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Marginalism Steven T. Call, Metropolitan State College of Denver Students must master relationships between averages and marginals. I use this example to focus on this issue: Suppose a woman currently has 3 children, whose names and birth weights are listed below: CHILD BIRTH
WEIGHT (pounds) No. 1 Tom 8 No. 2 Dick 9 No. 3 Harry 10 The average birth weight after three births is 9 pounds. Now suppose the woman bears another child (the "marginal" child) and the birth weight is 400 pounds. Since the "marginal" observation (400 pounds) exceeds the prevailing "average" (9 pounds), it is easy for all to see that the average must rise. If the marginal birth weight is 2 ounces, the average will fall. If the marginal birth weight is exactly 9 pounds, the average is unchanged . . . If marginal > average, average is rising If marginal < average, average is falling If marginal = average, average is stable Extending this example counters a typical student error: "If the marginal falls, the average will be falling." Let the woman bear a fifth baby, weighing 399 pounds. Now the marginal is falling, yet the average is quite obviously still rising. Hence, whether the average rises or falls is not related to whether the marginal rises or falls, but whether the marginal is greater or smaller than the average. When Every Unit is the Marginal
Unit Ralph T. Byrns One concept that many students find difficult is the idea that goods or resources are often fungible, so that every unit is the marginal unit. Examples such as the following can lead students away from thinking that marginal units are uniquely identifiable: 1. If you randomly remove a bucket of water from the ocean, it is the marginal gallon of water. 2. Express outrage that you have too many students and threaten to give an automatic F to the one who drove class enrollment past 35 (or whatever.) If you are a bit of a ham, every student in your class will begin squirming, recognizing that he or she is the culprit. 3. Show a full bag of candy to your class. Ask which piece was the marginal (last?) added, raising the total to 53 (or whatever) morsels in the bag. Distribute the candy, commenting that as each piece is withdrawn, the total has been reduced by one, and so it must have been the marginal piece. When only one piece remains, state that it is now "the last (marginal?) piece". Eat it yourself, asking your class if any of them get mad when someone else takes the last piece of some delicacy. Point out that, in a sense, each piece of candy that anyone ate was the marginal piece. Rewarding Marginal Exam
Improvement Kyoo Hong Kim, Bowling Green State University Students often have difficulty with the relationship between average product and marginal product. One way to help them understand this relationship is to reward them for marginal improvements in their quiz (or exam) scores over the semester. For instance, before professors give the second quizzes, they announce that an award of, say $1 (or in my case, an oriental recipe), will be given to the student with the highest `marginal' grade (improvement). This exposes students to the notion that eligibility for the prize requires their marginal grades to be higher than their average quiz grades. (Later, of course, students who think they are in the running report their performance confidentially to the professor). Repeated computations of marginal performance gradually lead the students to a solid understanding of the relationship between any general marginal and average function. The Relevance of Marginal
Analysis Michael Behr, University of Wisconsin‑Superior Where are the terms, "margin" or "marginal", encountered apart from economics? The margin of a sheet of paper is the area between the writing and the rest of the universe; the marginal student is one who shows prospects of becoming a non-student; the marginal business is one that shows prospects of becoming a nonbusiness, etc. The commonality of all usages is "edge": The edge of the paper, the edge of academic survival; the edge of economic viability. In human affairs, as in the last of these two uses, it is at the edge where the action occurs. It is when we go over the edge that the changes occur that move us from one condition to another. It is these changes that are supremely relevant because our current conditions are consequences of past actions in that they are beyond our control. Our future condition can be determined only by considering any changes that apply to our current condition. And these changes occur with the passage of time. Thus, life itself is lived at the margin of time where decisions are made and actions taken with respect to all of life's elements. Therefore, when you hear "marginal" you should hear "change" and you need only ask what variable is changing. Normally, marginal analysis in economics proceeds in terms of the ratios of changes in one variable relative to another, e.g., DC/DY, DPQ/DQ, etc. William J. Swift, Pace University In micro principles, how do you establish the relationship between the marginal cost, average variable cost, and average total cost curves? I tell my students to consider calculating their grade point averages. Their individual semester averages are the marginal component, their cumulative is the average component. Consider a typical frosh, I say. "He starts with a 2.5, slips to a 2.0 (what happens to his GPA?), then falls in love (they like this) and slips to a 0.4, then works hard because the dean sends him a stern letter and rises to a 0.6 (nervous laughter‑‑too close to home for some), while all the time his "average" is falling even though the marginal was falling, leveled off, and is now rising." If his `cumulative' hits 1.000 and his semester average is 1.0005, what happens? How can his GPA rise?.... they now see it. P.S.: I tell them that to end his (academic) troubles, we'll get our eager beaver married, boosting his GPA to 4.0. Of course, the married students recognize the trade off of one set of problems for another. Focusing on the Appropriate
