This Document Contains Chapters 23 and Appendix A CHAPTER 23 Modern Principles of Economics: Stock Markets and Personal Finance Facts and Tools 1. Before we plunge into the world of finance, let’s review the rule of 70. Suppose your rich aunt hands you a $3,000 check at the end of the school year. She tells you it’s for your education. But what should you really do with that extra money? Let’s see how much it would be worth if you saved it for a while. a. If you put it in a bank account earning 2% real annual return on average, how many years would it take before it was worth $6,000? Until it was worth $12,000? b. If you put it in a Standard and Poor’s 500 (S&P 500) mutual fund earning an average 7% real return every year, how many years would it take before it was worth $6,000? Until it was worth $12,000? c. Suppose you invest a little less than half your money in the bank and a little more than half in a mutual fund, just to play it somewhat safe, so that you can expect a 5% real return on average. How many years now until you reach $6,000 and $12,000? Solution 1. a. Approximately 35 years until $6,000, and 70 years until $12,000. b. 10 years until $6,000, 20 years until $12,000. c. 14 years until $6,000, 28 years until $12,000. 2. Let’s do something boring just to drive home a point: Count up the number of years in Figure 23.1 in which more than half of the mutual funds managed to beat the S&P 500 index. (Recall that the Standard and Poor’s 500 is just a list of 500 large U.S. corporations—it’s a list that overlaps a lot with the Fortune 500.) What percentage of the time did the experts actually beat the S&P 500? Solution 2. Fourteen years out of 36: 39% of the time, the experts did better. 3. Consider the supply and demand for oranges. Orange crops can be destroyed by below-freezing temperatures. a. If a weather report states that oranges are likely to freeze in a storm later this week, what probably happens to the demand for oranges today, before the storm comes? b. According to a simple supply and demand model, what happens to the price of oranges today given your answer to part a? c. How does this illustrate the idea that stock prices today “bake in” information about future events? In other words, how is a share of Microsoft like an orange? (Note: Wall Street people often use the expression, “That news is already baked into the price,” when they talk about the efficient markets hypothesis.) Solution 3. a. Demand rises today, well before the freeze. b. This pushes the price up today. c. Stock prices are like oranges because your demand for them today depends on what you think will happen to them in the future. And rumors or facts about the future health of an orange or Microsoft affect today’s demand. 4. In the United States, high-level corporate officials have to publicly state when they buy or sell a large number of shares in their own company. They have to make these statements a few days after their purchase or sale. What do you think probably happens (choose a, b, c, or d) when newspapers report these true “insider trades”? Note: The right answer according to theory is actually true in practice.) a. When insiders sell, prices rise, since investors increase their demand for the company’s shares. b. When insiders sell, prices fall, since investors increase their demand for the company’s shares. c. When insiders sell, prices fall, since investors decrease their demand for the company’s shares. d. When insiders sell, prices rise, since investors decrease their demand for the company’s shares. Solution 4. c. When people see insiders selling, they figure the insiders know something, so they want to get out as well. As a result, the share price falls. 5. Let’s see how fees can hurt your investment strategy. Let’s assume that your mutual fund grows at an average rate of 7% per year—before subtracting the fees. Using the rule of 70: a. How many years will it take for your money to double if fees are 0.5% per year? b. How many years will it take for your money to double if fees are 1.5% per year (not uncommon in the mutual fund industry)? c. How many years to double if fees are 2.5% per year? Solution 5. a. 10.7 years b. 12.7 years c. 15.5 years 6. a. If you talk to a broker selling the high-fee mutual fund, what will he or she probably tell you when you ask them, “Am I getting my money’s worth when I pay your high fees?” b. According to Figure 23.1, is your broker’s answer likely to be right most of the time? Solution 6. a. Your broker will always say that it is worth it. b. Your broker is usually wrong, even if he or she believes it deep down. Thinking and Problem Solving 7. Your brother calls you on the phone telling you that Google’s share price has fallen by about 25% over the past few days. Now you can own one small slice of Google for only $540 a share (the price on the day this question was written). Your brother says he is pretty sure the stock is going to head back up to $700 very soon and you should buy. Should you believe your brother? (Hint: Remember someone is selling shares whenever someone else is buying.) Solution 7. No, not unless your brother works at Google! Even if your brother is a smart person, millions of shares of Google were being bought and sold as the price fell. The sellers believe the price is going to fall further. The buyers believe the price will rise. It’s not obvious why your brother should be better informed than either the sellers or the buyers, so you should expect a share in Google to have about the same return whether the price has recently fallen or risen. If your brother works at Google and has inside information, however, then perhaps you should listen to him, but beware of the Securities and Exchange Commission (SEC)—insider trading can be illegal. 8. In most of your financial decisions early in life, you’ll be a buyer, but let’s think about the incentives of people who sell stocks, bonds, bank accounts, and other financial products. a. Walking in the shopping mall one day, you see a new store: the Dollar Store. Of course, you’ve seen plenty of dollar stores before, but none like this one: The sign in the window says “Dollars for sale: Fifty cents each.” Why will this store be out of business soon? b. If business owners are self-interested and fairly rational people, will they ever open up this dollar store in the first place? Why or why not? c. This dollar store is similar to stories people tell about “cheap stocks” that you might hear about on the news. Fill in the blank with any prices that make sense: “If the shares of this company were really worth ________, no one would really sell it for ____________.” Solution 8. a. The Dollar Store will be out of business because everyone in the world will come into the store with two quarters, and walk out with one full dollar. The business will lose 50 cents on every sale. It can’t lose 50 cents per sale forever. b. No business owner would open a store based on this business model. Greed would keep them from doing this. c. Any prices will do, so long as the number in the first blank is a higher price than the one in the second. If a stock is really “cheap” for more than a few minutes, then very rich people or investors with big piles of pooled money will come along and bid up the price. If the stock is “really” worth $100 per share, no one will sell it for $50. 9. How is “stock market diversification” like putting money in a bank account? Solution 9. Banks put your money into a lot of small investments, just like a strategy of stock market diversification. 10. Warren Buffett often says that he doesn’t want a lot of diversification in his portfolio. He says that diversification means buying stocks that go up along with stocks that go down; he only wants to buy the stocks that go up! From the point of view of the typical investor, what is wrong with this reasoning? Solution 10. Buffett’s advice might be good advice if you are a stock market genius (see the text for why we are skeptical about most such “geniuses”), but it’s bad advice for the typical investor. The typical investor cannot predict which stocks will go up and which will go down. After all, if it were easy to pick the winning stocks, the price of those stocks would already have risen! As a result, information about a stock’s real value tends to be already “baked in” or reflected in the current price; there is thus no reason to think that any particular stock is likely to fall or rise in value more than average. We know, however, that a diversified portfolio of stocks has paid a healthy return over many years, so if you invest in a diversified portfolio, chances are that your future return will also be healthy, even if you don’t get rich like Buffett. 11. There are three stocks available: a solar energy firm, an oil firm, and an airline. You can invest in two. Which two? Solution 11. The first secret to picking stocks is to diversify. Diversification lowers the risk of your portfolio and how much your portfolio fluctuates in value over time. We should buy many stocks but in different companies. Thus, given a choice between a solar energy firm, an oil firm, and an airline, we can invest in an oil firm and airline firm. Airline firms, which use oil as raw material, will prosper in an environment of low energy prices. So even if the oil firm stock falls, the losses accrued can be offset by the rise in airline stock. 