Comments on Macroeconomic Theory (under construction)

A Socratic Approach to Economic Theory: Comments and Questions

1.0: The applicability of macroeconomic theory

Since the recent economic meltdown, most of us have come to believe that economic theory is deeply wrong or lacking. But just what is wrong? Just what is lacking? It is not sufficient to realize that economic theory is imperfect. We continue to encounter economic data in our newspapers. How should we interpret them? Public policy continues to be influenced by such data. We need some guidelines for use of economic data, some way to envision the possible consequences of economic decisions. Must we develop a completely new theory? Can we correct or adjust the present unsuccessful theory so that it is useful? The following is my attempt to help you understand how economic theory is imperfect, so you can make appropriate corrections and use it to make economic decisions. My approach is to state economic theory as it is now, with all its errors still in it, then ask questions whose answers will help you correct the theory.

There is no consensus about how the present obviously failed theory should be corrected. I have some notions about how to do so, but rather than tell you what I advocate, I prefer to ask the questions that I think anyone trying to construct a sensible theory should ask. In effect, I am asking you to construct your own Economic Theory 2.0, now that Economic Theory 1.0 has caused the system to crash.

Why do I think you are qualified to do such programming? I think that economics is far from rocket science. I think that all you need is common sense plus a healthy dose of distrust of the sorts of "facts" everyone knows and agrees about, although nobody cares to question them or investigate whether they are, indeed, facts. You are that sort of person, aren't you? If you aren't, then I have some great derivative bonds to sell you. Or would you be interested in a marvelously generous adjustable-rate mortgage? You don't have to provide any information to prove you are credit-worthy, just agree I can come take your home away from you if you don't make those low low payments you promise to pay, which, of course, might happen to quintuple one day soon, whenever I decide that they should.

Economics in general and macroeconomics in particular base their predictions on a simplified model of how humans behave in the marketplace. Since real humans and real marketplaces are much more complex than their macroeconomic models, it is not surprising that real humans in real marketplaces do not always behave in conformity with macroeconomic models. In the following, I address where and how the macroeconomic model is likely to make correct or incorrect predictions, i.e., when to trust the model and when not to.

To accomplish this purpose, I encourage you to examine the model critically, to question its assumptions and its ways of arriving at conclusions.

There is no one comprehensive self-consistent set of beliefs that we may call the economic theory. However, there are certain beliefs that most contemporary economists share. I refer to these as comprising "standard" economic theory.

In my comments below, I often use the verb "tends." Economics deals with complex systems. Very little can be stated that is always true. When I use the verb "tends," I do not mean I am uncertain about what I state; I simply mean that there are or may be exceptions, that what I state only "tends" to be true. However, unless I explicitly state otherwise, I do not make such statements if I feel that the exceptions occur so often that the "tendency" is obscured, or that the exceptions are more important than what "tends" to be so.

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1.1: Scientific method

Economists like to regard economics as a science. A science is an organized effort accurately to describe and predict the real world. Different sciences differ in what aspect or part of the real world they seek to describe and predict. For example, entomologists try to describe bugs and predict their behavior. Ornithologists do the same with respect to birds. To the extent that economics is a science, economists try to describe and predict a particular aspect of human behavior, namely how (depending on which definition of economics you accept) (a) people choose to use their scarce resources to attempt to satisfy their unlimited wants, or (b) people's choices among alternatives are affected by their perceptions of the likelihoods and values (positive or negative) of the alternatives.

The first step in the development of a science is creating a way to describe accurately what is observed. Until that is accomplished, improving prediction accuracy is essentially impossible, because observers cannot compare their observations with predictions. This implies that in economics it is critical that the quantities that economists use and seek to predict and even control, such as the cost of living index, be measured accurately and honestly, and temptations to manipulate them for political advantage be strictly resisted.

In science, prediction accuracy is improved by a trial-and-error or evolutionary process. A recipe is proposed that can be used to derive predictions. (Such a recipe is often called a hypothesis.) Then the predictions it leads to are compared to observations. If the predictions prove incorrect, then the hypothesis is discarded or revised. If the predictions prove correct, then confidence in the hypothesis grows. Of course, this method never absolutely proves that a hypothesis is correct, because its next prediction may, at least conceivably, prove incorrect. Even the hypothesis that the sun will rise in the east has never been absolutely proven. Just wait till tomorrow. Who knows? If the hypothesis is still correct, wait till the day after tomorrow, and so on. (An exception is a hypothesis that leads to a limited number of predictions, and all are verified. Such a hypothesis can, indeed, be proven. However, such hypotheses are of little interest in science, which is persistently future-oriented, interested in predictions about observations that have not yet been made.)

