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Utility Analysis
Maximizing Constrained Marital Choices
Hugh H. Macaulay,
Many students have difficulty with constrained maximization as an objective whenever people make choices. I present my students with a story that deals with untraditional prices and budget constraints. I try to look morose as I begin this tale, as if I had just come out on the losing end of a spat with my wife.
"When I was young, I thought _____ (famous actress from my period) was just the epitome of lovely womanhood. In my heart, I lusted for her. My wife‑to‑be thought _____ (movie star of period) was everything a man could be. Why did I settle on her? More strangely, why did she settle for me? Well, I had looked around and discovered that, given my physical and mental attributes and general prospects, the best I could do was marry _____ (spouse's name). I just couldn't do better. But why did she marry me, knowing the way I viewed _____ (actress's name)? She had looked around a bit too, and decided that in spite of my many flaws, I was the best she could reasonably expect to catch‑‑_____ (movie star's name) had other choices available that he saw as preferable to my spouse. We both did the best we could."
Naturally, you can vary this language and embroider it with your own asides, etc., but it always captures students' attention, and helps them to see that economic choices and maximizing behavior extend far beyond the realm of standard choices about consumer goods, production decisions, and other examples we use in class. Further, the example shows that economists seek, and we usually get, the best that is attainable; perfection is not likely our lot.
Constrained Maximum in Principles of Economics
We live in a world of constraints. In fact constraints are so commonplace they go generally unnoticed. Gravity is a constraint that bounds us to the earth, though we pay no conscious attention to it. Money (or income) is also a constraint that bounds us to a "level" of living. We usually assert that given her income and given commodity prices, the consumer wishes to economize or maximize her utility by consuming the largest possible "bundle" of goods. Even after we plug in numbers for concreteness and draw a picture for further "clarity"--the abstraction of this concept of constraint does not go away. To add a measure of palpability, we offer the following analogy: suppose you live in a house with two rooms connected by a common wall with a door. One of the rooms (room A) has a fireplace in the center of the floor; the other room (room B) does not. On a fiercely cold winter day, room A will be hot and room B cold (see figure 21-1).
Figure 21-1
Someone standing at the east wall in room B would find that by moving toward the west wall of the room, she will feel increasingly warmer. If the door is locked and she has misplaced the key, then the constraint is "binding". The best she can do is stand next to the west wall of room B. However, if the door is open, the constraint is not binding and all the poor girl has to do is walk through the door and get comfortably close to the fireplace. Thus, there are two possible maxima.
Personal Computers: Economics and Rational Decisions
Eric K. Steger,
In my introductory economics classes, I typically use the decision regarding the purchase of a personal computer to help students use economic analysis in decision making. I first ask them to consider what needs they have. Do they need to compile a shopping list, an appointment calendar or a diary? If so, pen and paper for less then $5 can do the job. If their needs include school papers, documents of 8 pages or less and personal letters, then an electronic typewriter for $150‑$500 can do the job. Only when it is necessary to do college theses, lengthy documents, documents with graphics, serious creative writing and mail/merge for mailings do they need to spend $600‑$1500 for IBM PC/XT compatibles.
Consumer Reports, March 1988, was valuable for this idea.
Charles Diamond, American University n Cairo
Students need to realize that the principle of maximizing behavior does not assume that consumers' behavior is purposive or that they are consciously aware of their utility functions; this principle lends insights into describing consumer behavior, but it is not the behavior itself. Astronomers similarly describe the orbital paths of planets around the sun; presumably the planets are unaware of their behavior. On the other hand, some students may say that while the principle of maximizing behavior is a theoretical concept (borrowed from math) that does not correspond to real‑world behavior. I counter with an example of their decision‑making process in choosing their class schedules, and begin by writing a version of the following table on the chalkboard.
CLASSES ECON 200 ECON 221 ECON 245
Preferences Weight rank/score rank/score rank/score
a. no papers 10 10/100 7/70 0/0
b. 10:00‑2:00 8 6/48 10/80 8/64
c. lively instructor 10 2/20 10/100 5/50
d. small classes 5 4/20 6/30 10/50
e. discretion
TOTAL WEIGHTED SCORE 188 280 164
Students are asked for a list of alternative classes they could have taken along with a list of their preferences or wants associated with classes and a weighting on a 1‑10 scale (10 highest) as to its importance. The class with the highest score is signed up. This emphasizes that a choice or a decision made in the constrained maximizing framework involves trade‑offs between preferences and the alternatives (constraints) at hand whether visibly as above or lightning quick in the mind.