12. How easy is it to spot a bubble? Go to the FRED economic database (https://fred.stlouisfed.org/) and search for NASDAQ. You should find the NASDAQ Composite Index. Graph it and click Max to show all the data available. a. What happened to the index between November of 1998 and February of 2000? Then what happened? b. What happened to the index between October of 2009 and October of 2014? Then what happened? c. Are you willing to make a bet about the future direction of the NASDAQ? Solution 12. a. Between November of 1998 and February of 2000 the NASDAQ index more than doubled; rising from a level of 2000 to a level of 4696, but then it crashed over the next two years to around 1300 in 2002. b. Between October of 2009 and October of 2014 the NASDAQ index more than doubled, rising from a level of 2045 to 4630, and it kept going up over the next several years! c. Maybe you are willing to bet but we are not. It’s hard to predict future stock market movements, which is one reason why we buy and hold a diversified basket of stocks and assets. Challenges 13. What is so bad about bubbles? If the price of Internet stocks or housing rises and then falls, is that such a big problem? After all, some people say, most of the gains going up are “paper gains” and most of the losses going down are “paper losses.” Comment on this view. Solution 13. Remember that prices are signals, so when the price of Internet stocks or housing goes up, that is a signal to entrepreneurs to invest more in these fields. If the price isn’t sending the right signal, there will be a misallocation of resources. Construction of new houses, for example, boomed as house prices rose. When house prices began to fall, much of this new construction turned out to be worth less than builders expected. As a result, it now seems that too many homes were built and resources were wasted. When Internet stocks boomed, hundreds of millions of miles of fiber-optic cable were laid under the ground and sea. The companies laying this cable hoped for big profits, but in the end most of them went bust, revealing their investments to have been wasteful. It is true that the houses and the fiber-optic cable will be used—it’s not all waste—but we probably built too much, too soon. Of course, investment is always a gamble since no one knows the future for certain, but to the extent that prices depart from the fundamentals, the losses created by bubbles are not just paper losses but real resource losses. The workers and machines that built those houses and fiber-optic cables could have been better used elsewhere. Another story of opportunity cost. 14. Mr. Wolf calls you with what he says is a tremendous opportunity in the stock market. He has inside knowledge about a pharmaceutical company and he says that the price will go up tomorrow. Of course, you are skeptical and decline his offer. The next day the price does go up. Mr. Wolf calls again and says not to worry, tomorrow the price will go down and that will be a good time to buy. Again, you decline. The next day the price does go down. Mr. Wolf calls you over the next several weeks and every time he calls his predictions about the stock price prove to be amazingly accurate. Finally, he calls to tell you that tomorrow is the big one, the day the price will skyrocket. Mr. Wolf has been accurate many times in a row so you empty your bank account to buy as much stock as possible. The next day the price of the stick goes nowhere. What happened? Solution 14. Mr. Wolf scammed you. Let’s say that on day one Mr. Wolf called 1000 people, and to 500 of them he predicted the price would go up and to the other 500 he predicted the price would go down. Notice that 500 people will think that Mr. Wolf predicted the price correctly, so the next time Mr. Wolf calls just those 500 people and to 250 of them he predicts the price will go up and to 250 of them he predicts the price will go down. Once again, no matter what happens, 250 people will have received a correct prediction twice in a row. By continuing like this Mr. Wolf will soon have a small group of people who think that he is incredibly accurate, but what seems like uncanny accuracy is just random guessing plus selection. CHAPTER 24 Modern Principles of Economics: Asymmetric Information: Moral Hazard and Adverse Selection Facts and Tools 1. Determine whether the situations below represent problems caused by asymmetric information. If so, determine whether they represent problems of moral hazard or adverse selection. a. Unrest in the Middle East causes oil speculators to buy up oil futures, driving gasoline prices higher. b. Karol is halfway to work before he realizes that he forgot to lock the back door. Because he has renter’s insurance, he decides it is not worth being late to work just to go home to lock the door. c. Joanne applies for a job as a part-time manager at a fast-food restaurant. Her MBA makes her incredibly overqualified for the job, yet the position goes to someone else who doesn’t even have a college degree. d. Frances lives in an apartment above a restaurant, and her apartment always smells like burgers and fries. She has tried unsuccessfully to get the restaurant owner to remedy the problem. e. The potential costs of long-term care (such as a nursing home stay) can be very high and are also very uncertain. Despite this, the private market for long-term care in the United States has remained fairly small. Solution 1. a. This is not a problem of information asymmetry. Everyone has the same info (not much) about the future of the Middle East. b. This is an example of moral hazard—he has more information about his behav¬ior in situations like this than does his insurance company, which bears the risk. c. This could be an example of adverse selection. Perhaps the hiring manager was thinking, “if Joanne has an MBA but wants this job, she must not be a very talented businesswoman.” d. This is not a problem of information asymmetry. Everyone has the same infor¬mation. This is an example of a negative externality. e. This is an example of adverse selection. It is hard to grow this market when the people most interested in the insurance product are those most likely to need it and make claims. 2. Describe how the following facts represent solutions to problems of asymmetric information. a. Auto insurance rates are higher for teenagers than for nonteenage. b. Your car insurance coverage probably includes a deductible—an amount that you have to pay out of pocket before your insurance coverage kicks in. c. Many states have laws like Virginia’s that give customers the right to keep or inspect parts that are removed by an auto mechanic. d. For many couples, weddings are lavish affairs that cost tens of thousands of dollars and are attended by hundreds of guests. Solution 2. a. Not every teenage driver is a poor or unsafe driver but on average teenagers, especially male teenagers, do get into more accidents. Age is observable so the insurance firm charges more to people who are younger and, on average, less safe. If insurance companies did not do this, then safe drivers would be overcharged and might even buy less insurance, which would create an adverse selection death spiral as the safer drivers dropped out, leading to a riskier pool, higher rates, more safe drivers dropping out, and so forth. Requiring everyone to carry auto insurance is another way that the death spiral can be avoided. b. This addresses the problem of moral hazard. Because of the deductible, you are less likely to report every minor dent and scratch; instead, you wait until you have a major claim before you involve your insurance company. c. This addresses the problem of moral hazard. Your mechanic is less able to charge you for parts she didn’t replace—or that didn’t need replacing—if she has to allow you to inspect the parts that came out of your car. d. This addresses a potential problem of adverse selection. It is a signal that one intends to take a marriage seriously, given the high social cost of divorcing after throwing such a lavish party. Without signals such as these, some might be un¬willing to risk entering into a marriage. 3. George Akerlof ’s model of the used car market results in a market in which only lemons are sold and there is no market for high-quality used cars. But, in fact, we observe that the used car market is a robust market in which millions of used cars of varying quality are sold. Does that mean Akerlof ’s model is wrong? Why or why not? Solution 3. Akerlof ’s model shows what can happen when there is asymmetric information that has no remedy. His model shows that adverse selection has the potential to eliminate markets completely. However, since we know that the market has not been completely eliminated, Akerlof ’s model helps us to realize that institutions such as reputation, certification, and warranties must exist that help alleviate this problem. 