Chapter
Five. 110
Elasticity. 110
Chapter
Five
Elasticity
A Rubber
Band Analogy
Gary M. Galles, Pepperdine
University
I have found that the simplest way to help students remember
the concept of elasticity of supply is to use a rubber band analogy. I have
them define P as the pressure with which you pull on the rubber band and Q as
the length of the rubber band (length is, after all, a quantity), and
elasticity of supply as the relative responsiveness of the length of the rubber
band to changes in the pressure applied.
I demonstrate
in class a few points. First, as Pressure (P) increases, length (Q) increases,
as it should on a supply curve. Second, for equal percentage increases in
pressure (%DP) I get smaller percentage increases in length (%DQ)‑‑the
rubber band's elasticity (%DQ / %DP) is falling. I tie this to the fact that
for a typically shaped set of cost schedules, marginal cost increases at an
increasing rate in the relevant range in the short run: since marginal cost is
a competitive firm's short run supply curve, the standard case is one of
increasing elasticity of supply by a competitive firm. Third, I note that there
is a limit to the length that the rubber band can stretch, and tie that into
the possibility of a short run physical capacity constraint at some large
output, at which point supply would be perfectly inelastic.
Cocaine
and the Elasticity of Demand
Michael Kuehlwein, Pomona
College
To illustrate the concept of
the elasticity of demand and its implications for prices and output, I like to
discuss the world market for cocaine. In
the late 1980s, the Drug Enforcement Administration (DEA) estimated world
cocaine production was roughly 400 tons a year.
Then in 1989, authorities seized 160 tons of cocaine, or 40% of the
assumed world supply, and cocaine prices did not rise significantly. I ask my class what this seems to imply about
the demand curve for cocaine. Students
are usually able to determine it suggests the demand curve is close to
horizontal.
Figure 5-1
Then we
discuss what that implies about the demand for cocaine: that it is extremely sensitive to the price
of cocaine (very price elastic). That
usually strikes students as implausible, since cocaine addicts are probably
willing to spend almost any amount to satisfy their habit. This leads to a revision of the shape of our
demand curve to a more vertical inelastic one.
But then that seems inconsistent with the events of 1989:
Figure 5-2
Finally, we
usually conclude that these seizures probably did not have a significant effect
on the supply of cocaine. Perhaps
cocaine production was much higher than previously estimated, perhaps there
were significant inventories, or perhaps the seizures merely offset increases
in cocaine production which left supply fairly constant. I end the exercise by telling the class that
after the events of 1989, the DEA significantly boosted its estimates of world
cocaine production and consumption, consistent with our analysis.
The
Elasticity of the Demand for Murder
Mark Zupan, University of Rochester
As an application of elasticity, tell your students that
some applications are more lively and interesting than others. Take the case of
the demand curve for murder. There are some philosophers who believe that it's
completely an irrational act of passion and that murder would be committed no
matter what the expected price faced by a prospective murder. Ask your students
to graph the demand curve for murder if such philosophers are right. (This
demand curve is perfectly inelastic, with quantities of murders on the
horizontal axis and the price (punishment?) on the vertical axis.) Ask,
"What is the elasticity of demand for murder in this case? (Answer: zero.)
[As a side
note also ask them what the equilibrium price of murder equals‑‑i.e.
(cost of punishment x probability of being arrested) x (probability of being
convicted)]
There are other philosophers who believe that murderers
are rational and respond to the price of committing such crimes. Ask your
students to graph the demand curve for murder if this alternative school of
thought is right. Have them suppose that 30,000 murders are committed
nationally per year if the average sentence served is 30 years, but the murder
rate rises to 50,000 annually if the average prison term is only 12 years.
Assume that 60% of murderers are caught in either case. Ask your students to
calculate and name the elasticity for these numbers. (Answer: this sentence
elasticity of demand for murder is ‑7/12.) Now have them compute murder
elasticities based on varying the probability of getting caught and being
convicted, or varying the probability of execution.