Consumer Equilibrium in Burger King
Homayoun Hajiran,
The following example has helped me to illustrate the concept of consumer equilibrium to my students. I asked them to reflect on their eating habits during their last visit to their favorite fast food restaurant. Having ordered a hamburger, a small order of fries, and a drink, a typical consumer will have a bite or two of the hamburger, then a few fries and perhaps a sip or two of the drink. Why don't they finish each item completely before starting the next?
A higher rate of consumption of an item (e.g., hamburger) results in lower marginal utility of that item. Hence, by switching from consumption of one item to another, they must have been continually trying to maintain their consumer equilibrium status
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MUH = MUF = MUD
PH PF PD
Diminishing Marginal Utility, Fasting, and Sex
Hermilo Jasso, Jr.,
I try to illustrate the principle of diminishing marginal utility
in human terms by proposing the following thought experiment for students. Let's assume that you have been fasting for five days, perhaps you want to lose weight or because of spiritual reasons. You have gone five days without food and after the fifth day you to the nearest McDonald's and order a Big Mac. How will that first Big Mac taste?
(I give room for discussion)
Well, as you can see the first hamburger will taste like heaven. Let's say that you are still hungry, so you order a second hamburger. How will the second hamburger taste? Good, but not as good as the first one. Let's say we can measure the satisfaction on a scale of 1-10. We will call this utility. The first one will taste like a 10. The second one like an 9. So a picture will begin to develop. The third one like a 4, and so on. As you can see the principle of the diminishing margin utility begins to take effect. How will the fifth hamburger taste? Well, you will probably get a stomach ache or even diarrhea. (I give time for the class to laugh then I continue) This applies to the consumption of every product. Even to the more desirable product. On this planet it has to be sex and as you can see the same principle applies.
Eric K. Steger,
I often use myself as an example to illustrate diminishing marginal returns. I ask my students if they have ever eaten at a restaurant that serves "all you can eat" meals? Most have. I ask them if they ever behave irrationally as I do when I am determined to consume a second or third plate of food? I explain that my marginal utility received for the second plate of food is less than the first but I continue eating up to the point where the marginal utility per plate of food consumed is zero. I do this because the costs of the meal are fixed and therefore the cost per plate consumed falls. I explain that an "all you can eat" offer is a "personal challenge" to me. Occasionally, some students point out that the long run potential costs of this behavior involve obesity, etc.
Ralph T. Byrns
Some students erroneously get the idea that economists assume that marginal returns continuously diminish. To point out that returns may initially increase, but eventually diminish, ask why it some-times takes a few jokes before a stand-up comic has an audience warmed up. (Returns may initially increase.) Point out that, after several jokes, only increasingly funny jokes will rock a crowd with belly laughs. (Diminishing returns) Finally, point out that people's embarrassed titters upon hearing a familiar joke shows that activities that initially yield positive returns may eventually yield only negative marginal returns. Few people find a joke amusing after hearing it the second or third time.
How the Marginal Utility for Candy Falls
By Sherry Wetchler, Economic Research Services
The concept of diminishing marginal utility can be initially
difficult for students to grasp. First,
begin by drawing a marginal utility curve on the blackboard like the one
below. Explain that a consumer has
diminishing marginal utility from a good if each extra unit of the good
consumed adds less to total utility than the unit before. Next, ask the class if anyone likes candy
bars. Choose a student to come up to the
front of the classroom. Then, give the
student a candy bar to eat. After the
student finishes, ask the student to tell the class how much satisfaction
he/she received and how much he/she would pay for the good. Continue this procedure until the student
refuses to eat one more (I have found that this usually occurs after about
three candy bars) and then, summarize.
O. Henry Hoversten,
Time and place utilities can be demonstrated by exploring possible answers to such questions as:
a. Why is today's metropolitan newspaper "worth" the price charged at the newsstand and tomorrow it may have zero or even a negative value?
b. Why is a new wheelbarrow "worth" $25 at the hardware store on Saturday AM, but only a small fraction of $25 as soon as you bring it home and put it in your garage?
c. Why may a football ticket to the big game be "worth" several times what you paid for it a week or two before the game and only a fraction of what you paid for it minutes before the game, and worthless a few minutes into the game?
Value in Use vs. Value in Exchange
Eric K. Steger,
To illustrate the different concepts of value I ask students
what items would they try to get out of their homes if there was a fire, assuming
that people are safe and they have 20 seconds to decide. I give them 20 seconds
and then take up their papers. Typical answers include books, stereos, TVs,
etc. Some students indicate that they will rescue pictures. I point out that
the pictures have little value, if any, in exchange but substantial value in
use. Televisions, stereos, etc. have some value in exchange and use but can be
replaced rather easily whereas pictures are usually not replaceable.