4. In September of 2008, the Federal Reserve announced a “bailout” for AIG, which had gone bankrupt after having its credit rating downgraded in the wake of the financial crisis of 2007–2008. Can you think of an argument against such a bailout that is related to the material in this chapter? Where’s the information asymmetry? Solution 4. Bailing out financial institutions like AIG can lead to moral hazard. The companies have less incentive to avoid bankruptcy in the future if they recognize that they will be rescued again should they need it. The information asymmetry exists because they know more about the industry—and in particular their own decisions—than does the government. Even if the government monitors the behavior of the insur¬ance companies and financial institutions, bureaucrats may not be business-savvy enough to spot inappropriate or irresponsible behavior when they see it. 5. Explain the difference between moral hazard and adverse selection. In general, which problem is more likely to arise prior to making a transaction, and which problem is more likely to arise after the transaction has been made? Solution 5. Moral hazard occurs when a party to a transaction uses her or his information advantage in a way that harms the other party to the transaction. This often occurs after the transaction—such as when an insured person takes on too much risk. Adverse selection occurs when the reality of information asymmetry affects the transactions before they’re made, such as when people who expect to die when they are younger are more likely to demand life insurance, and life insurance companies respond accordingly. Thinking and Problem Solving 6. Insurance markets are often plagued by problems of asymmetric information. In part, this is because insurance markets themselves exist only because of incomplete information—nobody knows what the future holds, so households pay insurance companies to bear the risk of an uncertain future. Both households and insurance companies have incomplete information, but problems arise because the informa¬tion is asymmetrically incomplete. Consider the market for medical insurance. What information might buyers in this market have that insurance companies don’t have? Here’s a harder question: What information might sellers of medical insurance have that buyers don’t have? Solution 6. Buyers have information about their medical history, the medical history of their parents and grandparents, their diets, their sleeping habits, their exercise regimen, and so on. They also know more about how often they follow a doctor’s advice and how carefully they take medications. The sellers of medical insurance often have more information about the laws that govern insurance markets and their own legal responsibilities. They definitely know more about the complicated contracts they sign with their enrollees and the legal maneuvers available to them to avoid paying claims. Insurance companies also have better information about life expectancy by age, gender, race, occupation, and other characteristics than do most individuals. 7. Health economists use the phrase “supplier-induced demand” to describe the ability that physicians have to influence their patients’ demand for medical care. One of the reasons that this ability exists is asymmetric information. a. What do physicians know more about than patients? b. If physicians can influence their patients’ demand, then what would prevent them from always providing diagnoses of severe conditions that require expen¬sive (profitable) treatments? c. Health economists point out that third-party payment schemes (such as medi¬cal insurance that pays your medical bills for you) also contribute to supplier-induced demand. How would third-party payment exacerbate the problems of asymmetric information? Solution 7. a. Physicians know more about medicine. They know more about what a patient’s symptoms mean, what treatments exist, and the cost and efficacy of those treatments. b. Eventually, one would assume that such a physician would develop a bad reputation. Third-party payers, like insurance companies or the federal and state governments, devote resources to identifying and punishing “fraud,” so in some extreme cases the physician might be risking jail time to induce demand at this level. c. Third-party payment can exacerbate the problem because it reduces the cost to patients of allowing themselves to be duped. If patients have to pay out of pocket, they might be more likely to seek a second opinion or to investigate the real need for an expensive treatment; when someone else is paying, this incentive is much weaker. 8. Evan Soltas is a popular economics blogger (http://evansoltas.com/) who began capturing the attention of top economics thinkers while still in high school. His understanding of economics and economics issues would have been impressive even for a professional economist with years of training. After graduating from high school, he went off to Princeton to major in economics. Since Evan doesn’t have much to learn about economics—at least not much at the undergraduate level— this decision might seem confusing to some people, but you’re a gifted economist now too. Explain Evan’s decision. Solution 8. This could be an example of signaling. Evan may be a gifted economist, but he will never get a job at a university, for example, without a piece of paper (a couple of pieces of paper, really) confirming that he has jumped through enough hoops that an employer can be reasonably assured he is a conscientious person. 9. Suppose your band is about to take off, so you go out and buy a brand-new Marshall Tube Head and Cabinet amplifier for the list price of about $4,200. But your band breaks up after you’ve used it only once. You hang on to it for a year or so in case your drummer and bass player can work out their differences, but it never happens. You finally decide to sell it on Craigslist. Since you know it’s been used only once, and it’s been properly stored for a year, you reason that it’s still worth close to what you paid for it, so you list it for $3,800—almost 10% off of the new price. How is this going to turn out? Solution 9. Not well. This is an example of adverse selection. Craigslist shoppers are look¬ing for discounts on used gear, and will question whether your amp is really in as good a shape as you say it is. They will reason that a certain amount of stuff for sale is damaged or worn, and when they cannot verify the quality, their willingness to pay will be lower. Many buyers would rather pay the $400 difference for a new amp, since they can be assured of service around the sale, perhaps even a warranty. 10. Kaplan Test Prep offers courses and private tutoring arrangements that prepare students for standardized tests such as the GRE, GMAT, or LSAT (tests that you may take soon). Kaplan offers students a “Higher Score Guarantee,” which essen-tially promises that your score when you take the test after completing a Kaplan course will be higher than your prior test score (or your “diagnostic” score if it’s your first time taking the test). If it’s not, you can take the course again or get your money back. a. Discuss how this guarantee functions as insurance. b. Discuss how this guarantee functions as a signal. Solution 10. a. The guarantee is insurance against low-quality content. Prospective buyers cannot fully assess the quality of the instruction being offered, so the guarantee alleviates a potential problem of adverse selection. b. The guarantee is also a signal that Kaplan expects its classes to raise student scores. Since Kaplan would not make any money if it simply returned their tuition to all its students, students can assume that Kaplan’s incentives are aligned with their own: Higher scores benefit all involved. 11. Consider the following unusual insurance products. For each one, determine whether you think this insurance product could exist in the marketplace, or whether it would be subject to moral hazard or adverse selection (or both). a. GPA insurance for people with 4.0 GPAs after two years of college that pays out if you ever have a semester with a GPA lower than 3.50. b. GPA insurance for anyone that pays out if you ever have a semester with a GPA lower than 3.50. c. Loneliness insurance that pays out if you reach a certain age and still have not married. d. Toe-stubbing insurance that pays out any time you stub your toe. e. Insurance that pays out if and only if you get hit and killed by a school bus. Solution 11. a. This insurance product is subject to moral hazard. However, the conscientious¬ness of those involved may mitigate this problem slightly. b. This insurance product is subject to adverse selection—only those with low GPAs will want to buy this insurance. This product could not exist. c. This insurance product could not exist because of the potential for both adverse selection (only weirdos would buy it) and moral hazard (some may avoid “mar¬riage” while still maintaining a long-term monogamous relationship). d. This insurance product could not exist because of the moral hazard involved: you could claim to have stubbed your toe, but it will be difficult to establish this for a fact. e. Insurance for such a specific form of death has high transactions costs and may not be worthwhile, but a few (not zero!) people will jump in front of a bus to benefit their families; and, the adverse selection problems are likely to be minor so, in principle, this could exist. 12. When the cause of death is suicide, life insurance policies typically pay out only when the suicide occurred after an exclusionary period has passed, usually around a year after purchasing the life insurance. Why do life insurance companies insist on an exclusionary period? If you compared suicide rates in the year before and the year after the exclusionary period, what do you predict you would find? Solution 12. Life insurance companies fear an adverse selection problem. People contemplating suicide might buy a lot of insurance before suicide if they knew the insurance com¬pany would pay. Since suicide is often a spur-of-the-moment decision, requiring an exclusionary period reduces the problem. Incentives matter, however, so you will not be surprised to find that suicide rates do increase after the exclusionary period has passed. Countries with shorter exclusionary periods also seem to have higher suicide rates. (See Yip, P.S., and F. Chen. 2014. A study on the effect of exclusion period on the suicidal risk among the insured. Social Science & Medicine, 110: 26–30; and Chen, Joe, Yun Jeong Choi, and Yasuyuki Sawada. 