– Paul Woodburne
I had a conversation with my son the other day. He is changing majors at his university, from one that is not mathematical to one that is. He is in his sophomore year, so he may have an additional two years of school if things do not fall into place easily. He has strong math skills, but before they would let him into the major, they wanted him to take a refresher course to see how much math he’d have to take before he could take his new major classes. Essentially, they don’t want him to waste his time if he needs to start at a very basic math level.
The refresher course is online. It consists of several topics and questions, 95% of which he needs to complete. Even when he has completed a given section, a ‘knowledge quiz’ pops up. He has to complete this, too, which may then require him to redo some of the topic he has just finished. This often lowers his acquired percentage completed, which annoys him. What I found interesting for the purposes of this article was that he told me that these ‘knowledge quizzes’ at first asked him easy questions, but were now asking him hard questions. This makes sense. He first completed the more familiar sections, and only later completed what he considered the more difficult sections (trigonometry and logarithms, etc.). It makes sense that the questions are “harder,” as he has had less experience with these topics. In addition, sometimes online teaching tools have mechanisms to increase difficulty as the student masters the topic. This may have been the case, as well
I am perhaps not the most understanding dad. I told him that, of course, things are only difficult until they are understood, at which point they become easy. Mysteries are only mysterious until they are solved . . . then they become obvious. If students already know the answer, they would not need the course.
It seems to me that our purpose in the teaching profession is to make the difficult easy, to make the mysterious obvious. This is difficult to do—perhaps until it becomes easy and obvious. I imagine that how we transform the difficult to easy differs in every field. I also imagine that how we transform the difficult to easy differs for every student. Many Clarion students find mathematical fields (e.g., mathematics, physics, economics, finance, and chemistry) inherently difficult. This is, in part, because many of our students come to us with relatively weak mathematical backgrounds.
However, many students with good quantitative backgrounds find non-mathematical fields (e.g., political theory, history, comparative literature, and philosophy and many of the other humanities) inherently difficult, perhaps because often there are no definitive answers. The process in every field is often as much about the process, the questions, and the argumentation as about the ‘correct’ answer. I can imagine the engineering student who is trying to contribute to a discussion on the meaning and interpretation of a piece of literature saying, “but what is the answer?” I can also imagine the humanities student asking the math professor “how do we know when to use that technique?”
As a general rule, students believe that economics is hard. This is largely because economics is very abstract. We make unrealistic and heroic assumptions about human behavior. Many of these assumptions were made to facilitate the mathematization of the field some decades ago. This furthers the abstractions that students object to. Instead of talking to people, as one might in Psychology, Sociology, or Anthropology, we use abstract supply and demand models to discuss behavior. This method requires significant use of mathematics and graphs.
I see it as my job to make the hard science of economics easy, to make its mysteries obvious. Here are some examples of problems I present in order to make this difficult science easier:
Example 1: Why wear “biomechanically and orthopedically unsound” shoes?
We can ask why, for example, some women spend $550 or more for a pair of Manolo Blahnik (or similar) high heels (see Kelly & Branch, 2003). These shoes are “biomechanically and orthopedically unsound,” according to the American Podiatric Medical Association. The shoes can shorten the Achilles tendon and cause damage to ankles, knees, and hips. They are made so narrow that many women have to have foot surgery or toes removed or collagen injections into the balls of their feet to wear them. Sometimes women need surgery to remove bunions, either before or after wearing these shoes.
Yet, despite these difficulties, many women wear them willingly. They feel powerful, sexy, confident, professional, etc. A question arises: “Why put up with the pain and surgeries?” Are these women foolish? Can fashion really be so important? Is there a cabal of men making women feel that they need to objectify themselves to gain power (like ancient Chinese foot binding and the like)?
Example 2: When will we run out of oil?
Let’s say that we know that there are 1,696.6 billion barrels of oil in known reserves in the world (US Energy Information Administration, n.d.). Let’s say we consume 34.68 billion barrels per year (BP, 2016). These data are accurate and real. We can ask, “when do we run out of oil?” This is a standard question raised in countless documentaries and news programs. Our students, like most Americans, believe we will run out of oil in the near future.
It is very difficult to respond to these questions. Where do students start?
Is there a consistent method to answer these questions, or must all questions be answered on an ad hoc basis? To me, the process for getting to an answer is sometimes more important than the answer itself. Economics is famous for there never being a ONE correct answer. The nice thing about economic theory is that it gives a set of tools/assumptions that, we believe, apply to a wide range of topics and questions. It is my job to clarify the method and show students how to apply it.
Table 1. Basic Restrictive Assumptions
To do this, I have formalized the “Basic Restrictive Assumptions” for use in my principles of economics classes. See Table 1. This is my version of the standard set of assumptions that most economics texts refer to only obliquely. This list is ‘restrictive’ because it limits how we analyze questions and the sorts of questions we can analyze. I use this to guide discussions along the right path. A nice thing about this list is that we can alter (violate) some assumptions, and receive very different answers. All our answers are conditional, based upon the acceptance (or not) of assumptions/preconditions such as these.