A theory is a general hypothesis, one that gives rise to many different specific predictions. A law is a theory that people feel very confident about. Thus, we speak of the law of gravity, but Karl Marx's economic theories (rather than Karl Marx's laws).

Note: the discussion above defines scientific method and theory differently than many economists do. The study of scientific method is not, strictly speaking, itself very scientific. It is more a division of philosophy, and there is considerable disagreement among experts. You do not need to get into the fine points of these different viewpoints. What I feel you need to know is: (a) Economists aspire to be scientific, and consequently they (b) try to test their theories to see whether they make accurate predictions. I feel strongly that economic theories should be judged by how well they predict, and that there should be no cheating or hedging, such as claiming that a prediction failed because a ceteris paribus assumption failed. I feel that it is the job of a professional economist to take such problems into account and make predictions that can be tested. No excuses should be allowed.

Scientists need to avoid the fallacy, "post hoc, propter hoc," the mistaken conclusion that because A follows B, B must be the cause of A. On many a farm, the sun rises shortly after the rooster crows. Perhaps the rooster thinks so, but we surely don't think that he makes the sun rise. More generally, that two events, A and B, are associated does not mean that one causes the other. How may two events, A and B, be associated although A does not cause B? Well, B might cause A. Another possibility is that a third event, C, is the cause of both.

