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- Title: 101-3_07
- Type: Notes
- School: Cornell
- Course: ECON 1110
- Term: Spring
101 Econ Lecture 3 Some Common Pitfalls for Decision Makers Pitfall #1. Measuring Costs and Benefits as proportions rather than as absolute dollar amounts (as in the K-Mart vs. Campus Store examples from lecture 1) Exercise: Your employer has a travel discount voucher that can be redeemed on one of your next two business trips. You could use it to save $100 on a $2000 plane ticket to Tokyo; or you could save $90 on a $200 plane ticket to Chicago? If your goal is to do what would be best for your company, for which trip should you use the coupon? Pitfall #2. Ignoring Opportunity Costs If doing activity x means not being able to do activity y, then the value to you of doing y is an opportunity cost of doing x. Many people make bad decisions because they tend to ignore the value of such foregone opportunities. This insight suggests that it will almost always be instructive to translate questions like "Should I do x?" into ones like "Should I do x or y?" In the latter question, y is simply the most highly valued alternative to doing x. Example 3.1. Should I go skiing today? There is a ski area near your campus and you go skiing often. From experience you can confidently say that a day on the slopes is worth $50 to you. The charge for the day is $30 (which includes busfare, lift ticket, and equipment). But this is not the only cost of going skiing. You must also take into account the value of the most attractive alternative you will forego by heading for the slopes. Suppose that if you don't go skiing, you will work at your new job as a research assistant for one of your professors. The job pays $40 dollars per day, and you like it just well enough to have been willing to do it for free. So the question you face is "Should I go skiing or stay and work as a research assistant?" C(x) = cost of skiing plus value of forgone earnings = $30 + $40 = $70 B(x) = $50 < C(x), so don't go skiing. Note in Example 3.1 the role of your feelings about the job. The fact that you liked it just well enough to have been willing to do it for free is another way of saying that there are no psychic costs associated with doing it. This is important because it means that by not doing the job you would not be escaping something unpleasant. Of course, not all jobs fall into this category. Suppose instead that your job had been to scrape plates in the dining hall for the same pay, $40/day, and that the job was so unpleasant that you would be unwilling to do it for less than $25/day. Assuming your manager at the dining hall permits you to take a day off whenever you want, let us now reconsider your decision about whether to go skiing. Example 3.2. Same as Example 3.1, except that the alternative for the day is to scrape plates, not work as a research assistant. There are two equivalent ways to look at this decision: I. One of the benefits of going skiing is not having to scrape plates. B(x) = $25 + $50 = $75 In this view of the problem, C(x) is the same as before, namely the $30 ski charge plus the $40 opportunity cost of the lost earnings, or $70. So now B(x) > C(x), which means you should go skiing. II. Alternatively, we could have viewed the unpleasantness of the plate-scraping job as an offset against its salary. By this approach, the opportunity cost of not working in the dining hall is only $40 - $25 = $15/day. Then C(x) = $30 + $15 = $45 < B(x) = $50, and again the conclusion is that you should go skiing. It makes no difference which of these two ways you handle the valuation of the unpleasantness of scraping plates. It is critically important, however, that you do it either one way or the other. Don't count it twice! Example 3.2 makes clear that there is a reciprocal relationship between costs and benefits. Not incurring a cost is the same as getting a benefit. By the same token, not getting a benefit is the same as incurring a cost. Obvious as this sounds, it is often overlooked. Consider, for example, the case of a foreign graduate student who recently got his degree and was about to return to his home country. The trade regulations of his nation permitted people 2 returning from abroad to bring back a new automobile without having to pay the normal 50 percent tariff. The student's father-in-law asked him to bring him back a new $10,000 Chevrolet, and sent him a check for exactly that amount. This put the student in a quandary. He had been planning to bring back a Chevrolet and sell it in his home country. Because, as noted, new cars normally face a 50 percent import tax, such a car would sell at a dealership there for $15,000. The student conservatively estimated that he could easily sell it privately for $14,000, which would net him a $4000 profit. Example 3.3. Is it fair to charge interest when lending a friend some money? Suppose a friend lends you $10,000, and her primary concern in deciding whether to charge interest is to decide if it would be "fair" to do so. She could have put that same money in the bank, where it would have earned, say, 5 percent interest, or $500 each year. If she charges you $500 interest for each year the loan is out, she is merely recovering the opportunity cost of her money. If she didn't charge you any interest, it would be the same as making you a gift of $500/yr. Now, she might well wish to make you a yearly gift of that amount, or indeed even a much larger amount. But no one would say it was unfair if she didn't give you a large cash gift each year. And it makes no more sense to say that her recovery of the opportunity cost of lending you money is unfair. Dear Ann Landers: I have four children who are successful in their marriages and careers. I have always tried to treat them in an evenhanded way when it comes to matters such as college tuition and loans for home purchases. It has been my policy to charge a modest rate of interest for the loans in order not to favor one child over another. Recently my oldest daughter asked for a two-year loan to help finance a larger home. Both she and her husband have good jobs, but they wanted to avoid using nonliquid assets. ... As in the past, I mailed her a check accompanied by a note to sign and return to me. The note was an agreement to pay interest. I included a repayment schedule. To my surprise, she cashed the check and returned the note with the reference to interest crossed out. Subsequently, she has been making her monthly payments to me on principal only. In a recent visit to her home, my daughter and I discussed the situation but we were unable to resolve the issue.... Is my loan policy unreasonable? How would you handle this? Carl in Akron Dear Carl: For openers, I would never charge a child of mine interest on a loan. Since it is your money, however, you have every right to do with it whatever you wish. ... Ann Landers Example 3.4. Why do banks pay interest in the first place? Suppose you owned a bank and someone deposited $10,000 in it on January 1 without your having to pay him interest. You could then take the money and buy a productive asset, such as a stand of trees. Suppose that each year trees grow at the rate of 6 percent, and that the price of a tree is proportional to the amount of lumber in it. At the end of the year you could then sell the trees for $10,600, and have $600 more than before. But that same option was available to the person who put his money in your bank. Why should he give you the $600 he could have earned? He will be willing to let you use his money only if you compensate him for the opportunity cost of not using it himself. If you pay him 5 percent interest, he will get $500, which will probably be acceptable to him because he won't have to go to the trouble of tending the trees himself (or of lending the money to someone who will tend them). You get to keep the remaining $100 for taking care of that. If interest is really a reimbursement for the opportunity cost of money, why are so many people hostile to money lenders? Perhaps because people who borrow are often poor, while those who lend are often rich. This is not always the case. Billionaire Donald Trump borrows to finance his real-estate developments, and sometimes the money comes from the pension funds of low-wage workers. But more commonly, interest payments involve transfers of money from people who seem desperately to need it to those who seem to have more than they can spend. Note, though, that even here it is the differences in wealth, not the interest payments themselves, that are a more logical focus of concern. A poor person's lot can be improved if some way can be found to increase his wealth. He is not necessarily helped, however, by laws and customs that make it difficult to borrow money. As simple as the opportunity cost concept is, it is one of the most important in microeconomics. The art in applying the concept correctly lies in being able to recognize the most valuable alternative that is sacrificed by the pursuit of a given activity. Pitfall #3. Failure to ignore sunk costs. An opportunity cost will often not seem like a relevant cost when in reality it is. Another pitfall in decision making is that sometimes an expenditure will seem like a relevant cost when in reality it is not. Such is often the case with sunk costs, costs that are beyond recovery at the moment a decision is made. Unlike opportunity costs, these costs should be ignored. The principle of ignoring sunk costs emerges clearly in the following example. 3 Example 3.5. Should I drive to Boston or take the bus? You are planning a 250 mile trip to Boston. Except for the cost, you are completely indifferent between driving and taking the bus. Busfare is $100. You don't know how much it would cost to drive your car, so you call Hertz for an estimate. The person you speak with tells you that for your make of car the costs of a typical 10,000 mile driving year are as follows: Insurance $1000 Interest 2000 Fuel & oil 1000 Maintenance 1000 Total $5000 Suppose you calculate that these costs come to $0.50/mile and use this figure to compute that the 250 mile trip will cost you $125 by car. And since this is more than the $100 busfare, you decide to take the bus. If you decide in this fashion, you commit the error of not ignoring sunk costs. Your insurance and interest payments do not vary with the number of miles you drive each year. Both are sunk costs and will be the same whether you drive to Boston or not. Of the costs listed, fuel & oil and maintenance are the only ones that vary with miles driven. These come to $2000 for each 10,000 miles you drive, or $.20/mile. At $.20/mile, it costs you only $50 to drive to Boston, and since this is much less than the busfare, you should drive. In Example 3.5, note the role of the assumption that, costs aside, you are indifferent between the two modes of transport. This lets us say that the only comparison that matters is the actual cost of the two modes. If you had preferred one mode to the other, however, we would also have had to weigh that preference. Thus, for example, if you were willing to pay $60 to avoid the hassle of driving, the real cost of driving would be $110, not $50, and you should take the bus. You will find exercises like the one below sprinkled throughout the text to help you make sure that you understand important