Question 2 (20 Marks). a) A bond with a coupon rate of 7% makes semi-annual coupon payments on January 15 and July 15 of each year. The Wall Street Journal reports the ask price for the bond on February 15 at 101% of the par value. The par value of the bond is 1000. What is the invoice price of the bond? The coupon period has 182 days. (5 marks) b) Prices of zero-coupon bonds reveal the following pattern of forward rates: Year Forward rate (%) 5% 2 7% 8% In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $60 with par value $1,000. i. What is the price of the coupon bond? (5 marks) ii. Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond? (5 marks) ii. If you forecast that the yield curve in 1 year will be flat at 7%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period? (5 marks)Consider a closed economy that is characterised by the following equations: (1) Y= C+1+G (2) C = 200 + 0.75(Y-T) (3) I = 325 -25r (4) T=500 (5) G=500 (6) Md/P= L(r, Y) = 0.5Y - 50r (7) Ms=1000 (8) Ms=Md where Y is gross domestic product, C is private consumption expenditure, I is investment expenditure, G is government expenditure, T is lump sum taxes, Ms is money supply, Md/P is demand for real money balances, r is the real interest rate and P is the aggregate price level. Al. Derive the IS and LM curves of the economy, expressing Y as a function of r and assuming P is fixed at 2. [ 10 Marks] A2. Calculate the short-run equilibrium values of Y and r, assuming P is fixed at 2. [ 10 Marks] 3 of 9 ECON20031 A3. Calculate the long run equilibrium values of r and P, assuming that the potential level of output (Y*) is equal to 2300 monetary units. Use the IS/LM model and the AD/AS model to illustrate how the economy moves from the short run equilibrium to the long run equilibrium. [15 Marks] A4. An oil price shock causes the price level in the economy to increase from 2 to 2.5. Calculate the new equilibrium values of Y and r. Explain, using the AD/AS model, how the central bank might accommodate this adverse supply shock to stabilize income at its original level in the short run. [15 Marks]ECON 310: Problem Set #3 Please submit through Canvas Due Date: October 23, 2020 For all of the questions in this problem set, amume there is no tax at all. Stocks Consider stock A with a dividend yield equal to 2.5% (based on its dividend payments over the past year). The dividends are expected to grow at 8% per year. Stock A is currently traded at $52 per share. 1. According to Gordon's model, what would be the expected return on the stock? Answer: The Gordon's model states that 1+9 P = DI TE - 9 Rearrange the terms we get Pi(1+g) +9 = 2.5% . (1 +8%) + 8% = 10.7%% 2. Suppose the total dividends paid over the next year is $1.4 per share, leading to a downward revision of the expected dividend growth rate to 7.5%%, Assume the expected rate of return remains the same for this stock, what would be the actual rate of return from holding this stock over the next year? Answer: The price of stock A a year from now, according to Gordon's model, is 1+4 -14- 1+7.5% 10.7% -7:5%% =$47.03/share The rate of return is Rut - De + An -A 14+ 47.03-52 52 =-6.87% 3. Consider stock B which just paid $6 in dividends over the past year. The expected return on the stock is 12.5% and the stock is currently traded at $120 per share. At what rate are the dividends expected to grow for this stock according to Gordon's model? Answer: Again, starting with the Gordon's model 1+9 PEDITE - 9 and rearrange the terms we have Pi(TE - 9) = Di(1+ 9)Problems (Solusand to problemis mariged * appear at the bock of this book. Problems adapted to one calculus in availabit saint at 1. Which assumption about consumer preferences does by three different consumers (Augn, Barbara, and each of the following individuals violate? Camina), holding everything else constant: . Adam likes basketball more than football; Auon Football more than baseball; and baseball more Barbara Camira than basketball. b. Christina prefers prune juice to orange juice but 02 cannot decide how she feels about grapefruit juice. C. Blake likes superhero comic books but prefers 5 comic books to 10 comic books. 54 2. By assumption, individual preferences must be tran- sitive so that if A is preferred to B, and B is preferred to C. then A is preferred to C. Suppose that Marsha, 17 5 Jan, and Cindy individually have transitive prefer- ences over three goods: oranges, apples, and pears. Compute the marginal utility of X for each of the If Marsha, Jan, and Cindy were to vote on whether three consumers at each level of X. to name oranges, apples, or pears the "fruit of the b. Based on the data in the table, can you tell month," show that it is possible the preferences for whether any of these consumers are violating any the group might not be transitive. of the standard assumptions about preferences? 3. Draw two indifference curves for each of the follow- c. Is it possible that any of these three consumers ing pairs of goods. Put the quantity of the first good have the same preferences, and that columns for the on the horizontal axis and the quantity of the second three consumers differ only because of the arbitrary good on the vertical axis. units that are used to measure utility? Explain Paul likes pencils and pens, but does not care $6. A consumer's utility function is given by U- XY. which he writes with where MU, - F and MU, = X. Rhonda likes carrots and dislikes broccoli. a. What is the utility derived from 1 unit of X and C. Emily likes hip-hop iTunes downloads and 2 units of Y? What is the utility derived from doesn't care about heavy metal downloads. 2 units of X and I unit of F? What is the utility d. Michael only likes dress shirts and cufflinks in 1 derived from 5 units of X and 2 units of Y? to 2 proportions. b. How does the consumer rank the following e. Carlene likes pizza and shoes. bundles? *4. Suppose that John is indifferent between consuming Bundle Quantity of I Quantity of F bundle A. which consists of 4 apples and 1 peach, and bundle B, which consists of 4 peaches and A 2 1 apple. If John were given the choice between bun- 10 dle A and bundle C, which contained 3 peaches and 2 apples, which should be pick? (Hint: Draw an 5 indifference curve or two.) 3 2 5. The following table displays the total utility ((X ) that 2 3 comesponds to the number of units of X consumed