1.2: The definition of economics I think many economists would agree with the following: Economics is the study of how people choose to use their scarce resources to attempt to satisfy their unlimited wants. Consider the following alternative definition: Economics is the study of how people's choices among alternatives are affected by their perceptions of the likelihoods and values (positive or negative) of the alternatives. Which makes more sense? Why? Much of what you will find below this paragraph addresses these questions and, I hope, will help give you a better basis for answering them. Nevertheless, I encourage you to think about these questions now as preparation for what you may read below. 1.3: Rationality in choice -- rational self-interest One key component of standard economic theory is the belief that the choices people make are rational. As you may suspect, not all economists agree about what, in this context, "rational" means. Many economists hold that people make rational choices when they make choices that they may reasonably believe will make them happier or better off. Again, as you may suspect, there is no unanimity about the meaning of "happier" or "better off." Without getting embroiled at this point in examining what "rational," "happier," or "better off" mean, let us for the moment try to make do with commonsense interpretation of the words and see how far we can get. I start with some obvious questions: Do people always make logical, rational choices? Do they ever do things that they know are not in their best interest? Do people sometimes behave irrationally? Moreover, do people's choices only depend on their own happiness or how better off they are, without regard to how their choices affect those they care about? I suggest we should also consider the latter: Do people behave in ways that make not only themselves but also those they care about better off and happier? Why are many items sold for $2.99 rather than $3.00? How can this fact be reconciled with the notion of rational self-interest? Standard macroeconomic theory almost but not quite assumes that people do whatever makes them happy, and this is the sole basis for what they do. If that is so, then, to predict what they will do, we simply have to find out what makes them happy. Of course, things are considerably more complicated. Obviously, more than one action may make them happy. Which alternative will they choose? The alternative that makes them happiest? But that leads to more complications. We need a way to rank-order alternatives in terms of how happy they will make a person. We do not necessarily have to be able to assign a number, a quantity of happiness, to an alternative; however, we do have to be able to say that alternative A will give rise to more (or less) happiness than alternative B. How are we going to be able to do this? If we can't, then we are again facing great difficulty in predicting what people will do. Moreover, presumably economists must not only be able to evaluate accurately the relative happiness potential of different alternatives, but also the persons who choose among the alternatives must be able to do so -- or think they can. If a person is to choose the alternative he or she anticipates will lead to the greatest happiness, then the person must have a way of coming to such a conclusion. How do people do this? It seems, at this point, as if economics can only be a useful basis for predicting what people will do if, first, there is a well-developed science of psychology -- at least the psychology of choice and happiness. Moreover, to get back to the questions raised above: If people don't always do what makes themselves and those they care about better off and happier, then predicting what they will do obviously requires our knowing whether and when what they do will depend on making themselves and those they care about better off and happier, and whether and when it will depend on something else. In the latter case, we will have to look into what that "something else" may be, and try to understand its (or their, if there is more than one "something else") influence on behavior. It sounds that we are once more getting into psychology. And, by the way, while we are digging into this so deeply: Is there a distinction between becoming happier and becoming better off? Just what does "better off" mean? It has an economic sound to it. Does it mean more prosperous? What if an alternative makes a person less happy but better off? Suppose another alternative makes a person less well off but happier? Is this even possible? I suppose so, because if becoming better off always makes a person happier, and vice-versa, then why bother to mention both? Anyhow, if "better off" and "happier" are not interchangeable, then how would a person choose when they call for different choices? To make accurate predictions, it appears that we would need somehow to build a conversion table: so many units of happiness equal so many units of well-off-ness. Is this even possible? Another complication involves probability. For example, is one dollar as desirable as a fifty-fifty chance of getting two dollars? Everyday experience indicates that people have very different preferences when probability is involved. Some people like to gamble; some don't; many are willing to gamble about some things but not about others; some don't mind probability rather than certainty when it comes to possible gains, but do mind when it comes to possible losses. It is the prevalence of the latter attitude that enables insurance companies to make a profit. Another complication involves the expenditure of resources necessary to gather the information necessary to make a fully informed choice. The great organization management theorist, Herbert Simon, pointed out that organization managers usually find it impractical to gather all the information they need to be able to choose the best possible alternative. He calls choosing such an alternative "optimizing." He says that, instead, managers normally "satisfice," i.e., choose a reasonably satisfactory alternative, and then go on to the next choice that they have to make. If people do not always make the best possible choice, does this undermine economic theory? Furthermore, just as we appear to need a way to relate happiness to well-off-ness, the macroeconomic model appears to require a way to relate one's own happiness (or well-off-ness) to that of those we care about. Suppose an alternative makes a person happier but makes those she or he cares about less happy? Or vice-versa? Again, is this even possible? Perhaps, when we care about people, then their happiness makes us happy, their unhappiness makes us unhappy, etc. But it still seems as if we have gotten into more complications. We obviously don't necessarily care equally about everybody we care about. It seems as if we need a way to determine the relative amount of caring a person feels about different people. How would twice as much happiness for a person he or she cares about balance against half as much happiness for another person she or he cares about four times as much? Furthermore, do people care as much about their own well-offness and happiness as they do about how well off or happy others are? I suspect that at least some people find their own prosperity and happiness more vivid and immediate, something they care more about, than the prosperity and happiness of even those others they love and care about the most. To take this a step further: Don't we not only care about the well-being and happiness of other individuals but also care about more abstract entities. For example, I care about the well-being of my country. Again, it seems as if we need a way to weigh caring about A versus caring about B. This discussion seems to me to be getting weird, but I don't see how we can escape questions like this if we are going to use economics to make practical predictions. What do you think? To get back to the beginning of this discussion: Were your major life decisions, such as choice of a career, entirely rational choices? Did you spell out for yourself your goals and attitudes? Did you list for yourself all the alternatives available, then decide what benefits each offered, and what costs it might entail? Do you always make only rational choices? To what extent is the economists' notion that people make rational choices equivalent to assuming that humans are like the Vulcan ideal, that we behave logically and are never lured by emotion from the logical, i.e., rational path? If that is what economists assume, is it a logical or rational assumption? If that is not what economists assume, what are they assuming, and how does it differ? At the beginning of his book, "Listening with the Third Ear," the famous psychiatrist, Theodor Reik, recounts something that happened to him when he was a medical student in Vienna. I paraphrase his story. One of Reik's teachers was Sigmund Freud, the founder of psychoanalysis. One night, young Theodor was wandering in downtown Vienna, wondering whether he should specialize in psychiatry or, instead, some other medical specialty. While thinking, he stopped in front of a store window and stared at his reflection in the glass. Suddenly, he became aware that another person was also reflected in the window. Standing next to him was Freud. The professor