14.02 Problem Set 5Dennis V. Perepelitsa1 May 2006Ruben Segura-CayuelaT/F/U1. True. Let πet+1be the expe cted rate of inflation. When the expected inflation is not toolarge, then the relation between rt, it, and πet+1can be approximated by:rt≈ it− πet+1If the expec ted inflation remains roughly constant, the rate of change (the last term) is zero, andthus the movements in the real and nominal interest rates are roughly equal.2. False. Junk bonds are bonds with high default risk - that is, there is a relatively highprobability that the issuer will not pay back the promised amount. They may, however, have otherqualities that make them attractive to an investor.3. Uncertain. Correlation is not causation. When attem pting to explain an economic event,the expectations about reality that investors hold are as important as reality itself. Thus, theincrease in oil prices must be considered in context of these expectations - if investors had expectedoil prices to be even higher than they turned out to be, then “higher oil prices” could cause a boostin the stock market.4. True. If the federal funds rate is lower than expected, this will lead to a p ositive ∆Y0e, anda negative ∆r0e. This will shift the IS curve to the right, leading to an increase in output, and thusstock prices. Sometimes all that is needed to cause large shifts in the stock market is a disreprancybetween expectations and reality.5. Uncertain. It is thought that some of the strong performance of the U.S. s tock market inthe 1990s was in fact due to a bubble effect, but that much of the performance was also due tofundamentals - in particular, due to the increased rate of technological progress. At the beginningof the 21stcentury, the market corrected itself, and fell to a slightly lower level than it had justbeen at, but because of the fundamentals behind the increase, it remained at a high level relativeto the late 1980’s. Thus, only some of the strong performance of the stock market in the 1990’sreflected the strong performance of the U.S. e conomy.6. False. Rational investors have and do pay a positive price for a stock that will never yielddividends. A rational investor can hope to sell the stock at a higher price to an investor who thinkshe can sell it at an even higher one. The point is that until “the bubble bursts”, part of a stock’svalue is determined by people’s expectations of it.Short Question 1a. A bond that pays $1,000 in one year is worth this much to me today:Vt=0= $1, 000(1 + 10%)= $909.09b. A bond that pays $1,000 two years from now is worth this much to me now:Vt=0= $1, 000(1 + 10%)(1 + 8%)= $841.751c. Next year, the interest rate is 8%, and a bond that pays $1,000 a year from then, is worththis much to me at that time:Vt=1= $1, 000(1 + 8%)= $925.93Short Question 2a. Since inflation, expected inflation and the real interest rate are all zero, the expected presentdiscounted value of an amount of money any time in the future is equal to that amount of money.If there is a 50% chance that the consumer earns $40,000 a year for twenty years during middleage, and a 50% chance that she earns $100,000 a year, her overall expected earnings during middleage are:E = 20Xx∈XP (x)V (x) = 20(50%)($40, 000) + 20(50%)($100, 000) = $1, 400, 000Her expected earnings during youth and old age are (20)($20, 000) = $400, 000 and (20)($0) = $0,respectively. Thus, the present discounted value of her expected lifetime earnings is simply $1.8million. A constant level of expected consumption over sixty years is$1,800,00060= $30, 000 a year.To consume this level every year, our consumer will need to borrow $10,000 a year in her youth.b. If earnings turn out to be $40,000 a year during middle age, then the consumer’s lifetimeexpected earnings are (20)($20,000) + (20)($40,000) = $1.2 million. Distributed over sixty years,this is a level of$1,200,00060= $20, 000 a year. This is the minimum she wanted to consume everyyear, so to upkeep it, she will have to spend all her income in her youth, and save half of herincome in middle age for use while she is old. This is a lower level of consumption per year thanher expected level of consumption per year given in part a.c. The consumer spends her entire income during her youth ($20,000 a year), but when shegets to middle age and finds that her income is $100,000 a year, her goal becomes to spend a con-stant amount for the remaining forty years. This amount is(20)($100,000)40= $50, 000 a year, whichis certainly above her minimum $20,000 a year desire. Thus, she spends $20,000 a year for thefirst twenty years, and $50,000 a year for the next forty. Her consumption becomes constant themoment she knows her future income.d. Even though the consumer’s expected level of consumption for the first twenty years of herlife is $30,000 a year, she only spends $20,000 a year because she is unsure of her future income.Thus, uncertainty about the future makes young people save more (or, alternatively, borrow less).Long Question1. A contractionary monetary policy will shift the LM curve upward. If the Chairman im-plements a policy that is more contractionary than expected, then ∆Y0e, the change in expectedoutput, will be negative, and ∆r0e, the change in expected real interest rate, will be positive. Thiswill shift the IS curve to the left. Thus, as a result, the real interest rate will rise and the outputwill fall. Stock prices will fall.2. When the announcement is made today, the stock market will react immediately to theexpected contractionary monetary policy. Thus, when the Chairman is actually confirmed a yearfrom now, the effects of the expectations investors are forming about his policies have already takeneffect. The market has been fully expecting the mandate for a year now, and will not be affected2beyond this by it.3. If the Chairman implements a policy that is less contractionary than expected, then ∆Y0e,the change in expected output, will be positive, and ∆r0e, the change in expected real interestrate, will benegative. This will shift the IS curve to the right. Output and interest rate will bothincrease. Stock prices will rise.4. I think this was bec ause investors expected a Chairman of the Fed who would implementsome very contractionary monetary policies, and that while Ben Bernanke was would probablyimplement a contractionary monetary policy, it would be relatively less contractionary than theexpected one. Thus, by the reasoning in question 3, stock
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