2008. Suicide and life insurance. No CIRJE-F-558, CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo.) 13. You are driving on a trip and have two choices on the highway to stop for a snack: a well-known chain or a local restaurant that you have never heard of but that looks okay. What lessons from this chapter might lead you to choose the chain even if you think that their food is just average? Might you choose differently if you had access to the Internet? Might you choose differently if these two choices were in your neighborhood? Solution 13. Restaurants on the highway serve lots of nonrepeat customers. As a result, the costs to them of serving a poor meal are lower than the costs to a neighborhood res¬taurant, which relies on repeat customers and word of mouth. If the local highway restaurant serves you a bad meal, for example, what are you going to do—never eat there again? But you probably weren’t going to eat there again even if they served you a great meal! On the other hand, if the chain restaurant serves you a bad meal, you can still punish the chain. The chain relies on repeat customers even if they don’t rely on repeat customers at each particular location. As a result, the chain has a greater incentive to keep its reputation strong and its quality high, even on the highway. You might choose differently if you had access to the Internet and could check restaurant reviews on Yelp or other services. First, and most obviously, you would have better information about the local restaurant. Second, if lots of people do this, then you don’t actually have to check the Internet. Just knowing that lots of other people check the Internet means that the local restaurant also has a reputation to maintain and is probably pretty good. By the way, McDonald’s and many other chains were often very successful on highways in the age before the Internet precisely for these rea¬sons—they may have been average but they were consistently average and never let you down too much. With the advent of the Internet, we may expect to see more diverse and local restaurants even on highways. If the two choices were in your neighborhood, you might choose differently. First, you know the local restaurant has to maintain its reputation to survive. Second, the value to you of experimenting is higher when eating locally. If you discover a great local restaurant, you can go back there many times! Challenges 14. Consider a restaurant that wants to avoid kitchen fires. The restaurant could make many investments both to avoid the fires in the first place and to quickly and safely put them out if they do occur. Suppose that the marginal cost (MC) and marginal benefit (MB) of these investments in fire control technologies is illustrated in the following figure. a. If no fire insurance is available, how much investment in fire control would the restaurant purchase? b. If full insurance is available, how much investment in fire control would the restaurant purchase? c. The moral hazard incentivized by full insurance creates a deadweight loss. Show the deadweight loss in the diagram. d. Suppose that the insurance policy would only cover 50% of the losses from fire; that is, the restaurant has a 50% copay. How much fire control would the restau¬rant purchase? e. Suppose that the insurance policy would cover only 50% of the losses but the insurance company also offered a discount on insurance to restaurants that installed water sprinklers or other fire suppression technologies. How would the curves shift? What quantity of fire investment would be purchased? Comment on the role of copays and discounts. Solution 14. a. Without insurance, the restaurant would invest in fire control technology so long as the MB > MC, that is, up to the point Qe. b. If the insurance were truly full—that is, it covered all losses—then the marginal benefit of any investment in fire control to the restaurant would be zero, and the restaurant would not invest in fire control. QFI = 0. c. The deadweight loss is the value of the fire control investment that is not made when there is full insurance. The value of the investments that are not made is shown in the figure. d. If the insurance firm covered 50% of any losses, the MB to the restaurant of investments in fire control technologies would fall by half; that is, the MB would be half the height at all levels of investment. Thus, the amount of investment purchased would be given by Q50%. e. If the insurance company offered a discount for firms that installed fire suppression technologies, we can think of this as reducing the MC to the firm. Thus, with 50% insurance and discounts, the MC curve shifts down and the equilibrium is at QDiscount. Note that copays and discounts for taking certain actions increase the quantity of investment in fire control, potentially moving it much closer to the efficient amount. 15. “Black box” insurance is a new type of auto insurance that requires that the buyer install a black box in their car that monitors speed, distance traveled, acceleration, time of day, and other factors. Discuss the effects of this type of insurance on dif¬ferent drivers and their behavior. The terms “adverse selection,” “moral hazard,” and “signaling” should all be relevant. Solution 15. Black box insurance would reduce moral hazard because drivers would have an incentive to drive more safely, knowing that they were being monitored. Black box insurance would especially appeal to drivers who are already safe and careful driv¬ers. Black box insurance might also be especially valuable for teenage drivers who are truly safe and careful drivers, for example, because they would be able to signal their safety by purchasing this type of insurance. If black box insurance were successful, regular insurance might be driven out of the market because, as more safe driv¬ers choose black box insurance, the proportion of relatively unsafe drivers choosing regular insurance would increase, driving up the rates of regular insurance. In other words, black box insurance would create an adverse selection problem for sellers of regular insurance. In addition, current insurance is priced for an average amount of driving, around 12,000 miles a year, so people who drive less than average pay too much and people who drive more than average pay too little. Black box insurance would be able to price insurance by the mile, leading to a fairer allocation of expenses and perhaps also causing some efficiency adjustments because people who drive a lot would choose to drive less. 16. Home cleaning services and general contractors often advertise that they are bonded. What this means is that the seller of the service has put up money with a third party that is available to the buyer if, for example, the cleaners damage or steal property or if the general contractor fails to complete the project or completes it in a substandard way. Using the concepts of moral hazard and signaling, explain the purpose of bonding. As a bonus, why is bonding used for these services in particular? Solution 16. If buyers feel taken advantage of by a product or service, they won’t become repeat customers and that already is some incentive for sellers to look after buyers. A clean¬er, however, may damage or steal property worth tens of thousands of dollars even when the cost of their cleaning services is, say, only $100. Similarly, if a contractor fails to complete a project or completes it in a substandard way, fixing the problem the contractor created may be much more expensive than the cost of the original project. Bonding is especially important in these industries because the buyer wants more incentive than the threat of not being a repeat customer. Of course, the buyer can always sue in a court of law but that’s expensive and time-consuming, and if the cleaner has stolen thousands of dollars, they may be nowhere to be found. And if found, they will probably have already spent the money or fenced the goods! When the seller puts up a bond with a third party, the buyer knows that (a) if a problem does occur there is a pot of money from which they can be paid relatively quickly and easily; (b) the seller has a good incentive not to engage in the moral hazard of theft or failing to complete the project or using shoddy materials. Finally, imagine that there are two types of firms: fly-by-night operations just trying to make a quick buck and more honest firms in the business for the long haul. Which of these firms is more likely to be willing to post a bond? Since posting a bond is less costly for honest firms that plan on doing a good job, the willingness to post a bond is also a signal of quality. 