Increasing
the Elasticity of Demand for Having Babies
Gary Galles, Pepperdine
University
The
following true example has been an effective way to reinforce my students'
understanding of demand elasticity. The hospital where my youngest child was
born would reduce the price it charged insured couples for delivering babies:
if you furnished proof of insurance 30 days in advance of the due date and
committed yourself to delivering your baby there, the hospital would accept the
typical insurance payment of 80 percent as payment in full for the services
rendered (i.e., they would bill the insurance company, which paid 80 percent,
then forgive the remaining 20 percent owed by the parents). I use this as an
elasticity example in class. I show students how reducing their prices by 20
percent in the above manner would increase the number of births at the hospital
far more than a 20 percent cut in the total charge for delivery‑‑that
is, that the demand curve facing the hospital for delivering babies was far
more elastic under their policy than an across‑the‑board 20 percent
price reduction. I demonstrate that the reason for this is that an across‑
the‑board 20 percent cut in the hospital's price corresponds to a 20
percent price reduction to parents (who are still liable for 20 percent of 80
percent of the original price), while a 20 percent price reduction under their
policy corresponds to a 100 percent price cut to the parents, using a numerical
example like the following:
Customary Fee: $2000, 80% Insurance: $1600,
Parents' Liability: $400
20%
Fee Reduction: $1600, 80% of $1600
Insurance: $1280, Parents' Liability: $320
20%
Fee Reduction: $1600, 80% of $2000
Insurance: $1600, Parents' Liability: $0
This pricing policy
is a way for the hospital to generate a demand schedule with approximately five
times the elasticity of the parents' demand schedule (i.e., for a straight line
demand curve, a 100 percent reduction in price to the patient would increase
the quantity response to five times what it would be for a 20 percent reduction
in price to the patient), making it more profitable to lower prices in their
particular manner than across the board.
Elasticity
of Demand and Movie Theaters
James A. Kurre, The Pennsylvania State University—Erie
To motivate and enliven a discussion of price elasticity of
demand, I introduce the concept by posing the following problem:
"You
have just inherited a movie theater from a long‑lost uncle. When you
visit the theater, your uncle's manager enthusiastically greets you and says
that she has a good idea for increasing business. Specifically, she has noticed
that there are typically a large number of unfilled seats at each showing, and
she suggests that you cut the price of a ticket from the customary $4.50 to
$2.00. She cites the Law of Demand as support, stating that you'll get more
customers as a result. Does she have a good idea or not?"
This
problem leads naturally to a discussion of how many more tickets can be sold at
the lower price. Will the quantity demanded rise by a lot or a little? A good
way to introduce the necessity of using relative (percentage) measures of the
change in quantity and price is to tell them that 50 more tickets can be sold,
and then ask them if that is "a lot" or "a little."
Typically, someone will point out that the answer depends on the number of
tickets that you normally sell, and you can specify two cases‑‑one
in which 25 is the normal amount, and one in which 300 is the normal amount.
The idea of using percentage changes springs naturally from this. The next step
is to discuss the effect on total revenue generated by the different
price/quantity combinations, which leads naturally to a discussion of the
relationship between elasticity and total revenue.
After we've
discussed all the relevant issues, I show a list of actual elasticity estimates
for various goods, and discuss the determinants of elasticity in the process. I
then go back to the original problem and ask them to guesstimate the elasticity
of demand for motion pictures. I then show them the actual estimates, which are
‑.87 for the short‑run elasticity, and ‑3.7 for the long run.
This leads to discussion of why elasticity varies with the time period
considered. It is also interesting to point out that a strategy of "Let's
try the lower price for a couple of weeks and see what happens" will yield
a wrong answer!
In the course
of this example, students will frequently point out that more popcorn, candy,
and pop will be sold if you have more customers, and it is possible to discuss
complementary goods as a result. You can also discuss the cost side, since some
aspects of this business would have a near‑zero marginal cost. For
example, regardless of the number of people in the theater, the same amount of
labor is required to project the film.
Elasticity
and Membership Dues
Roger L. Adkins, Marshall
University
Most students are or have
been a member of an organization in which dues payments constitute a
requirement of membership. These students recognize that a dues increase, other
things equal, will result in a drop in membership. Many students recall that
some club discussions have centered on the extent of the decline in membership
given an increase in dues of X dollars. Generally, one group of students in
these sessions argues that a large number of members may drop out of the
organization given the increase in dues; others indicate that only a few at
best would do so. Even students who have never belonged to clubs seem to find
intuitive appeal in this example of elastic and inelastic demand.
Price
Elasticity of Demand and Higher Education Revenues
Eric Steger, East
Central University
At times, some students question the relevance of price
elasticity of demand. To drive home its
relevance I use the following table.