analytical concepts. You will master microeconomics effectively more if you do these exercises as you go along. Example 3.6. How, if at all, would your answer to the question posed in Example 3.5 be different if the hassle of driving is $20 and if you average one $28 traffic ticket for every 200 miles you drive? Someone who gets a $28 traffic ticket every 200 miles driven will pay $35 in fines, on the average, for every 250 miles driven. Adding that figure to the $20 hassle cost of driving, then adding the $50 fuel, oil, and maintenance cost, we have $105. This is more than the $100 busfare, which means taking the bus is best. Example 3.7. The Pizza Experiment. A local pizza parlor offers an all-you-can-eat lunch for $3. You pay at the door, and then the waiter brings you as many slices of pizza as you like. One of my colleagues performed this experiment: He had an assistant serve as the waiter for one group of tables. The "waiter" selected half of the tables at random and gave everyone at those tables a $3 refund before taking orders. The remaining half of his tables got no refund. He then kept careful count of the number of slices of pizza each diner ate. What difference, if any, do you predict in the amounts eaten by these two groups? Diners in each group confront this question: "Should I eat another slice of pizza?" Here, the activity x consists of eating one more slice. For both groups, C(x) is exactly zero. Because the refund group was chosen at random, there is no reason to suppose that its members like pizza any more or less than the others. Thus, B(x) should be the same for each group, on the average. People from both groups should keep eating until B(x) falls to zero. By this reasoning, the two groups should eat the same amount of pizza, on the average. The $3 admission fee is a sunk cost, and should have no influence on the amount of pizza one eats. In fact, however, the group that did not get the refund consumed substantially more pizza. Although our cost-benefit decision rule fails the test of prediction in this experiment, its message for the rational decision maker stands unchallenged. The two groups logically should have behaved the same. The only difference between them, after all, is that patrons in the refund group have lifetime incomes that are $3 higher than the others'. Surely no one believes that such a trivial difference should have any effect on pizza consumption. Members of the no-refund group seemed to want to make sure they "got their money's worth." In all likelihood, however, this motive merely led them to overeat.1 What's wrong with being motivated to "get your money's worth?" Absolutely nothing, as long as the force of this motive operates before you enter into transactions. Thus, for example, it makes perfectly good sense to be led by this motive alternative to the "get-your-money's-worth" explanation is that $3 is a significant fraction of the amount of cash many diners have available to spend in the short run. Thus, for example, members of the refund group might have held back in order to save room for the dessert they could now afford to buy. To test this alternative explanation, the experimenter could give members of the no-refund group a $3 cash gift earlier in the day, and then see if the amount of pizza consumed by the two groups still differed. 1An 4 to choose one restaurant over an otherwise identical competitor that costs more. Once the price of your lunch has been determined, however, the get-your-money's-worth motive should be abandoned. The satisfaction you get from eating another slice of pizza should then depend only on how hungry you are and on how much you like pizza, not on how much you paid for the privilege of eating all you can eat. Yet people often seem not to behave in this fashion. The difficulty may be that we are not creatures of complete flexibility. Perhaps motives that it makes sense to hold in one context are not easily abandoned in another. Pitfall # 4: Failure to understand the average-marginal distinction. Example 3.8. Suppose you own a fishing fleet of consisting of a given number of boats, and can send your boats in whatever numbers you wish to either of two ends of an extremely wide lake, east or west. Under your current allocation of boats, the ones fishing at the east end return daily with 100 pounds of fish each, while those in the west return daily with 120 pounds each. The fish populations at each end of the lake are completely independent, and your current yields can be sustained indefinitely. True or False: If you shift some of your boats from the east end to the west end, you will catch more fish. Example 3.9. You are a baseball pitcher who throws two different kinds of pitches: fastball and curve. Your team statistician tells you that at the current rate at which you employ these pitches, batters hit .275 against your curve, only .200 against your fastball. True or false: You should throw more fastballs and fewer curves. Most people, especially those who have not had a good course in microeconomics, answer confidently that the current allocations should be altered in each case. Specifically, they say that the fishing fleet owner should send more boats to the west side of the lake and that the baseball pitcher should throw more fastballs. Yet, as the following example illustrates, even a rudimentary understanding of the distinction between the average and marginal product of a productive resource makes clear that neither of these responses is justified. Example 3.10. In the fishing fleet scenario just described, suppose the relationship between the number of boats sent to each end and the number of pounds caught per boat is as summarized in