the PART
1
Introduction
limitedas fundamental economic problem. The chapter shows that deciding whether to take an action by comparing the cost and benet of the action is a useful approach for dealing with the inevitable trade-offs that scarcity creates. It also identies several pitfalls that plague many decision makers. Chapter 2 goes beyond individual decision making to consider trade among both individuals and countries. An important reason for trade is that it permits people (or countries) to specialize in the production of particular goods and services, which in turn enhances productivity and raises standards of living. Finally, Chapter 3 presents an overview of the concepts of supply and demand, perhaps the most basic and familiar tools of economists.
Economics is a way of thinking about the world. Over many years economists have developed some simple principles and tools that are useful for understanding a wide range of situations, from the relatively simple economic decisions that individuals make every day to the workings of highly complex markets, such as international nancial markets. A major objective of this book is to help you learn these principles and tools and also how to apply them to a variety of issues. The three chapters of Part I introduce the problem of scarcity and develop six core principles that will be used throughout the book. Chapter 1 presents scarcitythe unavoidable fact that although our needs and wants are limitless, the resources available to satisfy them are
Chapter
1
ThinkingL ike an Economist
CHAPTER OUTLINE
1.1 Economics: Studying Choice in a World of Scarcity 1.2 1.3 1.4 1.5 1.6
1.7 1.8 1.9
How many students are in your introductory economics class? Some classes have just 20 or so. Others average 35, 100, or 200 students. At some large universities, introductory economics Applying the Cost classes may have as many as 2000 students, while colleges and Benet Principle smaller universities may offer much smaller classes. What size is Three Common best? Pitfalls If cost was no object, the best size for an introductory economics course, or any other course for that matter, might be only a Pitfall 1: Ignoring single student. Everything could be tailored to your own background Opportunity Costs and ability, allowing you to cover the material at just the right pace. The tutorial format would also promote close communication and Pitfall 2: Failure to personal trust between you and your professor. Ignore Sunk Costs Why, then, have many Canadian universities reduced the numPitfall 3: Failure ber of introductory economics classes they offer while increasing to Understand the the number of students per class? The simple reason is that cost AverageMarginal does matter. The direct cost of providing you with your own personal introductory economics course, most notably the professors Distinction salary and the expense of providing a classroom in which to meet, Economics: Micro might easily top $20 000. Someone has to pay these costs. Since and Macro Canadian universities receive part of their revenue from governments and part from students fees, the cost would be covered by The Approach of higher tuition payments and higher tax payments. This Text With a larger class size, of course, the cost per student goes Economic Naturalism down. For example, in a class of 300 students, the cost of an introductory economics course might be as little as $100 per student. However, there is a trade-off. Although few students like large classes, they are signicantly more affordable. In choosing what size the introductory economics course should be, university and college administrators confront a classic economic trade-off. In making the class larger, they increase the studentfaculty ratio; but, at the same time, they reduce costs per student and hence the tuition students must pay.
ECONOMICS: STUDYING CHOICE IN A WORLD OF SCARCITY
3
1.1
ECONOMICS:ST UDYINGCH OICE IN A WORLD OF SCARCITY
If we could always have whatever we wanted, for free, right now, we would never have to chooseall we would ever have to say is more please, and we would get it. Unfortunately, the real world is not like that. Most things have a cost in time or money or other resources, all of which we have in only limited amounts. Scarcity means that we have to make choices. More of one good means choosing less of another. Economics is the study of how people make choices under conditions of scarcity and of the results of those choices for society. That such trade-offs are widespread and important is the core problem of economics. We call this the scarcity problem, because the simple fact of scarcity makes trade-offs necessary. Another name for the scarcity problem might be the no-free-lunch idea, which comes from the observation that even a lunch that is given to you takes time to eattime you could have spent doing other useful things. The Scarcity Problem: Although we have boundless needs and wants, the resources available to us, including time, are limited. Scarcity means that we have to make choiceshaving more of one good thing usually means having less of another. Trade-offs require choices that involve compromises between competing interests. Costbenet analysis is based on the disarmingly simple principle that an action will make an individual (or a rm or a society) better off if, and only if, its benets exceed its costs. We call this statement the costbenet principle. It is one of the core principles of economics. The CostBenet Principle: An individual (or a rm or a society) will be better off taking an action if, and only if, the extra benets from taking the action are greater than the extra costs.
COST COST BENEFIT
Are small classes better than large ones? economics the study of how people make choices under conditions of scarcity and of the results of those choices for society
The costbenet principle is simple, but to apply it we need to measure costs and benets, a task that is often difcult in practice. Nevertheless, a few simplifying assumptions can help us to demonstrate how the costbenet principle can be applied to the question of the best class size. First, suppose that because a university has only two sizes of classrooms, classes of 20 and 100 students are the only possibilities. Second, assume that the only relevant costs of offering a course are the instructors salary and the room expense, and also that the university charges tuition equal to the cost of providing a course. If room costs are $5000 and the instructors salary is $15 000 regardless of the class size, the costs are $200 per student for a class of 100 and $1000 per student for a class of 20. The cost of reducing class sizes from 100 to 20 students is then $800 per student ($1000 $200 $800). Will administrators choose the smaller class size? If they apply the costbenet principle, they will realize that the smaller class size makes sense only if the value to students of attending the smaller class is at least $800 per student greater than the value of attending the larger class. Would you (or your parents) be willing to pay an extra $800 for a smaller economics class? If not, and if other students feel the same way, then maintaining the larger class size makes sense. But if you and others would be willing to pay the extra tuition, then reducing the class size to 20 makes good economic sense. Notice that the best class size from an economic point of view may not be the same as the best size from the point of view of an educational psychologist. The difference arises because the economic denition of best takes into account both the benets and the costs of different class sizes as perceived by you (or your
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THINKING LIKE AN ECONOMIST
parents). The psychologist is only interested in the learning benets of different class sizes. In practice, of course, different people will feel differently about the value of smaller classes. People with high incomes, for example, tend to be willing to pay more for the advantage, which helps to explain why the average class size is smaller and tuition higher at those private schools whose students come predominantly from high-income families. We have used the costbenet framework to consider the question of the best class size. Next, we will use it to provide a possible reason for the gradual increase in average class size that has been taking place in Canadian colleges and universities. Between 199091 and 199899, public operating grants to Canadian universities decreased by about 25 percent. This reduction is part of a pattern of reduced expenditures that enabled the federal government to move from large decits in the early 1990s to large surpluses by the end of the decade. To address the shortfall, Canadian colleges and universities have increased class sizes and raised fees. By 200304, after adjusting for ination, fees were about twice what they had been ten years earlier. Students today borrow more to nance their education than did students in the past.1 Students are paying higher fees to attend larger classes. The size of classes could be reduced if a sufcient number of students paid even higher fees, or if governments increased their funding of universities. However, universities believe that students are not willing to pay even higher fees. Governments believe that taxpayers are not willing to pay more taxes to increase the funding of postsecondary education. Apparently, an insufcient number of people are willing to bear the cost of smaller classes; thus, class sizes have increased. The increase in class size follows from a governmental position concerning decits, not from market behaviour. Notice that the costbenet principle provides a plausible explanation of why class sizes have increased. You may believe that a policy that eliminated federal decits is appropriate. But you may also believe it would have been more fair to reduce the decit by raising taxes rather than by cutting spendingespecially the spending that kept student debt down and class sizes smaller. The costbenet principle helps to explain cause and effect; however, it is not helpful in determining whether a policy is distributionally fair.
1.2
rational person someone with well-dened goals who tries to fulll those goals as best he or she can
APPLYING THE COSTBENEFIT PRINCIPLE
In studying choice under scarcity, it is often useful to begin with the premise that people are rational, which means they have well-dened goals and try to fulll them as best they can. The costbenet principle is a fundamental tool for the study of how rational people make choices. Often the only real difculty in applying the costbenet principle is coming up with reasonable measures of all the relevant benets and costs. Only in rare instances will the dollar measures be conveniently available. But the costbenet framework can lend structure to your thinking even when no relevant market data are available. To illustrate how we proceed in such cases, the following example asks you to decide whether to perform an action whose cost and benets are described only in vague, qualitative terms.
1 Students Pay More for Less, CAUT ACPPU Bulletin, 48(6), June 2001, p. 1, and Students in for a Rough Ride, CAUT ACPPU Bulletin, 50(7), Sept. 2003, p. A9. Students fees are an important source of revenue and their increase has enabled many universities to prevent services from being cut even further. However, notice that if fees rise by 100 percent, a universitys revenue will rise by far less than 100 percent. Suppose that 25 cents of every dollar of a universitys revenue comes from students fees, which is typical. The university raises fees by 100 percent: 1.00 $0.25 $0.25. Thus, a 100 percent increase in students fees increases the universitys revenue by 25 percent.
APPLYING THE COSTBENEFIT PRINCIPLE
5
Will you be better off if you walk downtown to save $10 on a $25 computer game? Imagine you are about to buy a $25 computer game at the nearby campus store when a friend tells you that the same game is on sale at a downtown store for only $15. If the downtown store is a 30-minute walk away, and you have no other way of getting there, where will you buy the game? The costbenet principle tells us that you will buy it downtown if the benet of doing so exceeds the cost. The benet of taking any action is the dollar value of everything you gain by taking it. Here, the benet of buying downtown is exactly $10, since that is the amount you will save on the purchase price of the game. The cost of taking any action is the dollar value of everything you give up by taking it. Here, the cost of buying downtown is the dollar value of the time and trouble of making the trip. But how do we estimate that dollar value? One way is to perform the following hypothetical action. Imagine that a stranger has offered to pay you to do an errand that involves the same walk downtown (perhaps to drop off a letter for her at the post ofce). If she offered you a payment of, say, $100, would you accept? If so, we know that your cost of walking downtown and back must be less than $100. Now imagine her offer being reduced in small increments until you nally refuse the last offer. For example, if you agree to walk downtown and back for $9 but not for $8.99, then your perceived cost of making the trip is $9. Applying that to this case, you will be better off if you buy the game downtown, because the $10 you save (your benet) is greater than your $9 cost of making the trip. On the other hand, suppose that your cost of making the trip is greater than $10. In that case, the costbenet principle tells you to buy the game from the nearby campus store.