Steven E. Plaut,
Most students are disturbed by the rationality assumption. I make it appealing by using my large red cat, Tuli, as an example. Tuli is a rational consumer who:
a. Is capable of choosing among different foods.
b. Experiences diminishing marginal utility from food.
c. Has a transitive preference ordering (Tuna is preferred to milk is preferred to dry food).
POINT: Rationality is so loosely defined that even a cat fits. NOTE: Animals obey many other "laws" of consumer behavior, including risk aversion and the ability to choose under conditions of uncertainty.
Making Students Introspective About Consumption
Ralph T. Byrns
Challenge students about whether their consumption patterns conform to the principle of equal marginal utility per dollar. Try to get students thinking about this concept, and some will probably later report to you that they find themselves thinking about whether they are making optimal purchases as they go down supermarket aisles.
Income and Substitution Effects at the Center
Joe Walker,
Students need relevant and exaggerated examples to make some abstract economic concepts hit home. The following example does this for income and substitution effects:
You've been going to the center every day to eat lunch‑‑ usually a grilled cheese sandwich ($1.00) and a cola ($.50). One day you go in, though, and the grilled cheese now costs $1,000! Just as you begin to despair, your long lost rich uncle (or aunt) appears and, feeling sorry for you, gives you $1,000 so you can buy your favorite sandwich. Do you buy the sandwich? Why not! You can afford it now, can't you? What has happened is that your real (apparent) income has been held constant and only relative prices have changed. In accordance with the Slutsky substitution effect, you now go for some other good (like hot dogs) and substitute away from the relatively higher priced grilled cheese.
Love as Complementary Neuroses
Gary Galles, Pepperdine University
As a brief, humorous illustration of complements, I have had some success with the following (taken from a psychologist friend):
I ask my students what type of person they are likely to "fall in love" with (be attracted to), and try to summarize their disparate answers by saying that they will tend to "fall in love" with someone who is complementary (in both senses of the term) to the way they are. What does this mean for someone who is neurotic, though?
For example, I ask my class what type of woman a "macho man" would tend to fall in love with. I let them respond until they see (which won't take long) that he would tend to fall for a woman with a complementary (matching) neurosis‑‑one who tends to be overly dependent. I then ask about a woman who tends to be domineering‑‑who will she go for? She will tend to match up with a man who we might call overmothered (i.e., one who can be dominated), since that is a complementary neurosis to a domineering woman. In other words, "opposites attract" may be a cliché about complementary neurosis. In some cases, however, having the same neurosis can be complementary. For example, neat freaks would tend to be attracted to others of a similar streak rather than slobs (which is partly why Oscar Madison and Felix Unger could be called The Odd Couple, and why such mismatches are a constant scenario for situation comedies). Examples of what you would not tend to see would be a "macho" man with a domineering woman or two very shy and submissive types (how would they ever meet and raise the courage to start a relationship?).
This analysis also has implications for what happens when one partner acquires a new neurosis or overcomes an old one. If the respective neuroses become less complementary, disharmony in the relationship can arise and the change can be perceived as falling out of love. This may be why at the end of a relationship we tend to hear something like "I changed, but he (or she) didn't," with the implication that the changes made (or not made) were (or would have been) an improvement. Of course, we must note that the change could have been the beginning rather than the end of a neurosis. We could also ask about the chances for a neurotic couple whose neuroses don't exactly match, but she's sure she can change him to a more comfortable (for her) set of neuroses. She will always be trying to change him, and he will always resist ‑‑ discord will result and both will wonder why they aren't accepted for what they are (she, a meddler; he, comfortable with his own neuroses).
Is Public Transportation an Inferior Good?
Mark Zupan,
As an example of inferior goods, ask your students how many of them now use public transportation. After a show of hands, ask how many expect to use public transportation to get to their 25th class reunion (when they will presumably be substantially richer).
Gary Galles, Pepperdine University
I have found the following example very useful in: a) making students use and remember the concepts of normal and inferior goods; b) showing that the same good can be normal in some income ranges and inferior in others; and c) providing an example of a good that is at first inferior, and then normal, as income rises (all the other examples of this I have heard are for goods that are first normal and then inferior as income rises).