said, "You look troubled. Is something bothering you?" Reik explained that he was having a difficult time deciding which medical specialty to choose. "How have you gone about deciding?" Freud asked. Reik explained that he had made a list of the benefits and costs of the various alternatives, then assigned numerical values to each benefit and each cost. Next, he had added up the numbers, assigning positive values to the benefits and negative values to the costs. However, after all that, he still could not make up his mind. Somehow, that approach did not seem to address the real issues. "You are correct," Freud told him. "You couldn't have chosen a worse way to make an important decision. Your approach is fine for an unimportant decision, such as which show to go to or which restaurant to dine in. However, for an important decision, such as which person to marry, or which career to choose, it is almost worthless. You see, we humans don't really know our deepest, most important desires. We really don't know what drives us." Freud continued, "The best way to make an important decision is to try to picture as vividly and clearly as possible how it would feel to have chosen each alternative and have to live the life that would result. Then, note how you feel. If your emotional reaction is negative, avoid that alternative, no matter how logical it seems, no matter how high a score it gets when you add up the numbers. On the other hand, if you feel happy and excited about an alternative, that is likely to be the one you should choose." Is Freud's point of view compatible with standard economic theory? Certain types of injury to the brain's frontal lobes ruin people's ability to connect their experiences (including choices they may be considering) with their emotional reactions. Such people's ability to reason logically, e.g., to solve puzzles that require logical deduction, is not impaired. However, they usually make a terrible mess of their lives. Does this have any relevance to the discussion here? Suppose an economist asserts: "Whatever the reason, people choose the option that at the time gives them the greatest satisfaction. This is rational self-interest." Does this definition of rational self-interest so dilute its meaning that it can hardly be considered rational? The same economist or another might assert: "The term 'rational' refers to the comparison of costs and benefits." Are the two quotes in this paragraph mutually consistent? Moreover, do people always compare costs and benefits when they make choices? Can they always do so? Consider Freud's comments. Economists generally agree that people may differ with respect to what they like or dislike about an alternative. If we don't know what a person likes or dislikes, how can we predict what that person is going to do? If, by definition, people always choose what they like, this enables us -- after the fact -- always to be confident they chose rationally. But that seems to be circular reasoning. We assume that people choose rationally, then we conclude that whatever they chose must have been the rational choice because, by assumption, people choose rationally. What do you think? Two world-class economists, Daniel Kahneman and Vernon Smith, who won the Nobel Prize in economics, question the notion that humans are perfectly capable of rational judgments about how to handle money. They conclude that we humans may want as much money as possible, but we do not go about getting it in ways that are altogether rational. Finally, some economists have been known to assert: "Most of the time people consider costs and benefits." Are they hedging? Aren't they admitting that some of the time economic theory won't predict what people will do? If so, when can we count on economic theory, and when should we not count on it? 1.4: Is economics normative? Science seeks to describe and predict what does or will actually happen. Normative analysis seeks to describe and predict what should happen. Can it be that economic analysis is normative when economists assume that people base their decisions on rational self-interest, on comparison of costs and benefits? Can it be that economists think that people ought to decide in this way? 1.5: Are people's wants limitless? Standard economic theory assumes that people's wants are unlimited. Are people's wants truly unlimited? If so, then why is so much money and energy devoted to advertising, to trying to stimulate people's cravings and demands? Is it not at least conceivable that, if not in our society then in another culture, people might be contented with what they have? Could the economists' belief that people's wants are unlimited be self-fulfilling, because it leads those who make decisions that affect our economy to assume that people will never be satisfied with what they have, and consequently the decisionmakers do not plan or organize the economy in a way that permits people to feel they have enough and act on that belief? If wants were not unlimited, would people still have to make choices? More fundamentally, how critical to the theory of economics is the assumption that wants are unlimited? 1.6: The role of scarcity in macroeconomic theory If wants were not unlimited, could there still be scarcity? If wants are unlimited, can there ever be freedom from scarcity? In standard economic theory, an economic good is defined as something that there is not enough of to satisfy everyone who wants it. Does the assumption that wants are unlimited imply that anything that anyone wants is an economic good? Is there a difference between a want and a need? If they are different, how are they different? Is the difference, or absence of a difference, relevant to economics? If so, how? For example, might wants be unlimited but needs limited? 1.7: Microeconomics vs. macroeconomics According to the Encyclopedia of Business and Finance, "Economics . . . can be divided into two areas: macroeconomics and microeconomics. To differentiate between the two, the analogy of the forest and the individual trees can be helpful. Macroeconomics is the study of the behaviors and activities of the economy as a whole; hence, the forest. Microeconomics looks at the behaviors and activities of individual households and firms, the individual components that make up the whole economy; hence, the individual trees. . . . "Macroeconomics, being the study of the behaviors and activities of the economy as a whole, looks at such areas as the Federal Reserve System, unemployment, gross domestic product, and business cycles. . . . "Microeconomics looks at the individual components of the economy, such as costs of production, maximizing profits, and the different market structures." Usually, what applies to one member of a group, e.g., microeconomics, does not apply to the group as a whole because, in the latter case, the individuals that make up the group may interact in ways that change how each behaves, compared to how each would behave if the others were not there. It is a good general rule that, whenever more than one entity is involved, we consider how the different entities affect each other. A whole is more than the sum of its parts: it is the sum of its parts plus their interactions. To fail to take this into account leads to the fallacy of composition. An economic example: Suppose a merchant decides to keep his store open an hour after all his competitors have closed their stores. Thereby, he may get some additional customers. However, if all the competing merchants do the same, then none will gain any advantage, and they may indeed experience a loss due to the additional cost of staying open longer. Clearly, in macroeconomics we must beware of the fallacy of composition. Specifically, principals of microeconomics may not apply in macroeconomics. 1.8: Resources Standard macroeconomic theory recognizes three kinds of resources (also referred to as "productive inputs"or "factors of production": land, labor, and capital. They facilitate production, but are not the raw materials of production. In standard macroeconomic theory: land comprises all natural resources, i.e., whatever may be gotten from the ecosystem, including forests, fisheries, minerals, and water; labor comprises work done by people in the work force; and capital comprises human made tools or equipment, including factories and warehoused finished or unfinished goods. Land is distinguished from capital by not being produced by humans. Is outer space a resource? If so, what kind of resource is it -- land, labor, or capital? Does it make a difference whether resources can be used over and over or, once used (such as coal, when it is burned), are gone forever (or for a very long time)? If it does make a difference, what is that difference? Is it important? If so, why? Does capital include cash, stocks, bonds, or money in bank accounts? Economists differ about the answer to this question. What do you think? When this latter kind of capital multiplies, say, by earning interest, is this kind of increase in wealth different from increase in wealth by using the other kind of capital (e.g., factory equipment) to produce goods? Is capital (such as machinery) ever rented, i.e., does it earn money for its owner, while the renter uses it to produce goods? If so, is it still appropriate to consider it capital, or is it better to consider it land?