EXAMPLE 1.1
COST COST BENEFIT
ECONOMIC SURPLUS
Suppose again that in Example 1.1 your cost of making the trip downtown was $9. Compared to the alternative of buying the game at the campus store, buying it downtown resulted in an economic surplus of $1, the difference between the benet of making the trip and its cost. In general, you will be best off if you choose those actions that generate the largest possible economic surplus. This means taking all actions that yield a positive total economic surplus, which is just another way of restating the costbenet principle. Note that just because your best choice is to buy the game downtown does not imply that you enjoy making the trip any more than choosing a large class means that you prefer large classes to small ones. It simply means that the trip is less unpleasant than the prospect of paying $10 extra for the game. Once again, you have faced a trade-off: in this case, the choice between a cheaper game and the free time gained by avoiding the trip. Note also that if the time it would take to walk downtown and back has a value to you of more than $10, it is perfectly rational to decide not to save $10 on the computer game. Economists know that money isnt everything. But in order to compare the sizes of benets and costs we need some common unit of measurement, and economists often use dollar values for this because they are a convenient unit. This, however, does not imply that we will always choose the alternative that costs the least or saves the most money.
economic surplus the benet of taking any action minus its cost
OPPORTUNITY COST
Suppose, for example, that the time required for the trip downtown is the only time you have left to study for a difcult test the next day. Or suppose you are watching one of your favourite movies on cable, or that you are tired and would
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opportunity cost the value of the next-best alternative that must be foregone in order to undertake the activity
COST COST BENEFIT
love a short nap. In such cases, we say that the opportunity cost of making the trip, the value of what you must sacrice to walk downtown and back, is high and you are more likely to decide against making the trip. In this example, if watching the last hour of the movie is the most valuable opportunity that conicts with the trip downtown, the opportunity cost of making the trip is the dollar value you place on pursuing that opportunitythat is, the largest amount you would be willing to pay to avoid missing the end of the movie. Note that the opportunity cost of making the trip is not the combined value of all possible activities you could have pursued, but only the value of your best alternative, the one you would have chosen had you not made the trip. Throughout the text we will pose exercises like the one that follows. You will nd that pausing to answer them will help you to master key concepts in economics. Because doing these exercises is not very costly (indeed, many students report that they are actually fun), the costbenet principle indicates that it is well worth your while to do them. You would again save $10 by buying the game downtown rather than at the campus store, but your cost of making the trip is now $12, not $9. How much economic surplus would you get from buying the game downtown? Where does the costbenet principle tell you to buy the game? What is the opportunity cost of selling owers on the sidewalk? Suppose that you are a ower seller, with a stock of cut roses that will wilt by tomorrow morning. If you do not sell them tonight, their value tomorrow will be zero. You can think of two possible places to sell your owers: on the sidewalk outside your home or downtown in upscale romantic restaurants, where you can embarrass people into buying owers for their dates. However, to get into these restaurants, you must give the headwaiter a $30 payoff and it will cost you $10 in extra time and bus fares to travel downtown. Suppose that you expect to sell all the owers in about an hour wherever you are, and you expect to get about $50 for your owers if you sell downtown. You do not have anything else to do during the time you will spend selling owers. What would be the opportunity cost of selling them on the sidewalk? What is the least revenue from sidewalk sales that would make selling on the sidewalk your best choice? By selling on the sidewalk, you give up the surplus that you could get by selling downtown. If you had sold the owers downtown you would have gotten a net return of $10 ($50 revenue minus $30 payoff minus $10 in extra travel costs). So the opportunity cost of selling the owers on the sidewalk is $10. You are better off selling on the sidewalk only if you expect to make more than $10 at that location. (Notice that this and the next example do not specify how you got the owers. Whether you grew them yourself, bought them in the marketplace, or received them as a gift, it does not matter. The important thing is that the owers will wilt by tomorrow and be valueless, hence the opportunity cost of the owers themselves is zero.)
EXERCISE 1.1
EXAMPLE 1.2
EXAMPLE 1.3
Suppose that you think you could sell your owers for $8 on the sidewalk. What would be the opportunity cost of selling them downtown? If you sell your owers downtown, you forego $8 in revenue you could get from selling owers on the sidewalk, and you incur $30 in payoff costs and $10 in transportation expenses. Therefore, the total value of everything you give up in order to sell downtown is $48. Your surplus from sales downtown net of all opportunity costs is $2.
APPLYING THE COSTBENEFIT PRINCIPLE
7
Notice from Examples 1.2 and 1.3 that opportunity costs can be either explicit or implicit. An explicit opportunity cost requires an outlay or payment. For example, a payment of $30 to a headwaiter for access to customers in a restaurant is an explicit opportunity cost. The $30 cannot be used to purchase something else. An implicit opportunity cost does not involve an actual payment. If you choose to sell owers downtown, you forego the opportunity to earn $8 selling owers from the sidewalk. By sacricing an income, you are incurring an implicit opportunity cost. The total opportunity cost of any action is the sum of explicit and implicit opportunity costs.
THE ROLE OF ECONOMIC MODELS
Economists often use abstract models of how an idealized rational individual would choose among competing alternatives. When doing so, they consciously ignore inuences that they consider relatively unimportant in order to concentrate attention on the most important inuences. Physicists often construct idealized models of physical phenomena in a similar way. If, for example, the issue is how quickly a rock dropped from the top of a tower will hit the ground, a physicist could make a fairly good prediction even if she ignored the inuence of air resistance. Even though the physicist knows perfectly well that air resistance has an inuence, it is small enough to be ignored in this case given the force of gravity and the density of a rock. However, if a feather is dropped air resistance will make a difference and must be taken into consideration. Choosing the right assumptions makes the difference between a model that performs well and one that does not. Noneconomists are sometimes harshly critical of the economists costbenet model on the grounds that people in the real world rarely conduct complex mental calculations before making simple decisions. But economists know perfectly well that people do not conduct hypothetical mental actions when they make simple decisions. All the costbenet principle really says is that a rational decision is one that is explicitly or implicitly based on a weighing of costs and benets. Most of us make sensible decisions most of the time, without being consciously aware that we are weighing costs and benets, just as most people ride a bike without being consciously aware of what keeps them from falling. Through trial and error, we gradually learn what kinds of choices tend to work best in different contexts, just as bicycle riders internalize the relevant laws of physics, usually without being consciously aware of them. Economic models of rational behaviour analyze what individuals would do in theory if they explicitly calculated the costs and benets of their decisions. These models are useful because they enable economists to predict the behaviour of actual individuals, who are often intuitive and implicit in their decision making but are nonetheless trying to maximize their net benet. Hence, most economic models are examples of positive economics. Positive economics has two dimensions. First, it offers cause-and-effect explanations of economic relationships. Second, positive economics has an empirical dimension. In principle, data can be used to conrm or refute propositions, or hypotheses, that emerge from positive economics. Data also can be used to measure the magnitude of effects that emerge from cause-and-effect relationships. Thus, we can predict that if resources available to colleges and universities are reduced, class sizes will increase. We can use data to determine whether class sizes do, in fact, increase. If they do, data can be used to determine by how much they increase. Using the cost-benet principle to explain why class sizes have increased is an example of positive economics. Ideally, positive economics is value free.
positive economics economic analysis that offers cause-andeffect explanations of economic relationships; the propositions, or hypotheses, that emerge from positive economics can, in principle, be conrmed or refuted by data; in principle, data can also be used to measure the magnitude of effects predicted by positive economics
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normative economics economic statements that reect subjective value judgments and that are based on ethical positions fallacy of composition the argument that because something is true for a part, it also is true for the whole
post hoc fallacy the argument that because event A precedes event B, event A causes event B
In contrast, normative economics asks whether something should happen. It therefore reects subjective value judgments and is based on ethical positions. The question of whether or not larger classes and higher fees are unfair to students is a normative issue. Two logical errors are to be avoided when modelling economic relationships. The rst, the fallacy of composition, occurs if one argues that what is true for a part must also be true for the whole. The statement, If one farmer harvests a larger crop he will be better off; therefore, if all farmers harvest larger crops, all farmers will better off, is an example of the fallacy of composition. If all farmers harvest larger crops, prices may decrease by an amount that would more than offset the benet of larger harvests. What is true for an individual is not necessarily true for an entire group. The post hoc fallacy is second common logical error. The name stems from the Latin phrase post hoc, ergo propter hoc , meaning after this, therefore because of this. The fallacy leads one to argue that because event A precedes event B, event A causes event B. Suppose that in a t of anger, a person wishes that a neighbour was dead. A week later, the neighbour drops dead from a heart attack. To conclude that the wish caused the death is to commit the post hoc fallacy. Generally, correlation does not indicate causation. For example, the United States spends more per capita on health care than Canada does, but Canadians have a longer life expectancy than Americans have. It does not follow from these facts that larger expenditures on health care reduce life expectancy. While there might be a correlation here, various social, personal, and economic factors also play a role in determining life expectancy. Cause-and-effect and correlation are two very different things.
