) is the velocity of money; and because people hold less money on average (because they pay the credit card, say, once a month and not each time they make a transaction) less money is required to finance the same number (volume) of transactions, with the result that the velocity of money increases.

c. Intuitively, why would an increase in the interest rate lead to a decline in the demand for money? The opportunity cost of holding money (which bears no interest) becomes larger and thus people demand to hold less money

d. For what reason do people hold money? See Blanchard, page 66-67. e. Intuitively, why would interest rates fall when there is a decline in the demand for

money? The supply of money is fixed. If the demand for money falls, there is a leftward shift of the demand for money curve. People want to reduce their holdings of money and thus buy more bonds. The increased demand for bonds increases the price of bonds, and thus reduces the yield (i.e. interest rate) on them. As the interest rate falls people are happier to hold money, since the opportunity cost of holding money (i.e. the interest forgone) is less. The new equilibrium comes about when people hold the same quantity of money in total (because the supply has not changed), but at a lower interest rate.

f. In what three ways can the central bank influence the interest rate in the economy? Explain each of these three ways comprehensively. (1) Changes in the reserve requirement θ; (2) changes in H, through open market operations and (3) changes in the interest rate at which the central bank lends money to the commercial banks (called the Federal Funds Rate in the US, the Repurchase Rate in South Africa, The Bank Rate in some other countries, etc.)

g. Explain how banks create money. See Blanchard, pp. 83-84. h. How can the central bank’s actions affect the money multiplier? Primarily through

changes in the reserve requirements θ. However, if the central bank can affect c, the proportion of money held in the form of currency (cash) by people, they can also effect the multiplier. However, changes in c are probably not under the direct control of the central bank.