the table. Suppose further that you have four boats in your fleet, and that two currently fish the east end while the other two fish the west end. (Note that all of these suppositions are completely consistent with the facts outlined in the Example 3.8.) Should you move one of your boats from the east end to the west end? Catch per Boat for Two Fishing Areas Number of boats 1 2 3 4 East end 100 lbs/boat 100 lbs/boat 100 lbs/boat 100 lbs/boat West end 130 lbs/boat 120 lbs/boat 110 lbs/boat 100 lbs/boat Current output (2 east, 2 west) = 440 lbs. Output with 1 east, 3 west = 430 So, no, you should not move an extra boat to the west end. Neither, for that matter, should you send one of the west end boats to the east end. Loss of a boat from the west end would reduce the total daily catch at that end by 110 pounds (the difference between the 240 pounds caught by two boats and the 130 that would be caught by one), which is more than the extra 100 pounds you would get by having an extra boat at the east end. The current allocation of two boats to each end is optimal. The general rule for allocating a resource efficiently across different production activities is to allocate each unit of the resource to the production activity where its marginal benefit is highest. For a resource that is perfectly divisible, and for activities for which the marginal product of the resource is not always higher in one than in the others, the rule is: Allocate the resource so that its marginal benefit is the same in every activity. 5 Many people, however, "solve" these kinds of problems by allocating resources to the activity with the highest average benefit, or by trying to equalize average benefit across activities. The reason that this particular wrong answer often has appeal is that people often focus on only part of the relevant production process. By sending only two boats to the west end, the average catch at that end is 20 pounds per day greater than the average catch per boat at the east end. But note that if you send a third boat to the west end, that boat's contribution to the total amount of fish caught at the west end will be only 90 pounds per day (the difference between the 330 pounds caught by three boats and 240 pounds caught by two). What people often tend to overlook is that the third boat at the west end catches some of the fish that would otherwise have been caught by the first two. As the figures in the table illustrate, the opportunity cost of the sending a third boat to the west end is the 100 pounds of fish that will no longer be caught at the east end. But since that third boat will add only 90 pounds to the daily catch at the west end, the best that can be done is to keep sending two boats to each end of the lake. The fact that either of the two boats currently fishing at the east end could catch 10 pounds per day more by moving to the west end is no cause for concern to a fishing fleet owner who understands the distinction between average and marginal products. The scenario involving the baseball pitcher raises an identical set of issues. We cannot say that the pitcher should throw more fastballs without first knowing how a change in the proportion of pitches thrown would alter the effectiveness of both types of pitches. In particular, throwing more fastballs is likely to decrease the effectiveness not only of the additional fastballs thrown but of all other fastballs as well. And if this loss exceeds the gain from switching from curves to fastballs, more fastballs should not be thrown. Example 3.11. Same as Example 3.10, except now all entries in the right column of the table are equal to 120 pounds/day. Catch per Boat for Two Fishing Areas Number East end West end of boats 100 lbs/boat 120 lbs/boat 1 2 3 4 100 lbs/boat 100 lbs/boat 100 lbs/boat 120 lbs/boat 120 lbs/boat 120 lbs/boat Maximum output (480 lbs/day)occurs when all four boats go the west end The difference between this example and Example 3.10 is that this time there is no drop-off in the rate at which fish are caught as more boats are sent to the west end of the lake. So this time the average benefit of boats sent to the west end is identical to their marginal benefit. And since the marginal benefit is always higher for boats sent to the west end, the optimal allocation is to send all four boats to that end. Cases like the one illustrated in Example 3.11 are by no means unusual. But by far the more common, and more interesting, production decisions are the ones that involve interior solutions like the one we saw in Example 3.10, where some positive quantity of the productive input must be allocated to each activity. Example 3.12. Suppose that from the last seconds you devoted to problem 1 on your first economics exam you earned 4 extra points, while from the last seconds devoted to problem 2 you earned 6 extra points. The total number of points you earned on these two questions were 20 and 12, respectively, and the total time you spent on each was the same. How-- if at all-- should you have reallocated your time between them? The rule for efficient allocation of time spent on exams is the same as the rule for efficient allocation of any resource: the marginal benefit of the resource should be the same in each activity. From the information given, the marginal product of your last seconds spent on question 2 was 6 points, or 2 points more than the marginal product of the last seconds spent on question 1. Even though the average product of your time spent on question 1 was higher than on question 2, you would have scored more points if you had spent less time on question 1 and more time on question 2.
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