Tuition Number Semester Total
Price/ of Hours Semester Total
Hour Students Student Hours Revenue
$25 4000 15 60,000 60,000 * 25 = $1,500,000
$30 3900 15 58,500 58,500 * 30 = $1,755,000
Elasticity =
(1500/59,250)/(5/27.5) = .139
Once
the students see that Total University Revenue rises when tuition price rises,
the "relevance" of price elasticity is made clearer.
Price
Elasticity of Demand
William V. Williams, Hamline
University
Many students are best able to
see the applicability of economic analysis when assigned problems are related
to current events. The news media (unconsciously) cooperate with educational
purposes by frequently describing agricultural or other disasters in certain
product markets in sufficient detail that they provide fodder for student
exercise sets. I clip these articles, underline the parts germane for student
analysis, and devise problems for classroom distribution.
Figure
5-3
For example, an article from the
Associated Press described a devastating freeze in which a 30 percent loss of
the Florida orange crop was described as reducing the yield of frozen orange
juice concentrate by 65 million gallons.
The wholesale price of a dozen six-ounce cans of concentrate immediately
rose from $2.60 to $3.55, and experts forecasted a further rise to $4.25. I xeroxed the article with the assignment,
which was:
From this AP article, we can locate two points on the
implied demand curve.
If 30 percent of the
pre-freeze crop is 65 mil. gals.,
(crop x .30 = 65)
then the pre-freeze crop is
approximately 217 mil. gals. (65 / .30 =
217)
Since 1 doz. 6-ounce cans = 72
ounces, and 1 gal. = 128 ounces,
then 1 doz.6-ounce cans =
.5625 gals. (72 / 128
=
.5625)
Therefore, assuming a vertical
supply curve (in the very short run) --
the pre-freeze supply is about
386 mil. dozen 6-oz. cans (217 / .5625
= 386)
the post-freeze supply is 30
percent less, or 270 mil. doz. cans.
Before the freeze, at a price
of $2.60 a supply of 386 was sold.
Afterwards, when the price is
expected to be $4.25, supply will be 270.
This gives two points where the two supply curves intersect
the demand curve.
Assignment:
Compute the price elasticity of demand in the range between these
two points.
Will the wholesalers as a
group be worse off after the freeze?
Hint:
Compute total revenue before and after the freeze.)
Is this price rise socially desirable in efficiency and
equity terms? Explain.
Should government legislate a
juice price ceiling to prevent "price gouging"?
Solution:
Price elasticity e
= [-65/((152+217)/2)] /
[1.65/(4.25+2.60)/2)] = -.73
Total revenue after the
freeze = 4.25 x 270 mil. = $1147.5 million
Total revenue before the
freeze = 2.60 x 386 mil. = $1003.6 million
approximate
net gain = $ 144 million
From an efficiency standpoint,
the price rise is socially desirable because
a.) the reduced juice supply will be rationed
out to those who want it badly enough (and are able) to pay the higher price.
b.) the higher price will attract a supply of
oranges from producers in other states and countries, which will keep the price
from rising still further.
From an equity perspective, the
price rise is not necessarily desirable.
a.) The monetary gains and losses fall
capriciously.
b.) Those least able to afford the high price
(the poor) will be excluded from juice consumption. Of course, the real problem that needs to be
addressed is their poverty, not the "just price" of orange juice.
Government should not legislate a price ceiling.
To do so would cause inefficiency by distorting the
allocation of resources.
The inefficiency will result in lower overall real income,
making the poor even worse off.
Computing
Point Elasticity
James M. Rock, University
Of Utah
Point elasticity of demand or supply sometimes seems
impossible for students to calculate given its typical formula: DQ/Q /DP/P.
Rewritten as DP/DQ/P/Q, however, it is much easier to calculate point
elasticity from a graph or table. The numerator of the ratio is the slope of a
ray to the demand (supply) curve or price divided by quantity on the same row
of a table. The denominator of the ratio is the slope of a tangent line to the
demand (supply) curve or approximately the difference in price divided by the
difference in quantity of the row above and the row below the row the point is
at. If demand and supply curves are straight lines, the
"approximately" disappears, as differences are constant throughout
the table. This equation is also helpful in explaining that the slope of the
tangent line is only the denominator of the ratio of slopes that makes up
elasticity. The exercises for students that follow use this elasticity
equation. (Note: students may know that the slope of the ray to a total curve
is its average and the slope of a tangent line to it is its marginal.