17. The following demand and supply diagram represents the market for routine outpa¬tient appointments with a primary care physician. D1 shows the annual demand for a typical patient when he or she has no insurance and must pay the entire price of the appointment out of pocket. D2 shows how the typical patient responds to the price when he or she has to pay only 50% out of pocket, with the rest covered by medical insurance. a. Can you explain the shape/position of demand curve D2? Suppose the marginal cost of an appointment is $100 and the market is perfectly competitive. Answer all of the following questions twice: once considering a market without medical insurance and once considering a market with medical insurance. b. How many physician appointments will the typical patient have each year without and with insurance? c. How much will the patient pay for physician appointments each year? How much will be paid by the insurance company? d. What is the total annual value to the patient of the appointments? e. Comparing your answers to parts c and d, what is the amount of net total surplus generated by the market for these physician appointments? f. How does this relate to the chapter? Solution 17. a. The demand curve D2 is twice as high as D1 at every quantity because, with insurance, the real price would have to be twice as high for the out-of-pocket cost for the patient to be equal to what it would be without insurance. For example, without insurance, the patient will demand three appointments per year at $150 each. However, with insurance the patient would demand three appointments per year even if the price were $300 per appointment. b. Four without insurance; five with insurance. c. Without insurance, the patient will pay 4 × $100 = $400. With insurance, the patient pays 50% × 5 × $100 = $250. Without insurance, the insurance company pays nothing. With insurance, it pays the other $250. So total spending is $400 without insurance and $500 with insurance. d. The total annual value is the area under D1 at the quantity. For four appoint¬ments, this is the trapezoid under D1 up to a quantity of 4, which has an area of $800. For five appointments, this is the area under D1 up to a quantity of 5, which has an area of $875. (Do not use D2, because the patient is making decisions based on out-of-pocket costs, which is reflected by D1 in both cases.) e. Without insurance, total surplus is $800 – $400 = $400. With insurance, total surplus is $875 – $500 = $375. Total surplus is higher without insurance because the insurance inspires the fifth visit, which is valued lower than its $100 cost. f. This is an example of moral hazard. 18. Human-made diamonds, which are just as beautiful and essentially indistinguishable from mined diamonds, are becoming much cheaper to produce. Diamond engage¬ment rings, therefore, could soon become much less expensive. Great news for people who plan to get married, right? Or wrong? Explain. Solution 18. Probably wrong. Although diamonds do sparkle, the reason that they have become standard as an engagement item is more likely that they are also expensive. A dia¬mond ring signals that the giver is investing a great deal in the relationship, literally and figuratively. A two-carat diamond ring that was inexpensive would physically sparkle as much as a more expensive diamond, but it would no longer spark the emotions. If diamond rings became inexpensive, the signaling theory predicts that traditions would change so that an engagement would be marked by the gift of some other expensive but useless item made of such materials as platinum, palladium, or gold. Or perhaps suitors will increasingly have to hire airplanes to spell out their love in the sky or enter monasteries for several weeks of fasting and reflection before marriage. CHAPTER 25 Modern Principles of Economics: Consumer Choice Facts and Tools 1. The following table shows the marginal utility a consumer receives from the weekly consumption of On-Demand movie rentals and Thai takeout meals. One On-Demand movie rental costs $5, and Thai takeout costs $10 per meal. Suppose this consumer is currently (for some reason) eating Thai takeout 10 times per week and is spending all of her $100 income, so that she has no money left over for movie rentals. Is the consumer maximizing utility? Solution 1. The first movie would provide 50 utils of utility, and the second movie would provide 30 utils of utility. So if the consumer gave up one Thai meal, the consumer would lose 5 utils of utility but gain 50 + 30 = 80 utils from the two movies she could consume. It is clear then that the consumer is not maximizing utility. Another way to illustrate this is to note that the first movie has MU/$ = 50/$5 = 10, and the tenth Thai meal has MU/$ = 5/$10 = 0.5. The “bang for the buck” is very far from being equal—and that condition is necessary for utility maximization. 2. Imagine that for the past two years, you’ve consumed only two goods: lattes and scones. As you’re probably aware, prices tend to go up over time. If the price of your latte increased from $2 to $3 over the last two years, and the price of scones increased from $1.50 to $2.25, what impact would this have on your budget constraint if your $240 weekly take-home pay didn’t change at all over the same two-year period? Draw both budget constraints on the same set of axes. What if you were able to negotiate a raise to $360 per week? Draw this final budget constraint on the same set of axes as the first two. How does your final budget constraint compare to your original budget constraint from two years ago? Solution 2. When the two prices change, they both go up by 50%, so the price ratio (the slope of the budget constraint) would not change. Rather, the budget constraint would shift inward, as shown in the diagram below. After the raise is negotiated, income rises by 50% as well, so the budget constraint would return to the original position. 3. You learned in the chapter that the process of utility maximization involves a comparison of marginal utilities per dollar, which are calculated as marginal utility divided by price. Consider two goods that most people consume at least some of during their lives: apples and cars. a. If utility maximization was only about marginal utility (not marginal utility per dollar), which good (apples or cars) would consumers want to consume? Would they ever consume the other good? b. If utility maximization was only about price (as opposed to marginal utility divided by price), which good (apples or cars) would consumers want to consume? Would they ever consume the other good? c. Given your answers to parts a and b, and given the observation that some people eat apples and drive cars, explain why utility maximization involves a comparison of marginal utility divided by price, and not just one or the other. Solution 3. a. If utility was all that mattered, it would be more likely that consumers would consume cars, since a car provides more utility than an apple. Only after consuming many, many cars (which would reduce the marginal utility of a car) would a consumer ever consider consuming an apple. b. If price was all that mattered, consumers would only consume apples, since apples will always be cheaper than cars. c. Sometimes apples are a good purchase because, although they do not provide very much marginal utility, they likewise do not cost very much. Sometimes cars are a good purchase because, although they are very expensive (relative to apples), they likewise provide a lot of utility. To get the most utility from a fixed income, consumers must spend that income efficiently: getting the most utility for every dollar spent. Utility maximization thus requires a consideration of marginal utility per dollar, not just utility, and not just dollars. 4. Fill in the blanks with either “good X” or “good Y,” where good X is measured on the x-axis and good Y is measured on the y-axis (vertical axis). a. If the price of ____ is $8, and the price of ____ is $12, then the price ratio (also the slope of the budget constraint) is 1.5. b. A price ratio of 1.5 means that the consumer is able to trade 1 unit of ____ for 1.5 units of ____. c. If another unit of ____ would give a consumer 20 extra units of utility, and another unit of ____ would give a consumer 10 extra units of utility, then the marginal rate of substitution for this consumer is equal to 2. d. A marginal rate of substitution of 2 means that, from the consumer’s point of view, 1 more unit of ____ is as good as 2 more units of ____. e. If the price ratio is 1.5, and the marginal rate of substitution is 2, then the market values ____ more than the consumer does, and the consumer values ____ more than the market does. In this case, the consumer ought to buy less of ____ and more of ____. Solution 4. a. good Y; good X b. good X; good Y c. good X; good Y d. good X; good Y e. good Y; good X; good Y; good X 5. Suppose Haya has $120 of income left each week after she pays her bills and puts some money away in a savings account, and she has two ways to spend this extra money: go to the movies, which costs $18 with popcorn and soda, or go out to a club, which costs $33 including the cover charge and drinks. Assuming these are her only two choices to spend the extra money, what can you say about the following bundles of going to the movies and clubbing? Which of these could possibly be the utility-maximizing bundle? a. 3 movies and 2 nights out at the club b. 2 movies and 3 nights out at the club c. 2 movies and 2 nights out at the club Solution 5. a. This bundle would cost $54 + $66 = $120. This bundle is on the budget constraint. It is the only one that could possibly be the utility-maximizing bundle. b. This bundle would cost $36 + $99 = $135. This bundle is beyond the budget constraint and is too expensive for Haya. This cannot be her utility-maximizing bundle because she cannot afford it. c. This bundle would cost $36 + $66 = $102. This bundle is below the budget constraint. If Haya purchased this bundle, she would have $18 left over that she could use to see another movie. If she likes movies (which she does), then it would be wasteful not to use that $18 to see another movie. This cannot be Haya’s utility-maximizing bundle, because she forgoes the opportunity to consume more. 6. The utility-maximizing bundle of goods is found at the point of tangency between the budget constraint and an indifference curve. In the following diagram, the utility-maximizing bundle is the one labeled point K. There are two different, but equally important, ways to interpret this point. a. Of the three points on the consumer’s budget constraint (J, K, and L), what makes K special? b. Of the three points on the consumer’s indifference curve (M, K, and N), what makes K special? Solution 6. a. Point K is special because, of all of the points on the budget constraint, it provides the most utility. b. Point K is special because, of all of the points on that indifference curve, K is the cheapest. (Or, stated differently, it is the only one that is affordable.) 