I have students consider a dog lover who especially likes large dogs, but who is very poor. In fact, he is so poor that all he can afford to eat himself is one can of dog food a day. Several sounds of disgust emanate from the class at this point, to which I reply that some people, even in the United States, are in this situation. I then go on to make a joke like "Besides, what's wrong with that? Dog food may be better for you than what you do choose to eat‑‑at least it gives you a glossy coat and a healthy, wet nose, and if you're lucky, you might even get a "Hi‑Pro" glow. Our dog lover obviously cannot afford to exercise his preference for dogs, because the opportunity cost of feeding one would be extremely high: food for the dog is food that he would have eaten himself; instead he goes hungry.
I ask the students what will happen to our dog lover's demand for dog food as his income rises from its present low level. While at the very first he may buy more dog food when he still can't afford much in the way of higher quality food (it would be a normal good in this income range), he will quickly substitute out of eating dog food and into other, preferred types of food when his income allows it [it would be an inferior good in this range ‑‑ the range where easing the income constraint allows the purchase of preferred, higher quality goods instead of the less‑preferred, lower quality good, because the value of what is given up is less when more income allows more of your preferences to be satisfied (i.e., the marginal value of a dollar given up to buy the preferred quality item is lower, the higher is income)]. Once his income rises enough, however, he can begin to indulge his preferences for dogs. Over the range of incomes in which he would get more (or bigger) dogs as income rises, his demand for dog food would again rise, making it a normal good in that income range. If his income reaches a high enough level, he may even begin to replace the dog food with more expensive alternatives (such as Higgins, on Magnum, P.I., who feeds his "lads" steak), making dog food inferior in this income range as well.
I summarize this story by saying that a normal good is one you would like more of if you had additional income, but an inferior good is one you would like less of if you had additional income to buy the higher quality goods you really want.
Complementarity and Incompatible Goods
Ralph T. Byrns
Elaborate the idea that goods embody utility relevant attributes that determine price, cross, and income elasticities of demand, how rapidly utility diminishes, whether goods are substitutes or complements, etc. For example, candy has the positive attributes that it tastes good, provides quick energy, etc. It has the negative attributes that its sugar contributes to tooth decay, obesity, etc. The search for new cooking recipes is essentially the search for complementarities among different types of food. Combinations of attributes of certain goods makes the thought of fudge and sardine casseroles repulsive, while hot fudge, bananas, and ice cream sounds like a mouth‑watering treat. Similarly, most people avoid wearing stripes with plaids, tennis shoes with tuxedos, etc.
Ali T. Akarca, University of Illinois at Chicago
The following example helps in explaining the idea of Giffen goods.
Suppose that you want to make a 10‑quart pillow as a gift for a friend. You would really like it to be 100% down‑filled, but can only spare $40 for this pillow and down costs $12 per quart. Polyester is an alternative filling costing only $2 per quart. Consequently, you decide to make your pillow 20% down, and 80% polyester. What would happen if the price of polyester rose to $4 per quart? You would have to make the pillow 100% polyester‑filled. Its price, of course, need not rise to $4. Any increase in the price of polyester filling would cause you to buy more of it, making it a Giffen good for you.
After giving this example, I say to the students, suppose it is not a pillow but your stomach that you are filling, and invite them to come up with other examples of Giffen goods.
How to Illustrate the Case of a Giffen Good
Tran Huu Dung,
Most students find it very frustrating to illustrate the case of a Giffen good using indifference curves and budget lines because rarely does a diagram come out right the first time.
Suppose that there are two goods, X and Y, and we want to show that X is a Giffen good, i.e., a decrease in its price would cause its consumption to fall. Here is the trick:
1. Do not begin by drawing the indifference curves. Instead, after drawing the two perpendicular axis the next step is to draw the two budget lines with a common Y intercept. Hint: Do not make these budget lines too steep.
2. Now
draw the two indifference curves tangential to the two budget lines (I1
and I2 in Figure 21-3), making sure that (a)
the tangency on the lower budget line (point E) lies very close to the
horizontal axis, and (b) the tangency on the higher budget line (E') lies to
the left of E.
Voila, the diagram illustrates the case of a Giffen good.
Figure 21‑3
For advanced students, the reason why this would work can be given. Recall the Slutsky equation
ûQx/ûPx = (ûQ'x/ûPx) ‑ Qx (ûQx/ûM)
where the income effect (which is responsible for the perverse effect) is proportional to the budget share of the good. By locating E very close to the horizontal axis, we make this share large and, hence, increase the likelihood that the good would come out Giffen.
Distinguishing Normal, Inferior, And Giffen Goods
Alan Gin,
Understanding how the substitution and income effects differ among normal, inferior, and Giffen goods is a problem for intermediate micro students. Figure 21‑4 aids in resolving this problem by using arrows of different lengths to indicate the direction and relative magnitude of each effect for each type of good.