Consequently, given that economists typically put price on the vertical axis
and quantity on the horizontal axis, the total curve is a demand‑price
(supply‑price) curve, not a demand‑quantity or supply‑quantity
curve.)
Point
Elasticity Exercises: Assume that prices and quantities are measured in
equivalent units. (Hint: Is the ray or the tangent line absolutely steeper?)
a: Use geometry to determine which of the
three demand curves in Panel A is elastic?‑‑unitary elastic?‑‑inelastic?
With these easy
numbers you can point out how the relative changes of 1 unit in quantity and
price change along each axis, so students get a general feel for how elasticity
is measured. Clearly, revenue is maximized at a price of $4 million per
customer. You can show how revenue changes at different prices in the
relatively elastic area and in the relatively inelastic area of the demand
curve. The concept of marginal revenue can be introduced. The concept that even
the purest monopoly market we can imagine is going to be subject to market
demand can be introduced. We can introduce costs of production (advertising,
hiring guards, putting up a fence, etc.) and show how this would affect our
optimal "level of production." The example is easily recalled by students
and can frequently be referred to throughout the semester as these related
topics are introduced for more complete discussion and analysis.
Is the
Demand for a Spouse Perfectly Inelastic?
Curtis D. Scribner, Pittsburg
State University
Try to interpret the graph in Figure 5‑8 before
reading the explanation. Recall that for an item to exhibit perfect
inelasticity of demand, the quantity demand should not change when price
changes. The correct interpretation: I wouldn't take a million dollars for my
wife, but I wouldn't give a penny for another.
a. In the absence
of a law making polygamy illegal, would the demand curve be perfectly
inelastic?
b. Would you agree that quantity demanded is
one because one is a necessity while two is a luxury?
c. Does the absence
of marginal buyers at $.01 lead you to suspect that there is a hidden price?
Figure 5‑8
Elasticity,
Pimples, and Obesity
Steven T. Call, Metropolitan
State College‑Denver
The elasticity of pimples with respect to eating chocolate
candy is a measurement that most young college students can identify with.
"Eat a candy bar and how many pimples do you get?" If you get a lot
of pimples, the relationship is elastic. Otherwise it is inelastic. Extend the
example. Some students may have a clear complexion but a sluggish metabolism.
Although their elasticity of pimples with respect to chocolate may be low,
their elasticity of weight gained with respect to chocolate consumption may be
rather high. A two minute discussion along these lines helps students relax and
assimilate the nontrivial elasticities.
Umbrellas
and Rainfall
Pauline Fox, Southeast
Missouri State University
I introduce elasticity as a measure of the strength or
intensity of a causal relationship. Instead of starting with price elasticity of
demand, I start with rainfall elasticity. The amount of rainfall per week is an
important factor in the quantity of umbrellas purchased:
a. The concept: Elasticity measures the
strength or intensity of a causal relationship. A given change in rainfall
causes a change in purchases of umbrellas. By what proportion?
b. The point formula: % change in umbrella
sales / % change in rainfall
c. The arc formula:
Q1 -
Q0 P1
- P0
‑‑‑‑‑ ‑‑‑‑‑
Q1 +
Q0 P1
+ P0
d. What does the answer mean: I use the sentence
"A 1% change in (rainfall) will result in an X % change in (umbrella
sales)."
The next step
is to examine price elasticity of demand, using the same steps. From there, it
is easy to introduce income elasticity of demand, cross elasticity of demand, elasticity
of supply. In addition, I try to introduce some elasticity concepts which do
not have to do with quantities bought or sold. For example, I usually discuss
an elasticity to measure the intensity of the relationship between study time
and grade point average.
Linear
Demand and Elasticity
Hugh G. Evans, Jr., Elizabethtown
College
All
economics professors are aware of the importance of making sure the student
differentiates between elasticity and slope with regard to linear demand
functions. Not only do we point out that elasticity can vary from one point to
another on a given function, but we equally stress that for some commodities
elasticity can change dramatically over a very narrow quantity range. In order
to illustrate this point I use the following example.
I ask the
class to try and guess the commodity I will describe in terms of the elasticity
characteristics it might possess. These characteristics are as follows: (1)
over a very small quantity range the item could be close to perfectly inelastic;
(2) it then radically changes to become very elastic in nature, (3) and
finally, it can end up exhibiting a negative price relationship which I point
out is rather unusual. At this point the students are permitted to guess the
item and discussion can proceed based on the suggested answers as time allows.