RATIONALITY AND IMPERFECT DECISION MAKERS
When having to decide if an action will leave you better off or not, the action could be anything from eating another cookie to choosing Capilano College over Douglas College. The costbenet principle says that if the benets of the action exceed its costs, then performing the action will make you better off. However, if the benets are less than the costs, then performing the action will make you worse off. If its benets and costs happen to be equal, then it does not matter whether you perform the action or not. Rational people will apply the costbenet principle most of the time, although probably in an intuitive and approximate way rather than through explicit and precise calculation. To the extent that people are rational, their tendency to compare costs and benets will help economists to predict their likely behaviour. For example, we can predict that students from wealthy families are more likely than others to attend private foreign universities that offer smaller classes.
R ECAP
COST BENEFIT ANALYSIS Scarcity is a basic fact of economic life. Because of it, having more of one good often means having less of another, the scarcity problem. Economics is devoted to studying how we can make intelligent choices in a world of scarcity. The costbenet principle holds that an individual (or a rm or a society) is better off taking an action if, and only if, the extra benet from taking the action is greater than the extra cost. The benet of taking any action minus the cost of taking the action is called the economic surplus from that action.
PITFALL 1: IGNORING OPPORTUNITY COSTS
9
Thus, the costbenet principle suggests that we take only those actions that create additional economic surplus. Applying the costbenet principle requires measurement. The benet of an action is the most you would be willing to pay someone to perform it. The cost of an action is the value of the next-best alternative that you must forego to perform the action.
1.3
THREE COMMON PITFALLS
The costbene t principle suggests that an introductory economics course emphasizes a short list of those principles with the greatest power to predict and explain behaviour. But it also suggests that among those principles, we will focus especially on those that are most difcult to master. As we explore the cost benet approach in greater detail, we will emphasize the errors people commonly make when trying to implement it. People tend to ignore certain costs that are relevant to a decision at hand, for example, and sometimes they are inuenced by costs that are irrelevant. Three of the most commonly encountered pitfalls concern opportunity costs, sunk costs, and the difference between average and marginal costs.
COST COST BENEFIT
1.4
PITFALL 1: IGNORING OPPORTUNITY COSTS
Sherlock Holmes, Arthur Conan Doyles legendary detective, was successful because he saw details that most others overlooked. In Silver Blaze, Holmes is called on to investigate the theft of an expensive racehorse from its stable. A Scotland Yard inspector assigned to the case asks Holmes whether some particular aspect of the crime required further study. Yes, Holmes replies, and describes the curious incident of the dog in the nighttime. The dog did nothing in the nighttime, responds the puzzled inspector. But, as Holmes realized, that was precisely the problem. The watchdogs failure to bark when Silver Blaze was stolen meant that the watchdog knew the thief. This clue substantially reduced the number of suspects and eventually led to the thiefs apprehension. Just as we often dont notice when a dog fails to bark, many of us tend to overlook the implicit value of activities that fail to happen. As we have seen, however, intelligent decisions require taking the value of foregone opportunities into account. What is not stated may be as important as what is explicitly stated.
Opportunity costs are like dogs that fail to bark in the night.
RECOGNIZING THE RELEVANT ALTERNATIVE
Will you be better off if you use your frequent-yer coupon to y to Vancouver for winter break? With winter break only a week away, you are still undecided about whether to y to Vancouver and then then go to Whistler with a group of classmates from the University of Alberta. The round-trip airfare from Edmonton to Vancouver is $500. All other relevant costs for the vacation while at Whistler will total exactly $1000. The maximum you are willing to pay for the vacation is $1350. You could travel to Whistler by paying $500 to y from Edmonton to Vancouver, or by using a frequent-yer coupon to pay for the ight. Your only alternative use for your frequent- yer coupon is for your plane trip to Ottawa the weekend after winter break to attend your brothers wedding. (Your coupon expires shortly thereafter.) EXAMPLE 1.4
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COST COST BENEFIT
If the EdmontonOttawa round-trip airfare is $400, will you be better off if you use your frequent-yer coupon to y to Vancouver for winter break? The costbenet criterion tells you to go to Vancouver if the benets of the trip exceed its costs. If not for the complication of the frequent-yer coupon, solving this problem would be a straightforward matter of comparing the maximum price you would pay for the week at Whistler (your benet from the trip) to the sum of all relevant costs. And since your airfare and other costs would sum to $1500, or $150 more than what you are willing to pay for the trip, you would be better off not going. But what about the possibility of using your frequent-yer coupon to make the trip? Using it for that purpose might make the ight to Vancouver seem free, suggesting you would reap an economic surplus of $350 by making the trip. But doing so would also mean you would have to pay $400 for your airfare to Ottawa. So the opportunity cost of using your coupon to y to Vancouver is really $400. If you use it for that purpose, the cost of the trip still exceeds its benet and it still fails the costbenet test. In cases like these, you are much more likely to decide sensibly if you ask yourself, Will I be better off if I use my frequent-yer coupon for this trip or save it for an upcoming trip?
The key to using the concept of opportunity cost correctly lies in recognizing precisely what taking a given action prevents us from doing. To illustrate, suppose we modify Example 1.4 slightly, as follows: Same as Example 1.4, except that now your frequent-yer coupon expires in a week, so your only chance to use it will be for the ight to Vancouver. Will you be better off if you use your coupon? Since you now have no alternative use for your coupon, the opportunity cost of using it to pay for the ight to Vancouver is zero. That means your economic surplus from the trip will be $1350 $1000 $350 > 0, so the costbenet principle tells you to use your coupon and go to Whistler.
EXAMPLE 1.5
THE TIME VALUE OF MONEY
We saw that taking an action now can mean being unable to take some other action in the future. To take the value of future opportunities properly into account, we need to weigh future costs and benets against present costs and benets. As the next example illustrates, having to pay someone a dollar one year from now is not the same as having to pay someone a dollar today. Same as Example 1.4, except that instead of ying to Ottawa, your best alternative use for your frequent-yer coupon is a ight you expect to take one year from now, for which the airfare is $363. If your savings account pays 10 percent interest per year, does the costbenet principle tell you to y to Vancouver and then go to Whistler? How does this new information alter the opportunity cost of using your coupon to y to Vancouver? Using it now means having to pay $363 for your ight one year from now. The opportunity cost of using the coupon now might therefore seem to be exactly $363. But this way of thinking about the coupon misses an important aspect of opportunity cost.
EXAMPLE 1.6
PITFALL 2: FAILURE TO IGNORE SUNK COSTS
11
The question you must ask is, how much am I willing to pay today to avoid having to pay $363 one year from now? To answer this question, determine how much you need to put in your savings account today, at 10 percent annual interest, to have $363 one year from now. The answer is $330, because you will earn $33 in interest (10 percent of $330) over the next year, for a total of $363. Your economic surplus from the trip to Whistler is therefore $1350 $1000 $330 $20. Therefore, the costbenet principle tells you to take the trip to Whistler.
Would your answer to Example 1.6 have been different if the annual interest rate had been 2 percent instead of 10 percent? (Hint: Would a deposit of $350 in your account today earn enough money to pay for your $363 air ticket one year from now?) Example 1.6 and Exercise 1.2 drive home the point that the opportunity cost of a dollar spent today is not the same as the opportunity cost of a dollar spent one year from now. In general, the opportunity cost of resources that are expended in the future will be lower than the opportunity cost of resources that are expended in the present. The reason involves the time value of moneythe fact that money deposited in an interest-bearing account today will grow in value over time. Indeed, the very fact that banks and other borrowers pay interest is a consequence of the opportunity cost concept. As simple as the concept of opportunity cost is, it is one of the most important in economics. The art in applying the concept correctly lies in being able to recognize the most valuable alternative to a given activity. And though the concept is simple, its application can be subtle. For example, if we must choose between spending a dollar today or spending a dollar tomorrow, time itself will inuence opportunity cost through the time value of money.
EXERCISE 1.2
time value of money the fact that a given dollar amount today is equivalent to a larger dollar amount in the future, because the money can be invested in an interest-bearing account in the meantime
1.5
PITFALL 2: FAILURE TO IGNORE SUNK COSTS
The opportunity cost pitfall is one in which people ignore opportunity costs. In another common pitfall, the opposite is true: people are inuenced by costs that really are not opportunity costs. The only costs that are relevant to a decision about whether to take an action are the costs that we can avoid by not taking the action. As a practical matter, however, many decision makers appear to be inuenced by sunk costscosts that are beyond recovery at the moment a decision is made. For example, money spent on a nontransferable, nonrefundable airline ticket is a sunk cost. Because sunk costs must be borne whether or not an action is taken, they are irrelevant to the decision of whether to take the action. The sunk cost pitfall, the mistake of being inuenced by sunk costs, is illustrated clearly in the following examples.
sunk cost a cost that is beyond recovery at the moment a decision is made
Will you drive through a snowstorm to get to a hockey game? You and your friend Joe have identical tastes. At 2 P.M. you log on to Ticketmaster and buy a $30 nonrefundable ticket to a hockey game to be played that night in Ottawa, 70 km north of your home in Smiths Falls. Joe plans to attend the same game, but he plans to buy his ticket at the game. Tickets sold at the game
EXAMPLE 1.7
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cost only $25 because they dont carry a Ticketmaster surcharge. (Many people nonetheless pay the higher price at Ticketmaster to be sure of getting good seats.) At 4 P.M. an unexpected snowstorm begins, making the prospect of the drive to Ottawa much less attractive than before. If both you and Joe are rational, is one of you more likely to attend the game than the other? Since you have already bought your ticket, the $30 you spent on it is a sunk cost. It is money you cannot recover, whether you go to the game or not. In deciding whether to see the game then, the costbenet principle tells you to compare the benet of seeing the game (the largest dollar amount you would be willing to pay to see it) only to those additional costs you must incur to see the game; that is, the opportunity cost of your time, plus whatever cost you assign to the stress of driving through the snowstorm. Whether you attend the game or not, you will never see the $30 you paid for your ticket again. Therefore, it is a sunk cost, not an opportunity cost, and you will ignore the $30 if you apply the costbenet principle correctly. Joe, too, must weigh the opportunity cost of his time and the hassle of the drive in deciding whether to attend the game. But he must also weigh the $25 he will have to spend for his ticket. At the moment of deciding, therefore, the remaining costs Joe must incur to see the game are $25 higher than the remaining costs for you. And since you both have identical tastesthat is, since your respective benets of attending the game are exactly the sameJoe is less likely to make the trip. You might think the cost of seeing the game is higher for you, since your ticket cost $30, whereas Joes will cost only $25. But at the moment of deciding whether to make the drive, the $25 is a relevant cost for Joe, whereas your $30 is a sunk cost, and hence an irrelevant one for you.