2.0: Economic choices

Are all alternative economic choices comparable? Classical economic theory assumes that all kinds of happiness or net benefit (by the way, are these interchangeable?) can be measured against each other. Might one kind of happiness differ so much from another kind that it would not be feasible to measure one against the other? For example, how many delightful, satisfying desserts equal one beautiful love affair? 17.327? 41.8? How could such a comparison ever be made? If it could not be made, then what sense is there in economic theory's definition of "choice"?

2.1: Opportunity Costs

An "opportunity cost" is the value of an alternative choice that cannot be chosen because another, preferred choice has been chosen. Standard economic theory often refers to "the" opportunity cost, which is the value of the next most preferred alternative choice, second only to the most preferred choice, the one that is therefore presumably chosen.

How do we know which alternative is what economists term "the next best alternative"?

Is the economic theory definition of "opportunity cost" consistent? Is an opportunity cost "the forgone benefits of the next best alternative," or "the forgone benefits of whatever else you could be doing"? "Whatever else" doesn't seem to be the "next best alternative"; it sounds more like all the other alternatives. The two definitions of "opportunity cost" do not seem equivalent. The latter definition would appear to get us entangled with the probabilities of actually choosing various "other alternatives."

Is there such a thing as "opportunity benefit," i.e., the forgone cost of the next worst alternative? Might it ever be useful or prudent to consider "opportunity benefit"? If so, when?

2.2: Quantifiability of benefits and costs

In economic theory we may be on the most solid ground when we confine consideration to money costs and benefits. Money amounts are much easier to quantify and compare than other benefits and costs of, for example, going to college versus working. In addition to money, the costs and benefits clearly include, among many others, practical experience, friendships and acquaintances, skills acquired, documents such as academic transcripts or letters of recommendation from a boss. Is it ever possible to enumerate and consider all the benefits and costs of alternatives? If not, then at what point would it make sense to stop?

Furthermore, don't costs or benefits have consequences? May not at least some of these consequences be further costs or benefits? And may not they have additional consequences? How far can this go? Probably, the further into the future we try to look, the less certain our analysis becomes. Again, at what point would it make sense to stop? How do the issues raised in this paragraph relate to the old philosophical question about balancing means and ends, i.e., short-term versus long-term?

If we limit ourselves to money costs and benefits, we may be able to choose courses of action that lead to the most money acquired or the least money lost. But would such a course of action necessarily lead to the greatest happiness? Might this be one important limitation of economic theory?

The following may more properly belong in philosophical rather than economic discourse, but I am unwilling to disregard these issues because of jurisdictional or territorial limitations on what aspects of economic theory may be considered. I feel it is worthwhile to inquire: Which is wiser, to seek the most money or the most happiness? Are these two goals always consistent?