7. Is marginal utility always diminishing? Consider playing cards. If playing cards were purchased one at a time, what would be true about the marginal utility of the 51st playing card compared with the marginal utility of the 52nd playing card? Why do you think it’s okay for economists to assume that marginal utility diminishes? How does the concept of marginal utility explain why playing cards are not sold individually, but only as entire 52-card decks? Solution 7. The marginal utility of the 51st card would be almost zero, since a deck of 51 cards cannot be used to play any more games than can a deck of 50 cards. The marginal utility of the 52nd playing card would be very high, since with 52 cards one can play almost all card games. It’s okay for economists to assume that marginal utility decreases, however, because no one would ever buy just 51 cards. This is why cards are sold in decks of 52 cards; no rational person wants just 51 cards. With respect to decks of 52 cards, the law of diminishing marginal utility applies. The second 52-card deck provides less additional utility than did the first. Thinking and Problem Solving 8. In Major League Baseball, teams in the American League use a designated hitter (DH) to bat in place of the pitcher, while teams in the National League require their pitchers to bat. Sports economists have noted that in the National League, batters are hit by pitches 15% less often than in the American League. Can you use the concepts from the chapter to explain this behavior from the point of view of the pitcher’s utility-maximizing decision about whether to throw pitches high and inside (where they are more likely to hit the batter)? Solution 8. Think of the pitcher as choosing a “bundle” of pitches to throw. High-and-inside pitches are costlier in the National League because if a pitcher hits a batter (even accidentally), there is a greater chance that the opposing pitcher could retaliate by striking the pitcher when he is next up to bat. The DH rule decreases the “price” of a high-and-inside pitch. A decrease in price of high-and-inside pitches causes an increase in the quantity of that good in the optimal consumption bundle. 9. Consider Facts and Tools question 2. Explain the income and substitution effects of the price changes on your optimal consumption bundle when the latte and scone prices increased, but your income did not. Solution 9. When these two prices changed, the price ratio did not change: the price of a scone was still 25% less than the price of a latte. Since income did not also increase, the budget constraint shifted inward. Because the price ratio did not change, there would be no substitution effect at all—only an income effect. Although dollar income did not change, real income fell because the same dollar income didn’t go as far. The income effect would cause a decrease in the consumption of both scones and lattes, assuming they are both normal goods. 10. With inferior goods (like ramen noodles), the income effect works in the opposite direction from the income effect discussed in the text. If a consumer feels richer, she would buy less of an inferior good. If she feels poorer, more. a. Suppose that a consumer eats two different foods: potatoes and meat. Potatoes are inferior and meat is a luxury. Describe both the income and substitution effects on the consumer’s optimal choice of potatoes and meat if the price of potatoes were to rise. Put the two effects together. What can you conclude? b. What if you knew for sure that the substitution effect dominated the income effect? What would happen to the consumer’s optimal choices for potatoes and meat? c. What if instead you knew that the income effect dominated the substitution effect? What would happen in this case? Why is this result a bit unusual? Solution 10. a. If the price of potatoes were to rise, the substitution effect would cause the consumer to purchase fewer potatoes and more meat. The price increase, however, makes the consumer feel poorer, so the income effect would be to buy less meat (since it is a luxury) and more potatoes (since it is inferior). When the two effects are combined, it is impossible to say what will happen, without knowing which effect dominated. b. If the substitution effect dominated, then the consumer would purchase more meat and fewer potatoes after the increase in the price of potatoes. c. If the income effect dominated, then the consumer would purchase less meat and more potatoes after the increase in the price of potatoes. This is unusual because the consumer is responding to an increase in the price of potatoes by purchasing more potatoes, which appears to violate the law of demand. Economists call a good that people consume more of as the price rises a Giffen good. Giffen goods cannot be ruled out in theory but there are few convincing examples in practice. Believe it or not, however, some economists have demonstrated Giffen-type behavior in laboratory experiments using rats. See Raymond C. Battalio, John H. Kagel, and Carl A. Kogut. 1991. Experimental Confirmation of the Existence of a Giffen Good. The American Economic Review 81(4): 961–970; http://www.jstor.org/stable/2006656. 11. eMusic is a popular subscription MP3 Web site. For a monthly membership fee, you can download MP3s for a price that’s about half of what MP3s cost at iTunes or Amazon. Consider someone with $50 worth of income to spend on entertainment each month and who can choose to buy MP3s or “other stuff”—with a price equal to $1 per unit, so that other stuff is measured in dollars. Create budget constraints for each of the different eMusic membership plans. Prices have been rounded to make things simpler. (To simplify things, we’ll assume that the consumer will use his entire eMusic balance each month, even though eMusic members don’t have to do this. We’ll also just think about MP3 singles, not albums.) a. No membership: The consumer has to purchase MP3s from another Web site, for $1 each. b. eMusic Basic: For $12/month, the consumer gets 24 MP3 downloads. After that, the consumer would have to buy MP3s at another Web site for $1 each. c. eMusic Plus: For $16/month, the consumer gets 34 MP3 downloads. After that, the consumer would have to buy MP3s at another Web site for $1 each. d. eMusic Premium: For $21/month, the consumer gets 46 MP3 downloads. After that, the consumer would have to buy MP3s at another Web site for $1 each. e. eMusic Fan: For $32/month, the consumer gets 73 MP3 downloads. After that, the consumer would have to buy MP3s at another Web site for $1 each. Which plan do you think will be most popular? Which will be the least popular? Although eMusic has hundreds of thousands of members, most people are not members of eMusic. What must be true about their indifference curves? How many MP3s do these people download per month? Solution 11. The budget constraints are shown below. For some of the intermediate plans, it would seem that only consumers with very specific sets of indifference curves would choose those plans. Most consumers would either choose not to join (if the optimal number of MP3s is relatively low), or to join at the eMusic Premium or Fan level. For those who choose not to join (which is most people), they must download fewer than 12 MP3s per month. (This is because if they were to purchase 12 MP3s per month, they would be spending $12, at which point it would make more sense to join eMusic for $12 per month and get 24 MP3s.) 12. In this chapter, we focused a lot on budget constraints, but time is an additional constraint that consumers face. Jackson has $40 per week to spend on leisure activities. He likes to bowl and to play racquetball. Bowling costs $4 per game, and a day pass to the racquet club costs $8. Jackson only has 7 hours of leisure time per week, and both bowling and racquetball each take 1 hour per game. Construct Jackson’s budget constraint and his time constraint on the same diagram. Consider each of the consumption bundles that follow that could possibly be Jackson’s utility-maximizing bundle. How does each of these bundles relate to Jackson’s two constraints? a. Bowling twice per week and playing racquetball four times per week b. Bowling four times per week and playing racquetball three times per week c. Bowling six times per week and playing racquetball once per week Solution 12. The budget and time constraints are shown below. a. This bundle is on the budget constraint, but not the time constraint. This means that Jackson would have leftover time, during which he would like to bowl or play racquetball, but he has no money left over to spend on either activity. b. This bundle is on both of Jackson’s constraints. (It is at the intersection of the two.) This means he would have neither leftover time nor leftover money. c. This bundle is on Jackson’s time constraint but not his budget constraint. This means that Jackson would have money left over that he would like to spend on bowling or racquetball, but no time to engage in either activity. Challenges 13. The chapter argues that the ideal membership fee from Costco’s point of view would leave consumers indifferent between shopping at Costco and shopping elsewhere. Do you think most of the shoppers at Costco are indifferent? What prevents Costco from setting its ideal fee? Solution 13. Costco may try to get its membership fee close to its ideal maximum, but they don’t literally want consumers to be indifferent because then no one would have a reason to join. More important, different customers have a different willingness to pay. At a higher fee, Costco would have fewer members, but as Costco lowers the fee they get more members; but now the members who would have joined at the higher fee aren’t indifferent from buying at Costco (they earn a surplus). In fact, Costco would like to earn some of this surplus back, which they can do by setting prices above marginal cost. Of course, if Costco sets its prices too high, no one wants to join! Thus, Costco has a delicate balancing act between setting the membership fee and the prices at which it sells goods to members. The theory of industrial organization examines these types of issues in greater depth. 