Now suppose we change the structure of Example 1.7 slightly. Same as Example 1.7, except now a friend gives Joe a free ticket to the game at 2 P.M. Is one of you more likely to attend the game than the other? This time neither of you faces any additional ticket expenses at the moment you must decide whether to drive through the snowstorm. Since your respective costs and benets are the same, your decisions about whether to make the trip will be the same if you both apply the costbenet principle.
EXAMPLE 1.8
According to the costbenet criterion, the decision to attend the game does not depend on whether someone bought a ticket or was given one. A rational economic decision maker weighs the benet of seeing the game against only the additional costs he must incur to see it; in this example, the opportunity cost of time, the psychological cost, and the physical risk of driving through the snowstorm. How a person came to possess a ticket has no bearing on either the relevant benets or the relevant costs. Of course, a calculation of costs and benets is not the only thing that can inuence a decision. A sense of regret can play a powerful role as well. Suppose both Joe and his friend had purchased tickets on Ticketmaster. If only they had known that a storm was coming, they would not have spent $30 for each ticket they would have avoided a sunk cost. To avoid regret about purchasing tickets they will not use, the two friends could drive through the storm. Indeed, it seems that people who pay cash for a ticket often feel that they must use it to avoid wasting $30, while those who receive a ticket free of charge are more comfortable about staying home.
PITFALL 3: FAILURE TO UNDERSTAND THE AVERAGEMARGINAL DISTINCTION
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R ECAP
THE PITFALL OF NOT IGNORING SUNK COSTS When deciding whether to perform an action, it is important to ignore sunk coststhose costs that cannot be avoided even if the action is not taken. Even though a ticket to a concert may have cost you $100, if you have already bought it and cannot sell it to anyone else, the $100 is a sunk cost. If your decision to attend the concert is based entirely on the costbenet principle, sunk cost will be irrelevant.
1.6
PITFALL 3: FAILURE TO UNDERSTAND THE AVERAGEMARGINAL DISTINCTION
marginal cost the increase in total cost that results from carrying out one additional unit of an activity marginal benet the increase in total benet that results from carrying out one more unit of an activity average cost total cost of undertaking n units of an activity divided by n average benet total benet of undertaking n units of an activity divided by n
As we have seen, economic decisions take proper account of opportunity costs. Because sunk costs are not opportunity costs, sunk costs are irrelevant to economic decisions and are not counted when the costbenet principle is applied. Further, accurate application of the costbenet principle is not possible if marginal costs and benets are confused with average costs and benets. Often we are confronted with the choice of whether or not to engage in an activity. But in many situations, the issue is not whether to pursue the activity, but in whether or not to increase it or decrease it. The costbenet framework emphasizes that the only relevant costs and benets in deciding whether to change the amount of an activity are marginal costs and benets. Economists dene the marginal cost of an activity as the increase in total cost that results from carrying out one additional unit of the activity. Similarly, the marginal benet of an activity is the increase in total benet that results from carrying out one more unit of the activity. In many contexts, however, people seem more inclined to compare average costs and average benetstotal cost or benet per unit of activity. The next section shows why marginal, not average, costs and benets are relevant.
WEIGHING MARGINAL BENEFITS AND MARGINAL COSTS GRAPHICALLY
How much memory is worthwhile for your computer to have? Suppose you can add random-access memory (RAM) to your computer at a cost of $300 per gigabyte. Suppose also that the value to you of an additional gigabyte of memory, measured in terms of your willingness to pay for it, is as shown by curve MB in Figure 1.1 How many gigabytes of memory are worth purchasing? Curve MB plots the value to you of an additional gigabyte of memory (measured on the vertical axis in dollars per gigabyte) as a function of your computers existing memory (measured on the horizontal axis in gigabytes). For example, the value of additional memory is $600 per gigabyte if your computer has one gigabyte of memory but only $300 if it has 2 gigabytes. Curve MB is often called the marginal benet curve, to emphasize that it shows not the total value of memory but the value of having an additional unit of memory. (Marginal means extra or additional.) Curve MC in Figure 1.1 shows the cost, in dollars, of adding an additional gigabyte, assumed constant at $300. This curve is often called the marginal cost curve, to emphasize that it represents not the total cost of memory but the cost of adding an additional unit. The fact that curve MC is horizontal at $300 means EXAMPLE 1.9
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FIGURE 1.1 The Marginal Cost and Benet of Additional RAM Curve MB plots the benet of adding an additional gigabyte of memory. Curve MC plots the cost of an additional gigabyte of memory. It is rational to continue adding memory as long as the marginal benet of memory (curve MB) lies above the marginal cost of memory (curve MC). The optimal amount of RAM is 2 gigabytes, the amount for which the marginal benet of memory is equal to its marginal cost.
750 Dollars per gigabyte 600 450 300 150 75 0
MB
Value of an additional gigabyte Optimal amount of memory
Cost of an additional gigabyte
MC
1
2
3
4
5
6
7
8
Gigabyte of memory
that no matter how much memory your computer has, you can always add an extra gigabyte at a cost of exactly $300. (Later on, we will consider examples in which the cost of adding additional units depends on the number of units you already have.) Once we know the relevant marginal benet and cost curves, nding the optimal quantity of memory is straightforward. Note in Figure 1.1 that if your computer has fewer than 2 gigabytes of memory, then the marginal benet of adding memory (as measured by curve MB) is greater than its marginal cost (as measured by MC). So it is worthwhile to add memory if your computer currently has fewer than 2 gigabytes. Conversely, note that if your computer has more than 2 gigabytes of memory, the marginal benet of memory is less than its marginal cost, in which case you would have been better off buying less memory. The optimal amount of memory is thus 2 gigabytes, the amount at which the marginal benet of memory exactly equals its marginal cost.
A common question prompted by Example 1.9 is Why should I bother to add the second gigabyte of memory if its marginal benet is no greater than its marginal cost? The answer is that at any amount less than 2 gigabytes, the marginal benet of memory exceeds its marginal cost. Suppose, for example, that your computer had only 1.9 gigabytes of memory, if that were possible. The marginal benet of additional memory would then be greater than its marginal cost (albeit by only a tiny margin), which means that it is worthwhile to expand. The same reasoning would apply if your computer had 1.99 gigabytes, or even 1.999. So you can always do better by expanding unless you already have 2 gigabytes.2
2
Note that in this example we treated your computers memory bank as a perfectly divisible quantity. In practice, however, computer memory can be increased only by adding chunks of discrete size. A more realistic account of your decision of how much memory to buy for your computer would advise you to add the next chunk of memory if its benet exceeds its cost. The optimal quantity of memory could then be an amount for which the benet was greater than its cost. In that case, the benet of next discrete chunk would be less than its cost.
PITFALL 3: FAILURE TO UNDERSTAND THE AVERAGEMARGINAL DISTINCTION
15
Example 1.9 demonstrates why it is necessary to use marginal benets and marginal costs in determining if it is worthwhile to change the amount of an activity. Next, Example 1.10 demonstrates that it may not be worthwhile to increase an activity even though its average benet at the current level is signicantly greater than its average cost. Indeed, average cost and average benet are irrelevant to a decision about changing the amount of an activity. Does the costbenet principle tell NASA to expand the space shuttle program from four launches per year to ve? Professor Ksten Banifoot, a prominent supporter of the NASA space shuttle program, has estimated the that gains from the program are currently $24 billion per year (an average of $6 billion per launch) and that its costs are currently $20 billion per year (an average of $5 billion per launch). True or false: If these estimates are correct, the costbenet principle tells NASA to expand the program. (Canadian astronauts have own on the space shuttle, and Canada supplies components to NASA. Expansion of the space shuttle program would provide additional opportunities for Canadian science and technology.) To decide whether an additional launch makes sense, we need to compare the cost of adding that launch with the benet of adding it. The average benet and average cost per launch for all shuttles launched thus far simply are not useful in deciding whether to expand the program. Of course, the average cost of the launches undertaken so far might be the same as the cost of adding another launch. But it also might be either higher or lower than the marginal cost of a launch. The same statement holds true regarding average and marginal benets. Suppose, for example, that the benet of an additional launch is in fact the same as the average benet per launch thus far, namely, $6 billion. Does the costbenet principle tell NASA to add another launch? Not if the cost of adding the fth launch would be more than $6 billion. Suppose the relationship between the number of shuttles launched and the total cost of the program is as described in Table 1.1.