Margin Gary Galles, Pepperdine University I have used the following example in class as a way to remind students that the first step in solving any real world economic problem is identifying the appropriate margin for decision‑making. Suppose you are walking through Central Park at two in the morning and you have $200 in your wallet. Suppose further that a mugger pulls a knife on you and tells you to give him all your money. How do you respond? Do you say "I'll tell you what: I'll give you $200 if you leave me alone; $150 if you rough me up a little; $100 if you cut me a little; $50 if you put me in the hospital; but nothing if you kill me"? Of course not, because you would be focusing on the wrong margin for decision‑making; you are faced with an all or none decision, not one in which marginal adjustments can be made (i.e., the relevant marginal decision is the all or none decision of how to respond to the mugger‑‑fight or hand over the money. Once that decision is made, marginal ones may follow, like how hard to fight or how much money to try to withhold.) While this example is obvious, it makes an important point: before you can apply your analysis to a particular problem, you must correctly identify the relevant margin. It can also serve as a springboard to a discussion of types of decisions where this is crucial. This would include: a) all or none type decisions (like marriage, divorce, having a first child, declaring war, etc.); b) improper treatment of historical (sunk) costs (like refusing to sell below average cost, historical depreciation, treating average cost as if it were marginal cost, etc.); c) inframarginal external benefits (like justifying more (marginal) spending on health or education because of net external benefits in total rather than at the margin); d) indirect solutions when direct ones are better (such as a gas tax to reduce pollution); e) errors in analyzing the free rider problem (like the argument that if nobody is informed about the political arena, we will get bad government, therefore you individually should become well informed); etc. Roger W. Lizut, New Mexico Highlands University The following is offered as an aid to getting students to think in terms of increments and marginal quantities. Consider two featureless perfect spheres, one the size of the Earth and the other the size of a golf ball. Say that someone has wrapped a piece of string along the entire equator, with no space between the string and the surface, for each ball. Now comes along somebody with a lot of one inch high telephone poles and says that the entire string must be suspended one inch above the surface, and that it must be done for each ball. How much string must be added to the Earth‑sized ball and how much must be added to the golf ball sized one? The "intuitive" answer is that a lot more must be used for the Earth‑sized ball. The key concept is to think in terms of increments, regardless of the "sunk" values already given. It can be easily shown mathematically that the increment required for both balls is the same: Say the Earth‑sized ball radius is R inches and the smaller ball radius is r inches. The initial length of the large ball string is 2 P R inches and the small ball 2 P r inches. Both radii are to be increased by one inch to provide slack for the needed clearance. The new large ball length will be 2 P (R+1) and the new small ball length will be 2 P (r+1). The increment added to the large ball is then 2 P (R+1) ‑ 2 P R which is (2 P R + 2 p) ‑ 2 P R which is 2 P inches. The increment added to the small ball is 2 P (r+1) ‑ 2 P r which is (2 P r + 2 P) ‑ 2 P r which is 2 P inches. Therefore, the increment added to both balls is the same, despite "common sense." Demand Gary Galles, Pepperdine University Students often need help in distinguishing between changes in the quantity of a good demanded along its demand curve as the price changes and changes in the equilibrium price and quantity of a good demanded due to some other factor that shifted the entire curve. I ask my students why happy hour exists. Some student will reply that it occurs during periods of low demand, when regular prices would leave a bar largely empty. I then ask which of the following would increase demand the most: a reduction in the price of a complementary good (snack food?) or a reduction in the price of drinks? The first to respond almost always falls for the "trick" and says that cutting drink prices would increase demand the most. I tell him that this is incorrect, and then solicit explanations from the class as to why. Those who understand will explain (or I will) that a drop in the price of a drink does not alter the relationship between the price and quantity of drinks demanded (i.e., it leaves the demand curve unchanged)‑‑it just moves us to a different point on that relationship‑‑but reducing the price of a complementary good does change the entire demand relationship, causing more drinks to be demanded at each price. Therefore, a reduction in the price of the complementary good raises demand more, because a price reduction will have no effect on the demand for drinks. Which option is a better happy hour policy? A typical first response is that the complement good price cut will raise demand, while an own price reduction won't. I reply that while cutting complement prices boosts demand and a drink price cut doesn't, that doesn't necessarily make it the best decision. The standard answer is it depends, with further questions being: what does it depend on and how does it depend on these things? I show how it depends on demand elasticity, how complementary the two goods are, and the profit margin per drink, while I use graphical or numerical examples to illustrate these points. Then I ask why most bars give away munchies and charge for beer, rather than vice versa, to show how com | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