Do costs and benefits add and subtract like numbers in arithmetic? Do they even do so when we limit ourselves to money costs and benefits? For example, does a profit of one dollar exactly cancel a loss of one dollar? Clearly the amounts of money can cancel, but do the corresponding happinesses? Is the happiness produced by gaining one dollar exactly cancelled by the unhappiness produced by losing one dollar? Moreover, does winning then losing one dollar give the same amount of happiness or unhappiness as experiencing neither winning nor losing? If so, then how do we account for the pleasure some people appear to experience in gambling? Furthermore, do happinesses and unhappinesses cancel? Are they opposing vectors on the same coordinate? Is it not possible to feel concurrently happiness and unhappiness about the same event or outcome? How could this be if happiness and unhappiness mutually cancel?

2.3: Tradeoffs and Decisions at the Margin

When do choices apply to anything other than marginal costs and benefits? When, if ever, do we ever make choices other than at the margin? After all, choices always apply to the future. If all choices are marginal, what is the point of introducing the term "marginal"?

2.4: The Production Possibilities Curve (PPC)

Underlying the use of "the production possibilities curve" in economic theory are a number of assumptions. First, the PPC clearly assumes that both kinds of production draw on or compete for the same limited resources. Might not the shape of the PPC depend on the extent that different kinds of production draw on different resources? Suppose they drew on utterly different resources, then what would the curve look like? Might the PPC then be a rectangle, because regardless of the amount of production of the kind represented on the horizontal axis, the amount represented on the vertical axis would be the same, and vice versa?

Might there ever be a case when the PPC might slope upward to the right? Suppose, for example, increased production of nondefense goods and services would create new resources that could be used to produce more defense goods and services. What might that do to the PPC? More generally, are the total resources available always fixed, or are they ever changed by the very choice of what to produce?

Actual experience indicates that the demand that undertakings make on resources does not increase in direct proportion to the amount of production attempted. Usually, an attempt to produce a very small amount of something costs more per item than when a greater amount is produced. We refer to this phenomenon as "economy of scale." However, this phenomenon is not unlimited. When an attempt is made to produce more and more of something, eventually a point is reached where resources start to become less readily available. Typically, not all resources are equally available, and those more readily available tend to be used first. Eventually, then, cost per unit produced starts to rise again. In other words, a curve showing cost per unit produced on the vertical axis and amount produced on the horizontal axis is usually U-shaped. It is lowest for a middle range of amount produced, and high when either very much or very little is produced. Now, what might this do to a PPC?

2.5: Marginal Opportunity Cost

In economic theory, the PPC is a convex curve. In other words, as the production amount represented on the vertical axis increases, the production amount represented on the horizontal axis not only decreases but also decreases faster and faster. The convexity implies that as more and more of Type A goods and services are produced, adding just one more unit of Type A goods and services has a greater and greater impact on Type B goods and services. For example, it implies that the marginal opportunity costs of defense production increase as non-defense production increases. The convex PPC also indicates that, as defense production increases, it has a greater and greater negative impact on nondefense production. The marginal opportunity costs of non-defense production also increase as defense production increases. This should be no surprise, because the choice of which kind of production to represent on the vertical axis and which to represent on the horizontal axis is, after all, arbitrary. Therefore, anything that can be said about how the vertical-axis variable depends on the horizontal-axis variable should also apply if the two variables are exchanged.

Of course, a rectangular PPC is still convex. It is an extreme kind of convex curve. I draw attention to this issue of convexity because in the advanced mathematical theory that underlies much of economics, a common assumption is that the PPC and other similar curves are convex. If such assumptions do not hold, then conclusions that depend on them become doubtful.

Even if the PPC were to slope upward to the right, it still could be convex. To not be convex, i.e., to have a concave part, it would need a section where its downward slope to the right slows down (i.e., the marginal cost of A decreases with increasing production of B) or its (if that is possible) upward slope to the right speeds up. We might, perhaps, refer to the latter as an increase in "marginal benefit." To return to the example, a concave portion of the PPC would be a portion where as nondefense production increased, its negative impact on defense production would decline (i.e., the marginal opportunity costs of defense production would decrease as nondefense production incresed) (or, if that is possible, its positive impact would increase). Might this happen, for example, if non-defense production included production of goods and services that increased the productivity or efficiency of defense production?

2.6: "Specialize Where Opportunity Costs Are Lowest"

Note how the conclusion in favor of trade is related to the assumption that the PPC is convex.