TABLE 1.1
EXAMPLE 1.10
How Cost Varies with the Number of Launches
Number of launches per year 1 2 3 4 5 Total costs Marginal cost per launch per year ($ billions) ($ billions) 6 8 12 20 30 2 4 8 10
At the current level of four launches per year, the average cost is $20 billion/4 $5 billion per launch. But adding a fth launch would raise costs from $20 billion to $30 billion, so the marginal cost of the fth launch is $10 billion. If the benet of an additional launch is constant at $6 billion, the costbenet principle does not justify increasing the number of launches. Indeed, the fourth launch itself would not be justied, since it cost $8 billion and produced only $6 billion in additional benets. Based on the numbers shown in the table, which are completely consistent with Professor Banifoots data on average costs and benets, the optimal number of launches would be only three per year.
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EXERCISE 1.3
Suppose the marginal benet of each launch is $9 billion, not $6 billion. How many shuttles per year does the costbenet principle tell NASA to launch? The conclusion that some costs, especially marginal costs and opportunity costs, are important while others, like sunk costs and average costs, are irrelevant to economic decisions is implicit in our original explanation of the cost benet principle (an action should be taken if, and only if, the extra benets of taking it exceed the extra costs). Yet, the pitfalls of (1) ignoring opportunity costs, (2) considering sunk costs, and (3) confusing average with marginal cost are so important that we enumerate them separately. As a result, a core principle worthy of repeated emphasis emerges: The Principle of Relevant Costs: In considering whether to produce or consume more of a good, what matters is the cost of one more unit (marginal cost).
COST COST BENEFIT
RELEVANT COSTS
R ECAP
THREE IMPORTANT PITFALLS 1. The pitfall of ignoring opportunity costs. When performing a costbenet analysis of an action, it is important to account for the full opportunity cost of the action. The opportunity cost of an action is the value of the next best alternative that is foregone by taking the action. In calculating opportunity cost, it is important to consider the time value of money. Because money can be invested in an interest-bearing account, a dollar paid or received in the future is worth less than a dollar paid or received today. 2. The pitfall of not ignoring sunk costs. When deciding whether to perform an action, it is important to ignore sunk costscosts that cannot be avoided even if the action is not taken. Even though a ticket to a game may have cost $30, if you have already bought it and cannot sell it to anyone else the $30 is a sunk cost. If your decision to attend the game is based entirely on the costbenet principle, you will ignore the sunk cost. 3. The pitfall of using average instead of marginal costs and benets. Decision makers often have ready information about the total cost and benet of an activity, and from these it is easy to calculate the activitys average cost and benet. However, it is a mistake to increase an activity simply because its average benet is greater than its average cost. Likewise, it is a mistake to decrease an activity simply because its average benet is less than its average cost. The costbenet principle states that total benet can be increased by increasing the amount of an activity if, and only if, the marginal benet of the activity is greater than its marginal cost. Likewise, total benet can be increased by decreasing the activity if, and only if, its marginal benet is less than its marginal cost.
microeconomics the study of individual choice under scarcity, and its implications for the behaviour of prices and quantities in individual markets macroeconomics the study of the performance of national economies and the policies that governments use to try to improve that performance
1.7
ECONOMICS: MICRO AND MACRO
By convention, we use the term microeconomics to describe the study of individual choices and of group behaviour in individual markets. Macroeconomics, by contrast, is the study of the performance of national economies and of the policies
ECONOMIC NATURALISM
17
that governments use to try to affect that performance. Macroeconomics tries to understand the determinants of such things as the national unemployment rate, the overall price level, and the total value of national output. In both this chapter and the next one we focus on issues that confront the individual decision maker. Further on, we will consider economic models of groups of individuals, such as all buyers or all sellers in a specic market. Later still we will turn to broader economic issues and measures. No matter which of these levels we focus on, however, our thinking will be shaped by the fact that although economic needs and wants are effectively unlimited, the material and human resources that can be used to satisfy them are nite. Therefore, clear thinking about economic problems must always take into account the concept of trade-offsthe idea that having more of one good thing usually means having less of another. Our economy and our society are shaped to a substantial degree by the choices people make when faced with trade-offs.
1.8
THE APPROACH OF THIS TEXT
Choosing the number of students to register in each class is just one of many important decisions in planning an introductory economics course. Another decision that the scarcity problem applies to just as strongly concerns which of many different topics to include on the course syllabus. There is a virtually inexhaustible set of topics and issues that might be covered in an introductory course but only a limited amount of time in which to cover them. There is no free lunch; covering some topics inevitably means omitting others. Therefore, our strategy is to focus on a short list of core ideas. We promote the understanding of these ideas by returning to each of them repeatedly, in many different contexts. Economists study the workings of the economy in part to satisfy their inherent human curiosity about how and why things happen. Economic life is all around us, every day, and coming to an understanding of it is an intellectually fascinating study, with many interesting puzzles yet to be fully solved. But greater understanding, for its own sake, is only part of the motivation of most economists. Because the economy plays such an important role in all our lives, most economists are also interested in how economic analysis can be used to improve societys well-being. Because the basic issue underlying economic analysis is scarcity, efciency obtaining the largest possible total output from a given amount of inputsis the rst focus of economic analysis and policy. But efciency, by itself, is never enough. The total output of society has to be divided somehow, and the well-being of each person necessarily depends on her or his particular share of it. Hence, the well-being of society as a whole depends on both the efciency of production and the equity of distributionhow fairly goods are distributed among the people. The goal of economic analysis, and the objective of this text, is to increase our understanding of economic processes. Greater understanding is valuable in itself, and it can also serve a social purpose; that is, to better inform the public and private decisions aimed at improving the efciency and equity of production and distribution.
efciency obtaining the maximum possible output from a given amount of inputs
equity a state of impartiality and fairness
1.9
ECONOMIC NATURALISM
With the rudiments of the costbenet framework under your belt, you are now in a position to become an economic naturalist, someone who uses insights from economics to help make sense of observations from everyday life. People who have studied biology are able to observe and marvel at many details of nature that would otherwise escape their notice. For example, while the novice may see only trees on a walk in the woods in early April, the biology student
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notices many different species of trees and understands why some are already in leaf while others are still dormant. Likewise, the novice may notice that in some animal species, males are much larger and more impressive in appearance than females, but the biology student knows that that pattern occurs only in species in which males take several mates. Natural selection favours larger males because their greater size helps them to prevail in the often bloody contests among males for access to females. By contrast, males tend to be roughly the same size as females in monogamous species, where there is much less ghting for mates. In similar fashion, learning a few simple economic principles enables us to see the mundane details of ordinary human existence in a new light. Whereas the uninitiated often fail even to notice these details, the economic naturalist not only sees them but becomes actively engaged in the attempt to understand them by using positive economics. Lets consider an example of the type of questions that economic naturalists might pose for themselves.
ECONOMIC
N aturalist
1.1
Why are some places littered with beer cans and wrecked cars while others are not?
old heap. Driving (or towing) an old car to the scrap yard may be a sad event, but there are at least a few dollars to be had in recompense. However, this wasnt true in the U.K. in 2001. Because there had been a decline in the price of scrap iron, and because the British government had introduced an environmental charge for disposal of tires and car batteries, disposing of old cars cost moneyif done legally. Since the low scrap iron price meant that the value of the steel and parts in a car was now less than the environmental charge for disposal, old cars became a liability rather than a small asset. Faced with this liability, some drivers in the U.K. just took off the plates and walked away from their cars (which were usually soon stripped of anything valuable and vandalized). The visiting economic naturalist observed several cars abandoned outside the front gate of an auto wrecking yardthe yard owners wanted to be paid to accept the vehicles, but the car owners did not want to actually pay to dispose of their cars. Since they could just park their cars and leave, they did. Although littering is neither legally nor ethically defensible, it is inuenced by the basic costbenet principle. Therefore, public policy to reduce litter has to try to ensure that the benets to individuals of reducing litter exceeds their costs. In the U.K., government policy did not even try to inuence that costbenet calculation to make it worthwhile to avoid beer-can littering, and the new environmental charges on automobiles backred by increasing the private benets of littering, thereby creating a new (and worse) environmental problem.