Virtually all questions considered as ‘economics’ by my field can be answered with appropriate application of the above assumptions. Questions that these assumptions cannot usefully answer are, almost by definition, not ‘economics.’ These assumptions, if taken as valid, justify the supremacy of the perfectly competitive market, over a government-run economy; however, we know that these assumptions are NOT REAL in the absolute sense. Rather, they show what must occur for a perfectly competitive economy to exist. Violations of these assumptions lead to monopolies, crises, roles for government, financial collapse, etc. Specific violations lead to specific implications and policy prescriptions.
I use the examples described above in the first few days of my macroeconomics and microeconomics classes. I lead a discussion getting my students to apply assumptions in Table 1 to identify a solution using the numerical data available.
Example 1: Why wear “biomechanically and orthopedically unsound” shoes?
Economics rarely if ever delves into the world of name calling. Our assumption #5 means that we do not begin our analysis by thinking that people are simply mistaken or stupid. To answer the question posed by the article, we first start by applying our assumptions (see Kelly & Branch, 2003). These women are rational. They are weighing the known costs and benefits of their actions. So what can we conclude? The shoes cost $400 or more. In addition, real costs also include surgeries, the collagen injections, the powders and pads for toes, etc. Let’s say that the collagen injections cost $500 every 6 months, and the other things add up to about $500 per year. The bunion surgery may run to $10,000, but may be covered by insurance. These are the marginal costs of the shoes.
For women to be rational (as we assume they are) and for them to want to purchase the shoes, their calculation of the marginal benefits MUST be greater than these marginal costs. The perceived value these women place on sexiness, power, confidence, and professionalism in the workplace MUST be more than the marginal costs of the shoes.
This does not have to be the end of the argument. We can argue that some of the assumptions are violated. What if agents do not have perfect information? It seems reasonable that women may not really know the full cost, 20 years hence, on tendons, ankles, knees, and hips, from wearing these shoes now. If this is the case, then we can argue that women are underestimating the marginal costs, and that – if these costs were correctly accounted for – then perhaps some women would opt not to wear these shoes.
Example 2: When will we run out of oil?
The answer, from applying economic theory, is that we will never run out of oil. Why? For the sake of argument, let’s say that no more oil exists or will be found. This is simply an extreme version of Assumption 3.
At first blush, it appears that we’ll run out of oil in about 48.9 years. This is scary. We arrive at this amount by dividing 1,696.6 by 34.68 (BP, 2016; US Energy Information Administration, n.d.). This conclusion, though, is flawed. This assumes we divide the whole into equal parts and that we will consume the same amount of oil every year. However, it is unlikely that we will consume oil at the same pace every year. As we consume the easiest oil first (closest to the surface), the cost of additional oil rises. Assumptions 4 and 5 suggest that we will reduce consumption of oil and increase consumption of other forms of energy, which used to be more expensive. More research and development will go into solar, biomass, wind, nuclear, etc., as the price of oil rises. People will move to hybrid cars, electric cars, and mass transit, and firms will move toward powering buildings and factories with alternative fuels. Those cars, trains, and factories will be powered by electricity derived from non-oil sources.
As the next most expensive oil is used up, we’ll move to even more expensive oil. The process described above will continue. Eventually, the remaining oil will be too expensive to extract, and will be allowed to sit. We use the same logic to explain our reduced use of coal. The environmental costs are too high, and the cost of alternatives, particularly natural gas from fracking, has fallen dramatically. There is no ‘war on coal.’ New technologies and lax regulation have allowed the supply of natural gas to rise dramatically, lowering its price (both absolutely and in comparison to oil).
Easy does not mean obvious, though my students often conflate the two. Easy means solvable in a way that students can feel comfortable that they are getting the right answer and will continue to get right answers if they follow the rules and the logic.
My approach in my courses is to consistently go back to the model, to our list of assumptions, and to our first principles. The essential models, assumptions, or first principles vary across disciplines, but I see it as my job to help students find the essentials in my field and apply them in a way that eliminates the mystery and reduces the difficulty.
Most of our students are very naïve when they enter our classes or are exposed to our disciplines for the first time. They seldom have a structure on which to hang the concepts we want them to learn. Early on, all ideas seem equally important, and most cannot distinguish the important from the secondary. As I see it, my job is to provide the structure that helps students think like economists. As students develop the correct structure, the topic ceases to be mysterious, and becomes easy.
I will ask my son at the end of the next term if those mathematical topics are still hard, or whether they have become easy. My guess is that, as he has developed the structures and strategies used by mathematicians, he will conclude that they have become easy (or at least easier).
Kelly, K., & Branch, S. (2003). Agony of the feet: Fashion says if the shoe fits, what’s the point? Wall Street Journal. Retrieved from https://www.wsj.com/articles/SB106028946810231700
US Energy Information Administration. (n.d.). International. EIA. Retrieved from http://www.eia.gov/beta/international/
Paul Woodburne is an associate professor of Economics at Clarion University. He challenges his students to think critically and deeply about economic issues. He has written an intermediate money and banking text that he uses in his classes. About six years ago two freshmen in the dorms heard horror stories about how difficult his classes were and got together for mutual support and study. They found they liked each other and, having graduated and gotten good jobs, are now happily married.