14. Assume a consumer earns $50 in period 1 and $150 in period 2, and that saving and borrowing are both interest-free. Draw a budget constraint. Now let’s see if we can add some more real-life detail. a. Draw a new budget constraint for the consumer if the period 1 income remains at $50, but the period 2 income falls to $100. Use the ideas of the income and substitution effects to describe how this change would affect the optimal choice of the consumer. b. Now let’s add another wrinkle: an interest rate. Assume as before that the consumer earns $50 in period 1 and $150 in period 2. Construct a budget constraint for a consumer that can earn 20% interest by saving money in period 1 for use in period 2 but also has to pay 20% interest to borrow money from period 2 for use in period 1. (These interest rates are high so that the impact is obvious on your graph; the results will still hold—although less dramatically—with lower interest rates.) What is the substitution effect of the addition of the interest rate? The income effect is more complicated, because it depends on the consumer’s preferences, which could be revealed by the pre-interest-rate behavior. c. In February 2017, the average interest rate on money market and savings accounts was 0.26%, but the average rate on a variable-rate credit card was 16.43%. Obviously the previous assumption that the interest rate is the same for borrowers and savers is not very realistic. Again, using more dramatic interest rates, can you construct a budget constraint for a consumer with the same initial endowment as previously that faces a 1% interest rate for saving and a 50% interest rate for borrowing? What do you notice about this budget constraint? Solution 14. a. The budget constraint shifts in parallel to the old one, and hits both axes at $150 of consumption instead of at $200. There is no substitution effect because the price ratio has not changed. There is only an income effect. The consumer will consume less in both periods. If the consumer is attempting to smooth consumption, then the consumer would choose ($75, $75) after this change. b. The addition of an interest rate changes the slope of the budget constraint. In fact, it rotates the budget constraint through the point ($50, $150) because the consumer’s initial endowment is unchanged by an interest rate. Now, the maximum consumption in period 2 is $150 + (1.20 × $50) = $210. The maximum consumption in period 1 is $50 + ($150 ÷ 1.20) = $175. The budget constraint is shown below. The substitution effect has changed the price ratio. Now, $1 worth of consumption in period 1 causes a reduction in period 2 consumption of $1.20. By increasing the price of current consumption, the substitution effect will cause the consumer to consume less now and more later; in other words, it will inspire relatively more saving behavior. The income effect for a borrower, like the live-for-the-moment consumer, will be negative, since this interest rate punishes borrowers. This consumer would need to be compensated with additional income to return to their old level of utility. (For a saver, however, the income effect would be positive.) c. This consumer will have a kinked budget constraint. It is kinked because the initial endowment of ($50, $150) is still available, but the slope of the budget constraint is different in either direction from this point. The highest possible period 2 consumption is $150 + (1.01 × $50) = $200.50. The highest point for period 1 consumption is $50 + ($150 ÷ 1.5) = $150. In the diagram, this is the dashed budget constraint. 15. Currently, if you join Disney’s movie club, you get 5 DVDs for $1 each, but you have to commit to buying at least 4 more DVDs at $20 each over the next year. Suppose the normal market price of a DVD is $16. a. Construct two budget constraints: one for a consumer who joins Disney’s movie club and another for a consumer who doesn’t. Assume that both consumers have $112 worth of income. Place income on the vertical axis just like in Figure 25.12. b. What kind of consumer is likely to get more utility from joining Disney’s movie club? What kind of consumer would not? c. If Disney’s movie club wanted to charge an additional membership fee to generate more revenue, what would be the maximum they could charge for membership? Solution 15. a. The consumer who does not join has a simple budget constraint. It begins at ($112, 0 DVDs) and falls at a rate of $16/DVD. The DVD intercept is at ($0, 7 DVDs). (Instructors may wish to have the student construct a stepped budget constraint with whole DVDs only.) The joining budget constraint begins at ($37, 9 DVDs) because joining costs at least $1 + $1 + $1 + $1 + $1 + $20 + $20 + $20 + $20 = $85 but provides 9 DVDs (5 cheap and 4 costly). From that point, however, the consumer would be better off buying DVDs in the market, so that the budget constraint slopes downward from that point at a rate of $16 per DVD. The DVD intercept should be 9 + ($27/$16) = 10.6875 DVDs. Adjust the values of the axes according to the new data and outcome: b. A consumer with preferences for DVDs would get more utility from joining Disney’s movie club. Another way to say this is that there will be no utility-maximizing consumers who do not join Disney’s club but still buy 6 or more DVDs. c. The most that Disney’s movie club could charge for membership would be the amount that makes consumers indifferent between joining and not joining. In order to do this, the “join” budget constraint would have to be shifted downward until it lies right on top of the “no join” budget constraint. A membership fee of ($16 × 9) − $85 = $59. This is because a consumer who does not join must give up $144 to get 9 DVDs. A consumer who does join already gives up $85 to get 9 DVDs. So the $59 represents the savings on 9 DVDs that joiners currently get. The maximum membership fee would exploit that entire $59 gain. 16. Two special cases might result in indifference curves that look a little different from the ones discussed in the text. a. If two goods are perfect substitutes, that means the consumer would always be willing to trade one for the other in a certain, fixed proportion. In this case, the MRS would be constant, which means that indifference curves would be straight lines. Suppose a consumer’s MRS between two goods X and Y is a constant 2.5, which means that the consumer is always willing to give up 1 unit of good X for 2.5 units of good Y. If the consumer has $180 in income to spend, and the price of good X is $20 per unit, and the price of good Y is $10 per unit, what is this consumer’s utility-maximizing bundle of X and Y? Answer the question by thinking through it, and then show with a diagram (including a budget constraint and an indifference curve) why your answer works. b. If two goods are perfect complements, indifference curves have a very unusual shape. Let’s see if you can reason through this one. Consider left and right shoes. For most people, having left shoes alone (or right shoes alone) does not really provide any utility; rather, people get utility from having a pair of shoes that they can wear. In this case, left and right shoes are perfect 1:1 complements. Can you figure out what indifference curves would look like in this case? To figure it out, it might be helpful to think about questions like the following: If someone has 4 right shoes and 4 (matching) left shoes, what’s the marginal utility of an extra right shoe? If a consumer had to compare the bundles (4 left shoes, 4 right shoes), (4 left shoes, 5 right shoes) and (7 left shoes, 4 right shoes), how would these bundles rank? Would any of these bundles be better than the others? Solution 16. a. In this case, the price ratio is 2, but the MRS is a constant 2.5. The consumer always values X (in terms of Y) more than the amount of Y he must give up to get another unit of X. So, trading away Y in exchange for X always increases utility. This consumer should consume only X. Another way to think of this is to think about the endpoints of the budget constraint. The consumer can afford $180/$20 = 9 units of X or $180/$10 = 18 units of Y. The 9 units of X are as good to the consumer as 9 × 2.5 = 22.5 units of Y. So 9 units of X provide more utility than 18 units of Y. The diagram below shows that the indifference curve is a straight line that is steeper than the budget constraint; thus to reach the highest indifference curve, the consumer consumes the point (9, 0). b. When someone has 4 of each type of shoe, they have four pairs of shoes. Having one more of either type provides no utility, because the number of pairs is still 4. The bundles described all provide exactly the same level of utility because they all leave the consumer with exactly four pairs of shoes. The only way to increase utility is to increase the number of both left and right shoes. When two goods are perfect complements, the indifference curves are right