Arriving in the U.K. from Nova Scotia in the summer of 2001, a visiting economic naturalist was surprised to see how much the back alleys of British towns were littered with discarded beer cans and how many abandoned cars could be seen at the side of English roads. Why did the U.K. have these problems of littering when Nova Scotia (and other Canadian provinces) did not? The beer can litter problem has an easy explanation in the U.K. there was no system of deposits on beverage containers, so they were often thrown away after they were emptied, and aluminium cans accumulated at the roadside and in back alleys. Although aluminium can be recycled, scrap yards did not pay enough per can to make it worthwhile for people to collect them. By contrast, in Nova Scotia (and other Canadian provinces) consumers pay a deposit on beverage containerseven if they do not bother to return their empties, the cans and bottles they discard in public places are collected and returned for the refund. Although the deposit on each container is not large, it is enough to motivate street people and kids to collect them. Although collecting discarded cans is, on an hourly basis, a poorly paid job, it still pays more than the opportunity costs of their time. The deposit system means that discarded bottles and cans have, effectively, a market value. It turns out that the same idea of market value explains the problem of abandoned cars in the U.K. Typically, auto wrecking yards in Canada are willing to pay a few dollars for old cars because the steel has value as scrap iron and there are often usable parts, even on an
SUMMARY
19
SUMMARY
1.1 Economics is the study of how people make choices under conditions of scarcity and of the results of those choices for society. Economic analysis of human behaviour begins with the assumption that people are rationalthat they have well-dened goals and try to achieve them as best they can. In trying to achieve their goals, people normally face trade-offs. Because material and human resources are limited, having more of one good thing usually means making do with less of some other good thing. 1.2 Our focus in this chapter was on how rational people make choices between alternative courses of action. Our basic tool for analyzing these decisions is costbenet analysis. The costbenet principle says that a person will be better off by taking an action if, and only if, the benet of that action is greater than its cost. The benet of an action is measured as the largest dollar amount the person would be willing to pay to take the action. The cost of an action is measured as the dollar value of everything the person must give up to take the action. 1.3 Often the question is not whether to pursue an activity but rather how many units of it to pursue. In these cases, the rational actor pursues additional units as long as the marginal benet of the activity (the benet from pursuing an additional unit of it) exceeds its marginal cost (the cost of pursuing an additional unit of it). 1.4 Three common pitfalls can undermine economic decisions. The rst involves the mistake of failing to consider opportunity costs. The opportunity cost of an activity is the value of the next-best alternative that must be foregone to engage in that activity. If people make the mistake of ignoring the value of foregone alternatives, they are much more likely to make erroneous decisions. We are less likely to make this mistake if we translate questions such as, Should I use my one frequent-yer coupon on the next ight I take? into Will I be better off if I use my one frequent-yer coupon on the next ight, or wait and use it on another ight? 1.5 The second pitfall involves the tendency not to ignore sunk costs. A sunk cost is a cost that is already irretrievably committed at the moment a decision must be made. In deciding whether to drive through a snowstorm to see a hockey game, the amount you have already paid for your ticket is irrelevant. In deciding whether to pursue an activity, the only costs and benets that matter are the ones that will change with your pursuit of that activity. All other costs and benets are irrelevant. 1.6 The third and nal pitfall is the tendency to confuse average costs and benets with marginal cost and benets. A comparison of average cost with average benet is irrelevant when making a decision to increase or decrease an activity. To apply the costbenet principle correctly, we must compare marginal cost with marginal benet. A decision based on a comparison of average cost with average benet will often be contrary to the costbenet principle and cause the parties affected by the decision to be worse off.
CORE
The Scarcity Problem We have boundless needs and wants, but limited resources. Scarcity requires us to make choices among alternatives. The CostBenet Principle An individual (or a rm or a society) will be better off by taking an action if, and only if, the extra benets from taking the action are greater than the extra costs. The Principle of Relevant Costs In considering whether to produce or consume more of a good, what matters is the cost of one more unit (marginal cost).
KEYT ERMS
average cost (13) average benet (13) economics (3) economic surplus (5) efciency (17) equity (17) fallacy of composition (8) macroeconomics (16) marginal benet (13) marginal cost (13) microeconomics (16) normative economics (8) opportunity cost (6) positive economics (7) post hoc fallacy (8) rational person (4) sunk cost (11) time value of money (11)
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REVIEWQUEST IONS
1. A friend of yours on the tennis team says, Private tennis lessons are denitely better than group lessons. Explain what you think your friend means by this statement. Then use the costbenet principle to explain why private lessons are not necessarily the best choice for everyone. 2. One of the two bicycle shops near campus is having a sale on new mountain bikes. Sam decides to buy his new bike from the other shop, paying $30 more in the process. Describe an example of conditions under which his decision might nonetheless be considered rational. 3. True or false: Your willingness to drive downtown to save $30 on a new appliance should depend on what fraction of the total selling price $30 is. Explain. 4. Why might someone who is trying to decide whether to see a movie be more likely to focus on the $9 ticket price than on the $20 she would fail to earn by not babysitting? 5. Many people think of their air travel as being free when they use frequent-yer coupons. Explain why these people are likely to make wasteful travel decisions. 6. Why is a lottery ticket that pays you $10 million now worth more than a lottery ticket that pays you $1 million each year for the next 10 years? 7. Is the nonrefundable tuition payment you made to your university this semester a sunk cost? How would your answer differ if your university were to offer a full tuition refund to any student who dropped out of school during the rst two months of the semester?
PROBLEMS
1. Refer to Figure 1.1 when answering questions (a) through (c). a. Suppose the marginal cost of a gigabyte drops from $300, as shown in Figure 1.1, to $150. What is the optimum amount of memory to install on the computer? Why? b. Suppose that new software makes new and more powerful applications available. What will happen to the marginal benet curve portrayed in Figure 1.1? If the marginal cost of one gigabyte remains at $300, will the optimum amount of memory increase, decrease, or remain the same when the new software becomes available? Why? c. Use your answers to (a) and (b) to explain why the amount of memory installed on new computers has increased rapidly ever since personal computers were introduced. 2. The maximum price you would pay for having a freshly washed car when you go out to dinner is $6. The smallest amount for which you would be willing to wash someone elses car is $3.50. You are going out to dinner this evening, and your car is dirty. How much economic surplus would you receive from washing it? 3. To earn extra money in the summer, you grow tomatoes and sell them at the farmers market for 30 cents per kilogram. By adding compost to your garden, you can increase your yield as shown in the following table. If compost costs 50 cents per kilogram and your goal is to make as much money as possible, how many kilograms of compost will you add? Kilograms of compost 0 1 2 3 4 5 6 Kilograms of tomatoes 100.0 120.0 125.0 128.0 130.0 131.0 131.5
4. For each long-distance call anywhere in Canada, a new phone service will charge users 30 cents per minute for the rst 2 minutes and 2 cents per minute for additional minutes in each call. Toms current phone service charges 10 cents per minute for all calls, and his calls are never shorter than 7 minutes. If Toms dorm switches to the new phone service, what will happen to the average length of his calls? 5. The meal plan at university A lets students eat as much as they like for a xed fee of $500 per semester. The average student there eats 125 kg of food per semester. University B charges $500 for a book of meal tickets that entitles the student to eat 125 kg of food per semester. If the student eats more than 125 kg, he or she pays extra; if the student
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PROBLEMS
21
eats less, he or she gets a refund. If students are rational, at which university will average food consumption be higher? At which university is more food likely to be wasted? Explain briey. 6. Residents of your city are charged a xed weekly fee of $6 for garbage collection. They are allowed to put out as many cans as they wish. The average household disposes of three cans of garbage per week under this plan. Now suppose that your city changes to a tag system. Each can of refuse to be collected must have a tag afxed to it. The tags cost $2 each and are not reusable. What effect do you think the introduction of the tag system will have on the number of bags of garbage collected in your city? Explain briey. 7. Once a week, Smith purchases a six-pack of cola and puts it in his refrigerator for his two children. He invariably discovers that all six cans are gone on the rst day. Jones also purchases a six-pack of cola once a week for his two children, but unlike Smith, he tells them that each may drink no more than three cans. Explain briey why the cola lasts much longer at Joness house than at Smiths. 8. Tom is a mushroom farmer. He invests all his spare cash in additional mushrooms, which grow on otherwise useless land behind his barn. The mushrooms double in weight during their rst year, after which time they are harvested and sold at a constant price per kilogram. Toms friend Dushan asks Tom for a loan of $200, which he promises to repay after 1 year. How much interest will Dushan have to pay Tom for Tom to be no worse off than if he had not made the loan? Explain briey. 9. When John increased his computers RAM by 64 gigabytes, the total benet he received from using the computer went up $55. John purchased the additional memory at a cost of $4 per gigabyte, for a total cost of $48. a. How much economic surplus did John receive from the additional memory? Explain briey. b. True or false: Because the total benet of the additional memory was larger than its total cost, John should have added more than 4 gigabytes of memory. Explain briey. 10. A shirt company spends $1000 per week on rent for its factory. Each shirt made at the factory requires $2 worth of cloth and $6 worth of labour and energy. If the factory produces 2000 shirts per week: a. What is the average cost of a shirt? b. What is the marginal cost of a shirt? If the factory produces 3000 shirts per week: c. What is the average cost of a shirt? d. What is the marginal cost of a shirt? 11. You have won a prize in a provincial lottery. In exchange for your lottery ticket, the provincial government will send you a cheque for $424 one year from now. If bank deposits pay interest at the rate of 6 percent a year, and you already have several thousand dollars in your account, what is the lowest price at which you would be willing to sell your lottery ticket today? 12. A group has chartered a bus trip to Niagara Falls. The drivers fee is $95, the bus rental $500, and the fuel charge $75. The drivers fee is nonrefundable, but the bus rental may be cancelled a week in advance at a charge of $100. At $25 a ticket, how many people must buy tickets a week before so that cancelling the trip denitely will not pay? 13. Sam bought a Trek bicycle for $800 instead of a Cannondale for $1000. Now he nds out that another bike store in town is selling the Cannondale for $800. Mikkel, Sams friend, offers him $600 for his Trek. If Sam is a rational consumer, should he sell Mikkel his Trek and buy the Cannondale? 14. Courtney planned to travel from Ottawa to Toronto to see Shania Twain in a free Canada Day concert, and had already purchased her $50 round-trip bus ticket (nonrefundable, nontransferable) when she found out that the Tragically Hip was giving a show at the same time in Ottawa for $50. Had she known about the Tragically Hips show before she bought her bus ticket, she would have chosen to see the Tragically Hip in her hometown. If she is a rational person and her friend Sally offers to give her one of several extra tickets she has for the Tragically Hips show, what will she do? 15. Mandy and Tomas, who live in Calgary, have identical tastes. They both plan to attend a concert by Alanis Morisette at the Stampede Grounds. The tickets cost $20. Mandy has bought her ticket by phone using her credit card, but Tomas, who doesnt have a credit card, plans to buy his ticket at the door. On the same evening the University of Calgary announces a surprise free reworks display on campus. If Mandy had known about the reworks display in advance, she would not have bought the concert ticket. True or false: Assuming Mandy and Tomas are rational and that Mandy cannot resell her ticket, it follows that Mandy will go to the concert, while Tomas will go to the reworks display. Explain briey.