The answer is
WATER. A possible explanation is as follows. Water can be a life sustaining
commodity (necessity) which would carry a very high elasticity coefficient, but
only over a rather small quantity range. Once a small amount has been consumed,
water being abundant, it then might have a low elasticity measure. It might be
noted to students that it is one of the few items which we sometimes expend
large quantities of in order to consume a small amount. For example, in the
summertime when we let the water run for a period of time until it becomes cold
enough to drink. Finally, the negative price aspect comes in when you pay
someone to relieve you of a commodity. For example, you pay to have the snow
removed or your basement pumped, etc.
Elasticity
Made Simple
Djehane Hosni, University
of Central Florida
The concept of elasticity is always confusing to the
students at first. It is important to
emphasize the two separate elements embodied in elasticity:
1. Direction of change
2. Size of change in relative terms.
To simplify the presentation I rely on the
use of arrow symbols.
Figure 5-9
This use of
symbols clarified:
1. Relative change by noting the size of the
arrows.
2. Demand and supply elasticity as the same in
terms of size of change, but different in terms of direction of change where
demand is inverse and supply is direct.
3. The common error of confusing change of
direction with change in elasticity.
Demonstrating
the Concept of Elasticity
Timothy E. Sullivan, Towson
State University
Many students find the concept
of elasticity a difficult one to "visualize" and harder still to see
how the notion of elasticity can be applied in practical situations. I first
describe elasticity as simply a measure of responsiveness to a stimulus. Things
that are elastic have a greater "response" to a given stimulus than
do things that are inelastic. To demonstrate this I bring a racket ball and a
squash ball to class and drop them from an identical height onto the front
desk. The racket ball, which is more elastic than the squash ball, of course
bounces much higher and longer than the relatively inelastic squash ball. Not
only is the point of elasticity more intuitively obvious by visually
demonstrating this, but you can then point out that the strategy of playing a
game of racket ball versus playing squash is, in part, dictated by the
properties of the ball. That is, relative elasticity alters the practical
aspects of these two similar, yet different, games.
A further use
of this example is to illustrate that while the squash ball is relatively
inelastic, it is not perfectly inelastic. That is, it does respond somewhat to
the given stimulus. Likewise, the relatively elastic racket ball is not
perfectly elastic because it does respond "through the ceiling" in
response to the given stimulus. The relevant comparison is often is how often
one ball bounces relative to the other ball.
A Mnemonic
Trick for Distinguishing Elastic and Inelastic Demand
Tran Huu Dung, Wright
State University
After
a lecture on the price elasticity of demand, most students can associate
perfectly inelastic and perfectly elastic demand curves with the vertical and
the horizontal lines. However, it is almost certain that very soon thereafter
few students would remember which case corresponds to which shape. Even for
experienced teachers, it could take a split second to recall. The following
mnemonic trick guarantees that they will never forget this concept for the rest
of their lives.
Simply
notice that (1) the word inelastic begins with an "i," which
resembles the vertical shape of the perfectly inelastic demand curve, and (2)
the word "elastic" begins with an "e," whose horizontal
middle bar should bring to mind the horizontal shape of the perfectly elastic
demand curve (see Figure 5‑10).
Figure 5‑10
A
Pythagorean Lesson on Elasticity
Josef M. Broder, University of
Georgia
I
have long been fascinated by Pythagoras' sand‑box proof of his famous
geometric theorem. As described in Jacob Bronowski's Ascent of Man, Pythagoras proved his theorem by placing and
rearranging small squares and triangles in a sand box. The simplicity of his
approach lead me to develop a similar lesson for explaining relationships
between elasticity, marginal revenue, and total revenue.
My Pythagorean lesson consists of a
metal board upon which three graphs are drawn in a vertical sequence. At the
top is a demand schedule, in the center a total revenue schedule, and at the bottom
a marginal revenue schedule. Magnetized color‑coded squares and triangles
are used to show the relationships between elasticity, total revenue, and
marginal revenue.
First, three red rectangles are used to illustrate total
revenue associated with P1 on the uppermost demand graph. Next, these
rectangles are transferred to the center total revenue graph to plot total
revenue associated with P1 and Q1. Returning to the top graph, four green
rectangles are used to illustrate total revenue at P2. These rectangles are
also transferred to the center graph where a total revenue at P2 and Q2 is
plotted. This procedure is then repeated for P3, using three blue rectangles.