angles. An example is shown below. Since all three bundles provide the same utility, they must all be on the same indifference curve. Only a right angle can achieve this. APPENDIX A Modern Principles of Economics: Reading Graphs and Making Graphs 1. We start with a simple idea from algebra: Which of the following graphs have a positive slope and which have a negative slope? Solution 1. A (demand curve): Negative B (employment rigidity and long-term unemployment): Positive C (Real GDP per person and rate of child labor): Negative D (supply curve): Positive 2. When social scientists talk about social and economic facts, they usually talk about a “positive relationship” or a “negative relationship” instead of “positive slope” or “negative slope.” Based on your knowledge, which of the following pairs of variables tend to have a “positive relationship” (a positive slope when graphed), and which have a negative relationship? (Note: “Negative relationship” and “inverse relationship” mean the same thing. Also, in this question, we’re only talking about correlation, not causation.) a. A professional baseball player’s batting average and his annual salary. b. A professional golfer’s average score and her average salary. c. The number of cigarettes a person smokes and her life expectancy. d. The size of the car you drive and your probability of surviving a serious accident. e. A country’s distance from the equator and how rich its citizens tend to be. (For the answer, see Robert Hall and Charles Jones. 1999. Why Do Some Countries Produce So Much More Output per Worker than Others? Journal of Political Economy, vol. 114, No. 1 (Feb. 1999), pp. 83-116.) Solution 2. a. Positive relationship: Better players earn more on average. b. Negative or inverse relationship: A lower score is better. c. Negative or inverse relationship: People who smoke more tend to have shorter lives. d. Positive relationship: People in bigger cars or trucks tend to more often survive accidents. e. Positive relationship: The richest countries tend to be closer to the poles, as Hall and Jones note. The poorest countries tend to be closer to the equator. There are many exceptions, as there are in parts a–d of this question—but as social scientists, we’re focusing on the overall tendency, not any particular case. 3. Let’s convert Klick and Tabarrok’s research on crime into a simple algebra equation. We reported the result as the effect of a 10% increase in police on the crime rate in Washington, D.C. In the equation below, fill in the effect of a 1% increase in the police on the crime rate: The percent change in crime = _____ × The percent change in police officers Solution 3. –0.3%; a 10% rise in police causes about a 3% fall in crime, so we divide 3 by 10. 4. Let’s read the child labor graph (A.10) horizontally and then vertically: a. According to the trendline, in a typical country with 10% of the children in the labor force, what’s the real GDP per person? b. According to the trendline, when a country’s GDP per person is $2,000, roughly what percentage of children are in the labor force? Solution 4. a. $6,000 per person: A bit higher than Thailand. b. About 25%—clearly somewhere between 20% and 30% of the children are in the workforce at this low level of GDP per person: 25% is the same as one-fourth, or one out of four. 5. Let’s take another look at the ratio scale, and compare it to a normal scale. a. In Figure A.7, which one is presented in ratio scale and which in normal scale? b. In the top graph, every time the S&P 500 crosses a horizontal line, how many points did the S&P rise? c. In the bottom graph, every time the S&P 500 crosses a horizontal line, how many times higher is the S&P? Solution 5. a. The top is in the normal scale, the bottom in the ratio scale. b. 200 points per horizontal line c. Every time the data cross a new horizontal line, the S&P is 10 times higher: Quite a difference from the normal scale. The log scale is 10, 100, 1,000, 10,000. 6. As a scientist, you have to plot the following data: The number of bacteria you have in a large petri dish, measured every hour over the course of a week. (Note: E. coli bacteria populations can double every 20 minutes.) Should this data be plotted on a ratio scale and why? Solution 6. The bacteria data should be plotted on a ratio scale: If it’s really doubling every 20 minutes or so, then the data would shoot up quite quickly and steeply on a normal scale graph. But on a ratio or log scale, the overall data would look more like a straight line if the bacteria grew at a constant rate. So if there were a big change in the growth rate, you could immediately tell by looking at the ratio scale graph. 7. Educated people are supposed to point out (correctly) that “correlation isn’t proof of causation.” This is an important fact—which explains why economists, medical doctors, and other researchers spend a lot of time trying to look for proof of causation. But sometimes, correlation is good enough. In the following examples, take the correlation as a true fact, and explain why the correlation is, all by itself, useful for the task presented in each question. a. Your task is to decide what brand of car to buy. You know that Brand H usually gets higher quality ratings than Brand C. You don’t know what causes Brand H to get higher ratings—maybe Brand H hires better workers, maybe Brand H buys better raw materials. All you have is the correlation. b. Your task is to hire the job applicant who appears to be the smartest. Applicant M has a degree from MIT, and applicant S has a degree from a typical state university. You don’t know what causes MIT graduates to be smarter than typical state university graduates—maybe they start off smarter before they get to MIT, maybe their professors teach them a lot more, maybe having smart classmates for four years gives them constant brain exercise. c. Your task is to decide which city to move to, and you want to move to the city that is probably the safest. For some strange reason, the only fact you have to help you with your decision is the number of police per person. Solution 7. a. You don’t care why one brand is better than another—you don’t care about causation. You just care about having a good car to drive, and the quality ratings are a useful predictor of which one is better. b. People at MIT tend to be smarter than graduates of state universities. Of course, as with car quality, there are many exceptions, but the tendency is clear. And as in part a, what you care about is predicting who will be good, with little concern for how the MIT people got to be so smart. c. This brings us back to the chapter: If you want to live in a safe city, and police presence is literally the only fact you have, you should choose the city with the fewest police officers. The overarching theme in this question is that if you only need to forecast or predict the future of an overall relationship, then you don’t need to worry about causation. In each case, your choice isn’t changing the overall relationship: You’re not trying to make Brand C’s cars better, you’re not changing the curriculum at MIT, you’re not deciding whether to add more cops to a town’s budget. You’re just an outsider with no influence on the big trends: And that makes it much easier to use data. (Aside: This explains why economic forecasting is very different from economic policy, and why forecasters can usually ignore “correlation not causation” arguments.) 8. If you haven’t practiced in a while, let’s calculate some slopes. In each case, we give two points, and you can use the “rise over run” formula to get the right answer. a. Point 1: x = 0, y = 0. Point 2: x = 3, y = 6 b. Point 1: x = 6, y = –9. Point 2: x = 3, y = 6 c. Point 1: x = 4, y = 8. Point 2: x = 1, y = 12 Solution 8. a. Rise = 6, Run = 3. Slope = 6/3 = 2. b. Rise = 15, Run = –3. Slope = 15/–3 = –5. c. Rise = 4, Run = –3. Slope = 4/–3 = –4/3. 9. We mentioned that a demand curve is a hypothetical relationship. It answers a “what if” question: “What if today’s price of oil rose (or fell), but the average consumer’s income, beliefs about future oil prices, and the prices of everything else in the economy stayed the same?” When some of those other features change, then the demand curve isn’t fixed any more: It shifts up (and right) or left (and down). In Figure A.3, we showed one shift graphically: Let’s make some changes in algebra: The economy of Perovia has the following demand for oil: Price = B – M x Quantity When will B tend to be a larger number: a. When population in Perovia is high or when it is low? b. When the price of autos in Perovia is high or when it is low? c. When Perovian income is high or when it is low? Solution 9. B will tend to be larger when population is higher, autos are cheaper, and income is higher. We cover these forces in more detail in the textbook, but all three are discussed in this Appendix: The mathematical idea is that a rise in B is the same as a shift up (and right) of the demand curve. It’s the same as an increase in the y-intercept. 10. Using the FRED economic database (https://fred.stlouisfed.org) search for U.S. Real Gross Domestic Product and graph the seasonally adjusted quarterly series. a. What was U.S. real GDP in the first quarter of 1980? b. Click on Edit Graph and change the Units to Percent Change from Year Ago and Modify Frequency to Annual. By how much did the U.S. economy shrink in 2009? Solution 10. a. In 1980, real U.S. GDP was 6,635.7 billion dollars. b. The U.S. economy shrank by 2.77% in 2009. Solution Manual for Modern Principles: Microeconomics Tyler Cowen, Alex Tabarrok 9781319098766
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