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22
CHAPTER 1
THINKING LIKE AN ECONOMIST
16. Do any of the following statements represent examples of the fallacy of composition? Do any of them represent examples of the post hoc fallacy? Explain. a. What is good for business is good for the country. b. If our city builds a new super-stadium to accommodate the Olympic Games, it will be necessary for residents to pay more taxes. However, the new stadium ensures that the next Olympic Games will be in our city. The games will generate many spinoff economic benets: people will be hired to build various facilities and to work in them; roads and other infrastructure will be improved; and bars, restaurants, and hotels will be busier and earn greater prots. The federal and provincial governments will contribute money as well. The entire city will be better off. c. Students at schools that have introduced sex education programs have higher rates of sexual activity. Therefore, sex education programs cause students to engage in more sexual activity. d. Statistics show that as time passes, people who smoke are at greater risk of developing lung cancer than are nonsmokers. Therefore, smoking increases the risk of lung cancer. e. If one farmer produces a bigger crop, she will be better off. Therefore, if all farmers produce bigger crops they will all be better off. f. A tariff on steel will protect the steel industry and increase dividends paid to owners of shares in steel corporations. The shareholders will spend their larger incomes on goods and services. As a result, the number of jobs will increase, making the entire population better off. g. A large part of the human population is lactose intolerant. People who are lactose intolerant suffer from health problems if they consume dairy products. This is an indicator that nature never intended humans to consume dairy products and that dairy products are unhealthy for humans. Therefore, if no one consumed any dairy products everyone would be healthier.
ANSWERS TO IN-CHAPTER EXERCISES
1.1 The benet of buying the game downtown is again $10 but the cost is now $12, so your economic surplus from buying it downtown would be $10 $12 $2. Since your economic surplus from making the trip would be negative, you are better off if you buy at the campus store. 1.2 Example 1.4 tells you that if the opportunity cost of the round-trip ight from Edmonton to Vancouver is zero, your economic surplus for the winter vacation will be $350. However, in this case your frequent-yer coupon has an opportunity cost. Using the frequent-yer coupon for the trip to Vancouver means having to pay $363 for your airfare one year from now. How much would you be willing to spend today to avoid paying $363 one year from now? Suppose you deposit $350 in your account today at 2 percent interest. By the end of the year, your deposit would be worth $357 (the original $350 plus $7 interest). Because that amount is not enough to pay for your $363 air ticket, the opportunity cost of using the frequent-yer coupon now must be more than $350. Therefore, the cost of the trip to Vancouver is greater than its $1350 benet, and the costbenet principle tells you not to go to Vancouver. 1.3 If the marginal benet of each launch is $9 billion, the costbenet principle tells NASA to launch four shuttles per year. Why? The marginal benet of the rst, second, third, and fourth launch is greater than the marginal cost. The fth launch does not pass the costbenet test because its marginal benet is less than its marginal cost.
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Appendix
1A Working with
Equations, Graphs, and Tables
APPENDIX OUTLINE
1A.1 Using a Verbal Description to Construct an Equation 1A.2 Graphing the Equation of a Straight Line 1A.3 Deriving the Equation of a Straight Line from its Graph 1A.4 Changes in the Vertical Intercept and Slope 1A.5 Constructing Equations and Graphs from Tables
Although many of the examples and most of the end-of-chapter problems in this book are quantitative, none require mathematical skills beyond basic high-school algebra and geometry. In this brief appendix we review some of the skills you will need for dealing with these examples and problems. The ability to translate simple verbal descriptions into the relevant equations or graphs is important. You will also need to translate tabular information into equations or graphs, and sometimes you will need to translate graphical information into a table or equation. The following examples illustrate all the tools you will need.
24
APPENDIX 1A WORKING WITH EQUATIONS, GRAPHS, AND TABLES
1A.1
USING A VERBAL DESCRIPTION TO CONSTRUCT AN EQUATION
We begin with an example that shows how to construct a long-distance telephone billing equation from a verbal description of the billing plan.
EXAMPLE 1A.1
equation a mathematical expression that describes the relationship between two or more variables variable a quantity that is free to take a range of different values dependent variable a variable in an equation whose value is determined by the value taken by another variable in the equation independent variable a variable in an equation whose value determines the value taken by another variable in the equation constant (or parameter) a quantity that is xed in value
Your long-distance telephone plan charges you $5/month plus 10 cents/ minute for long-distance calls. Write an equation that describes your monthly telephone bill. An equation is a simple mathematical expression that describes the relationship between two or more variablesquantities that are free to assume different values in some range. The most common type of equation well work with contains two types of variables: dependent variables and independent variables. In this example, the dependent variable is the dollar amount of your monthly telephone bill, and the independent variable is the variable on which your bill depends, namely, the volume of long-distance calls you make during the month. Your bill also depends on the $5 monthly fee and the 10 cents/minute charge. But in this example, those amounts are constants, not variables. A constant, also called a parameter, is a quantity in an equation that is xed in value, not free to vary. As the terms suggest, the dependent variable describes an outcome that depends on the value taken by the independent variable. Once you have identied the dependent variable and the independent variable, choose simple symbols to represent them. In algebra courses, X is typically used to represent the independent variable and Y the dependent variable. Many people nd it easier to remember what the variables stand for, however, if they choose symbols that are linked in some straightforward way to the quantities that the variables represent. Thus, in this example, we might use B to represent your monthly bill in dollars and T to represent the total time in minutes you spent during the month on long-distance calls. Having identied the relevant variables and chosen symbols to represent them, you are now in a position to write the equation that links them: B 5 0.10T, (1A.1)
where B is your monthly long-distance bill in dollars and T is your monthly total long-distance calling time in minutes. The xed monthly fee (5) and the charge per minute (0.10) are parameters in this equation. Note the importance of being clear about the units of measure. Because B represents the monthly bill in dollars, we must also express the xed monthly fee and the per-minute charge in dollars, which is why the latter number appears in Equation 1A.1 as 0.10 rather than 10. Equation 1A.1 follows the normal convention in which the dependent variable appears by itself on the left-hand side while the independent variable or variables and constants appear on the right-hand side. Once we have the equation for the monthly bill, we can use it to calculate how much you will owe as a function of your monthly volume of long-distance calls. For example, if you make 32 minutes of calls, you can calculate your monthly bill by simply substituting 32 minutes for T in Equation 1A.1: B 5 0.10(32) 8.20. (1A.2)
Your monthly bill when you make 32 minutes of calls is thus equal to $8.20.
GRAPHING THE EQUATION OF A STRAIGHT LINE
25
Under the monthly billing plan described in Example 1A.1, how much would you owe for a month during which you made 45 minutes of longdistance calls?
EXCERCISE 1A.1
1A.2
GRAPHING THE EQUATION OF A STRAIGHT LINE
The next example shows how to portray the billing plan described in Example 1A.1 as a graph. Construct a graph that portrays the monthly long-distance telephone billing plan described in Example 1A.1, putting your telephone charges, in dollars per month, on the vertical axis, and your total volume of calls, in minutes per month, on the horizontal axis. The rst step in responding to this instruction is the one we just took, namely, to translate the verbal description of the billing plan into an equation. When graphing an equation, the normal convention is to use the vertical axis to represent the dependent variable and the horizontal axis to represent the independent variable. In Figure 1A.1, we therefore put B on the vertical axis and T on the horizontal axis. One way to construct the graph shown in the gure is to begin by plotting the monthly bill values that correspond to several different total amounts of long-distance calls. For example, someone who makes 10 minutes of calls during the month would have a bill of B 5 0.10(10) $6. Thus, in Figure 1A.1 the value of 10 minutes/month on the horizontal axis corresponds to a bill of $6/month on the vertical axis (point A). Someone who makes 30 minutes of long-distance calls during the month will have a monthly bill of B 5 0.10(30) $8, so the value of 30 minutes/month on the horizontal axis corresponds to $8/month on the vertical axis (point C). Similarly, someone who makes 70 minutes of long-distance calls during the month will have a monthly bill of B 5 0.10(70) $12, so the value of 70 minutes on the horizontal axis corresponds to $12 on the vertical axis (point D). The line joining these points is the graph of the monthly billing equation, 1A.1.
EXAMPLE 1A.2
12 B ($/month) C A
D
Monthly bill
8 6 5
FIGURE 1A.1 The Monthly Telephone Bill in Example 1A.1 The graph of the equation B 5 0.10T is the straight line shown. Its vertical intercept is 5, and its slope is 0.10.
0
10
20
30 40 50 T (minutes/month)
60
70
As shown in Figure 1A.1, the graph of the equation B 5 0.10T is a straight line. The parameter 5 is the vertical intercept of the linethe value of B when T 0, or the point at which the line intersects the vertical axis. The
vertical vertical intercept in a straight line, the value taken by the dependent variable when the independent variable equals zero
26
APPENDIX 1A WORKING WITH EQUATIONS, GRAPHS, AND TABLES
slope in a straight line, the ratio of the vertical distance the straight line travels between any two points (rise) to the corresponding horizontal distance (run)
parameter 0.10 is the slope of the line, which is the ratio of the rise of the line to the corresponding run. The ratio rise/run is simply the vertical distance between any two points on the line divided by the horizontal distance between those points. For example, if we choose points A and C in Figure 1A.1, the rise is 8 6 2 and the corresponding run is 30 10 20, so rise/run 2/20 0.10. More generally, for the graph of any equation Y a bX, the parameter a is the vertical intercept and the parameter b is the slope.