As the rectangles are arranged on the board, I instruct students to observe
changes in total revenue associated with price changes toward and away from
unitary elasticity.
Marginal
revenue relationships are shown by placing triangles in a step‑wise
fashion on the center total revenue graph. The height of each triangle
designates the change in total revenue from a change in quantity. Next, these
triangles are moved to the lower marginal revenue graph and a marginal revenue
function which becomes negative at unitary elasticity is plotted. Given the
large price and quantity changes, total revenue squares and marginal revenue
triangles are plotted on the midpoints.
This
elasticity lesson is simple, straight‑forward and requires a minimum of
mathematics. A magnetic board can be viewed upright and works well for large
class presentation. Similar models can be constructed on a flat surface or, if
one were a true Pythagorean, in a sand box.
Figure 5‑11
Figure 5-11A
Explaining Why Relative Demand\Supply
Elasticities Determine the Proportion of a Per Unit Tax that Will be Borne by
Demanders
Mark Zupan, University of Rochester
After explaining to my class why the proportion of any per
unit tax borne by demanders equals Es/(Es + Ed)
and giving a few examples, e.g., Ed = 0 and Es
= infinity, I provide the following analogy:
Two fellows
are walking along in the woods when they spot a grizzly bear coming over the
horizon. Terrified, the two fellows break into a cold sweat and start to run as
quickly as they can, with the bear in hot pursuit. The bear, being a faster
runner, keeps gaining on them.
After
running for awhile, one of the two fellows suddenly stops dead in his tracks
and begins to change out of his loafers and into the running shoes he has been
carrying with him in his backpack.
His
companion can't believe how stupid a move such a shoe change is. The companion
yells, "You must be crazy. Even with running shoes you can't possibly
outrun a bear!"
The fellow
who has stopped to change shoes replies, "I don't need to outrun the
grizzly. I just need to outrun you."
The moral of
the analogy is that if you see a bear in the woods, i.e., if the government is
definitely going to place a tax on a good, it doesn't matter how fast you run
relative to the bear. The only thing that really matters is how fast you run
relative to the other fellow. The slowest, least price‑responsive, most‑pinned‑down
among the market participants, i.e., suppliers and demanders, is the party that
will end up bearing proportionately more of the tax.
The Effect
of Time on Own‑Price Elasticity of Demand
Mark Zupan, University of Rochester
To convince my students that own‑price elasticity of
demand decreases the less time a consumer has to find substitutes, I ask my
class whether they are more likely to be sensitive to the price charged by a
store for a Christmas gift two months before Christmas or two hours before
Christmas Eve.
Holding
All Else Constant When Calculating Elasticities
Mark Zupan, University of Rochester
To
convince my students that correct elasticity measures require that all determinants
of supply and demand, save one, must be held constant, I give them the results
of a survey of household energy consumption in an eastern city of the US.
The survey was conducted over 5 successive weeks. For each week, data collected
included the price of heating oil, the price of natural gas, the average
quantities of heating oil and natural gas bought by each household, and the
average income per household.
Week Oil Price Gas Price Income Oil Q Gas
Q
1 1.10 1.12 200 100 90
2 1.09 1.10 190 90 80
3 1.10 1.12 210 102 108
4 1.09 1.11 190 100 70
5 1.08 1.10 190 100 70
I ask my students to calculate
arc own‑price, income, and cross‑price elasticities of demand.
The
students invariably become stuck at the start of the problem and ask over which
arc the elasticities should be calculated. Most calculate arc elasticities
based on the beginning and ending weeks' data and get screwy answers because
they fail to realize that even though the oil price changes from week 1 to week
5, one cannot use the data from weeks 1 and 5 to calculate oil price elasticity
of demand since the gas price and income also change over that arc.
To help the
students along, I give them the following hint:
Suppose
that you are driving home on the Santa Monica Freeway and that it is one of
your unlucky days. You are driving in the middle lane and there are cars in the
lanes on either side of you. The guy driving the beat‑up pickup on your
right takes out a shotgun and points it at you. Meanwhile, the guy in the low‑rider
on your left pulls out a 44 magnum. Both drivers shoot at you simultaneously
and both hit you. You crash and burn. To what extent would it be correct to
attribute your demise solely to the guy with the shotgun on your right?