1A.3
DERIVING THE EQUATION OF A STRAIGHT LINE FROM ITS GRAPH
The next example shows how to derive the equation for a straight line from a graph of the line. Figure 1A.2 shows the graph of the monthly billing plan for a new longdistance plan. What is the equation for this graph? How much is the xed monthly fee under this plan? How much is the charge per minute?
EXAMPLE 1A.3
FIGURE 1A.2 Another Monthly Long-Distance Plan The vertical distance between points A and C is 12 8 4 units, and the horizontal distance between points A and C is 40 20 20, so the slope of the line is 4/20 1/5 0.20. The vertical intercept (the value of B when T 0) is 4. So the equation for the billing plan shown is B 4 0.20T.
16 C Rise 8 A Run 20 4
D Monthly bill
B ($/month)
12
4
0
10
20
30 40 50 T (minutes/month)
60
The slope of the line shown is the rise between any two points divided by the corresponding run. For points A and C, rise 12 8 4, and run 40 20 20, so the slope equals rise/run 4/20 1/5 0.20. And since the horizontal intercept of the line is 4, its equation must be given by B 4 0.20T. (1A.3)
Under this plan, the xed monthly fee is the value of the bill when T 0, which is $4. The charge per minute is the slope of the billing line, 0.20, or 20 cents/ minute.
EXERCISE 1A.2
Write the equation for the billing plan shown in the accompanying graph on the next page. How much is its xed monthly fee? its charge per minute?
CHANGES IN THE VERTICAL INTERCEPT AND SLOPE
27
30
B ($/month)
C
24 18
A
Monthly bill
0
5
10
15 20 25 T (minutes/month)
30
1A.4
CHANGES IN THE VERTICAL INTERCEPT AND SLOPE
Examples 1A.4 and 1A.5 and Exercises 1A.3 and 1A.4 provide practise in seeing how a line shifts with a change in its vertical intercept or slope. Show how the billing plan whose graph is in Figure 1A.2 of Example 1A.3 would change if the monthly xed fee were increased from $4 to $8. An increase in the monthly xed fee from $4 to $8 would increase the vertical intercept of the billing plan by $4 but would leave its slope unchanged. An increase in the xed fee thus leads to a parallel upward shift in the billing plan by $4, as shown in Figure 1A.3. For any given number of minutes of long-distance calls, the monthly charge on the new bill will be $4 higher than on the old bill. Thus 20 minutes of calls per month cost $8 under the original plan (point A) but $12 under the new plan (point A). And 40 minutes costs $12 under the original plan (point C), $16 under the new plan (point C); and 60 minutes costs $16 under the original plan (point D), $20 under the new plan (point D).
FIGURE 1A.3 The Effect of an Increase in the Vertical Intercept An increase in the vertical intercept of a straight line produces an upward parallel shift in the line.
EXAMPLE 1A.4
20 C
D
New monthly bill
16 B ($/month) A
Original monthly bill D
12
C
8
A
4
0
10
20
30 40 50 T (minutes/month)
60
28
APPENDIX 1A WORKING WITH EQUATIONS, GRAPHS, AND TABLES
EXERCISE 1A.3
Show how the billing plan whose graph is in Figure 1A.2 would change if the monthly xed fee were reduced from $4 to $2. Show how the billing plan whose graph is in Figure 1A.2 would change if the charge per minute were increased from 20 cents to 40 cents. Because the monthly xed fee is unchanged, the vertical intercept of the new billing plan continues to be 4. But the slope of the new plan, shown in Figure 1A.4, is 0.40, or twice the slope of the original plan. More generally, in the equation Y a bX, an increase in b makes the slope of the graph of the equation steeper.
EXAMPLE 1A.5
FIGURE 1A.4 The Effect of an Increase in the Charge per Minute Because the xed monthly fee continues to be $4, the vertical intercept of the new plan is the same as that of the original plan. With the new charge per minute of 40 cents, the slope of the billing plan rises from 0.20 to 0.40.
20
C
New monthly bill
16 A Run 20
Rise
8
Original monthly bill
B ($/month)
12
C
8
A
4
0
10
20
30 40 50 T (minutes/month)
60
EXERCISE 1A.4
Show how the billing plan whose graph is in Figure 1A.2 would change if the charge per minute were reduced from 20 cents to 10 cents. Exercise 1A.4 illustrates the general rule that in an equation Y a reduction in b makes the slope of the graph of the equation less steep. bX, a
1A.5
CONSTRUCTING EQUATIONS AND GRAPHS FROM TABLES
Example 1A.6 and Exercise 1A.5 show how to transform tabular information into an equation or graph. Table 1A.1 shows four points from a monthly long-distance telephone billing equation. If all points on this billing equation lie on a straight line, nd the vertical intercept of the equation and graph it. What is the monthly xed fee? What is the charge per minute? Calculate the total bill for a month with one hour of long-distance calls. One approach to this problem is simply to plot any two points from the table on a graph. Since we are told that the billing equation is a straight line, that line must
EXAMPLE 1A.6
CONSTRUCTING EQUATIONS AND GRAPHS FROM TABLES
29
TABLE 1A.1
Points on a Long-Distance Billing Plan
Long-distance bill ($/month) 10.50 11 11 12 Total long-distance calls (minutes/month) 10 20 30 40
13 12 11 10 B ($/month)
C A Run 20 Rise 1
D
Monthly bill
FIGURE 1A.5 Plotting the Monthly Billing Equation from a Sample of Points Point A is taken from row 2, Table 1A.1, and point C from row 4. The monthly billing plan is the straight line that passes through these points.
0
10
20
30 40 50 T (minutes/month)
60
be the one that passes through any two of its points. Thus, in Figure 1A.5 we use A to denote the point from Table 1A.1 for which a monthly bill of $11 corresponds to 20 minutes/month of calls (second row) and C to denote the point for which a monthly bill of $12 corresponds to 40 minutes/month of calls (fourth row). The straight line passing through these points is the graph of the billing equation. Unless you have a steady hand, however, or use extremely large graph paper, the method of extending a line between two points on the billing plan is unlikely to be very accurate. An alternative approach is to calculate the equation for the billing plan directly. Since the equation is a straight line, we know that it takes the general form B f sT, where f is the xed monthly fee and s is the slope. Our goal is to calculate the vertical intercept f and the slope s. From the same two points we plotted earlier, A and C, we can calculate the slope of the billing plan as s rise/run 1/20 0.05. So all that remains is to calculate f, the xed monthly fee. At point C on the billing plan, the total monthly bill is $12 for 40 minutes, so we can substitute B 12, s 0.05, and T 40 into the general equation B f sT to obtain 12 or 12 f 2, (1A.5) f 0.05(40), (1A.4)
30
APPENDIX 1A WORKING WITH EQUATIONS, GRAPHS, AND TABLES
which solves for f
10. So the monthly billing equation must be B 10 0.05T. (1A.6)
For this billing equation, the xed fee is $10/month, the calling charge is 5 cents/ minute ($0.05/minute), and the total bill for a month with one hour of long-distance calls is B 10 0.05(60) $13, just as shown in Figure 1A.5.
EXERCISE 1A.5
The following table shows four points from a monthly long-distance telephone billing plan.
Long-distance bill ($/month) 20 30 40 50
Total long-distance calls (minutes/month) 10 20 30 40
If all points on this billing plan lie on a straight line, nd the vertical intercept of the corresponding equation without graphing it. What is the monthly xed fee? What is the charge per minute? How much would the charges be for one hour of long-distance calls per month? See www.mcgrawhill.ca/olc/frankbernanke for a brief discussion of how simultaneous equations can be used to decide which of two different long-distance billing plans is best for your purposes.
KEY TERMS
constant (24) dependent variable (24) equation (24) independent variable (24) parameter (24) rise (26) run (26) slope (26) variable (24) vertical intercept (25)
ANSWERS TO IN-APPENDIX EXERCISES
1A.1 To calculate your monthly bill for 45 minutes of calls, substitute 45 minutes for T in Equation 1A.1 to get B 0.10(45) $9.50. 5.00
1A.2 Calculating the slope using points A and C, we have rise 30.00 24.00 6.00 and run 30.00 15.00 15.00, so rise/run 6/15 2/5 0.40. And since the horizontal intercept of the line is 18, its equation is B 18 0.40T. Under this plan, the xed monthly fee is $18, and the charge per minute is the slope of the billing line, 0.40, or 40 cents/minute.
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ANSWERS TO IN-APPENDIX EXERCISES
31
1A.3 A $2 reduction in the monthly xed fee would produce a downward parallel shift in the billing plan by $2.
16 14
B ($/month)
D D
Original monthly bill New monthly bill
12 10 8 6 4 2 0 10 20 A A
C C
30 40 50 T (minutes/month)
60
1A.4 With an unchanged monthly xed fee, the vertical intercept of the new billing plan continues to be 4. The slope of the new plan is 0.10, half the slope of the original plan.
12
B ($/month)
C
Original monthly bill New monthly bill
8 6 4
A A Run 20
C Rise 2
0
10
20
30 40 50 T (minutes/month)
60
1A.5 Let the billing equation be B f sT, where f is the xed monthly fee and s is the slope. From the rst two points in the table, calculate the slope s rise/run 10/10 1. To calculate f, we can use the information in row 1 of the table to write the billing equation as 20 f 1(10) and solve for f 10. So the monthly billing equation must be B 10 1.0T. For this billing equation, the xed fee is $10/month, the calling charge is $1/minute, and the total bill for a month with one hour of long-distance calls is B 10 1(60) $70.
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