As another
hint, I ask my students to imagine that they were the CEO of American Airlines
and that American was the sole provider of air service between Lubbock and Dallas,
Texas. Suppose that, over a two‑year
stretch, you lower fares 50% and watch the quantity of passengers on this city‑pair
route increase by 50%. Over the same two‑year stretch, however, income
levels in the Dallas and Lubbock areas rise by around 100% on account of the
rebound in oil prices. To what extent can you attribute the increase in
passenger levels just to the fact that you lowered fares?
The two
preceding hints encourage the students to realize that they shouldn't use
contaminated elasticity measures, that they need to find data where only one
determinant of demand and supply changes and all other determinants remain
constant, e.g., the data from weeks 2 and 5 if they are trying to calculate the
own‑price elasticity of demand for heating oil.
Stretching
Unrealistic Elasticity Concepts into Reality
Joseph Alexander, Babson
College
For
many economics students understanding how theoretical abstracts may be applied
to the real world can be very frustrating. The graphic explanation of the
elasticity of demand concept is a classic example, especially when the
coefficient of elasticity is infinity or zero. The assumption that at a certain
price, an infinite amount of a commodity would be bought, or that any amount
would be paid for a needed service seems absurd. Nevertheless, it can easily be
shown that perfectly elastic and inelastic demand curves are useful
constructions for explaining extreme cases of demand/price relationships.
Consider
Figure 5‑12, which shows that an infinite amount of gold would be bought
at a fixed price of $35 per ounce. Indeed, for many years the U.S. Treasury was
willing to accept all the gold it was offered at that price. The theoretical
implication is that the demand for gold must be constant and that its supply is
inexhaustible. The only way this can be expressed graphically is by a perfectly
elastic demand curve. But the curve also shows that some lesser, and realistic,
quantity, for example OQ, could be the actual amount taken by the Treasury!
Figure 5‑12
The practical usefulness of the
perfectly inelastic demand curve can be demonstrated similarly. To illustrate,
suppose critically ill Mr. Smith faces imminent death unless he receives both
heart and bone marrow transplants. As shown by the perfectly inelastic demand
curve for medical treatment, he would willingly pay any amount for life‑saving
surgery, even if the price were infinite! Although this scenario is totally
unrealistic, a demand curve for something regardless of price must slope
vertically. But the curve also indicates that the actual price he would have to
pay, say OP, could lie anywhere between 0 and infinity!
These
illustrative interpretations of the extreme cases of elasticity should help
convince students that economic theory and economic reality are indeed
compatible!
Unconventional
Elasticity Measures
Ralph T. Byrns
When
you introduce the concept of elasticity, emphasize its general applicability to
any situation where quantifiable variables are systematically related.
Untraditional examples include:
a. The TV football game elasticity of divorce
rates.
b. The snow elasticity of ski lift ticket sales;
c. The temperature elasticity of lemonade sales;
d. The homerun elasticity of beer sales at a
ballpark.
Then use
such nonstandard examples to illustrate calculations of elasticity
coefficients. Challenge your students to come up with their own examples. This
makes these computations far less of a purely mechanical exercise for students,
and aids them in retaining this concept. In the same vein, show how income
elasticities can be used to predict the changes in demand if income grows or
falls. Ask your students to indicate whether they think the following products
are inferior (ey < 0), normal (0 < ey < 1), or superior (ey >
1) goods.
a. Winnebagoes
b. canned vegetables
c. Nissan 300ZX cars
d. Seeds for home gardens
e. College tuitions
f. compact American cars
g. rice and potatoes
h. Tickets to horse races
i. Vacations to Hawaii
j. Lottery tickets
Now discuss
how cross price elasticities can be used by a firm to predict changes in demand
when the price of some other good is expected to change. Ask your students to
predict whether cross elasticities will be positive (substitutes) or negative
(complements) for the following sets of goods.
a. golf carts and country club dues
b. steak and
potatoes
c. Corvettes
and Mazda RX‑7s
d. heavy
shoes and galoshes
e. shoelaces
and tennis shoes
f. lobster
and crab
g. MacDonald's
and Burger King
h. professors
and textbooks
i. typewriters
and computerized word processors
j. video recorders and cable TV
If you ask students to first specify
sign, and then whether the goods are complements or substitutes, they will
remember these relationships longer. NOTE: Some relationships are not
intuitively obvious (e.g., video recorders and cable TV). This allows you to
make the point that the answer is ultimately empirical.
Notes:
