Solutions
Step 1: Using markers, drop a vertical line to the
horizontal axis from point B.
Step 2: Technically speaking, the elasticity of demand at point B equals line
segment AB divided by line segment BC, but those results are also proportionally
equal to line segment AE divided by line segment DE.
Step 3: How long is AE? Answer: ____12
- 6 = 6______
Step 4. How long is DE? Answer: _____6
- 0 = 6_____
Step 5. What is AE divided by DE? Answer: ___1 / 1 =
1_____
Step 6. If the number you calculated is “1,” yell out
“Demand is of unitary
elasticity and total revenue is maximized!" If not, ask the instructor for help.
Step 7. Prove that by multiplying the price times the quantity demanded for
each point and by calculating the result called total revenues in the chart
below and by plotting the total revenue for each quantity demanded on the graph
on the board. Ask the instructor for help if necessary, and to check your work.
Price X Quantity Demanded = Total Revenue Dollars
$1.00
0
____$0.00_______
.75 3 ___ __2.25_______
.50
6 ______3.00______
.25 9
______2.25______
.00 12 ______0.00______
Congratulations Chessies! You have solved problem #1 correctly. Pick up your song sheet, join hands and sing the appropriate verse. Then go on to the next problem.
Imagine that point F bisects line segment AB and that F represents the price of a slice of pizza.
Step 1: Using markers, drop a vertical line to the
horizontal axis from point F, connecting it to point L.
Step 2: Technically speaking, the elasticity of demand at point F equals line
segment AF divided by line segment FC, that is, (AF/FC)
but those results are also proportionally equal to line segment AL
divided by line segment LD, that is, (AL/LD).
Step 3: How long is AL? Answer: ____12
- 9 = 3______
Step 4. How long is LD? Answer: _____9
- 0 = 9_____
Step 5. What is AL divided by AD? Answer: ___3 / 9 =
1/3_______
Step 6. If the number you calculated is “less than 1,” yell out
“Demand is
inelastic and total revenue will be increased if we raise the price of a slice
of pizza! "
(If not, ask the instructor for help.)
Step 7. Prove that by multiplying the price times the quantity demanded for
each point and by calculating the result called total revenues in the chart
below and by plotting the total revenue for each quantity demanded on the graph
on the board. Ask the instructor for help if necessary, and to check your work.
Price X Quantity Demanded = Total Revenue Dollars
$1.00 0 ____$0.00_______
.75 3 ___ __2.25_______
.50
6 ______3.00______
.25 9
______2.25______
.00 12 ______0.00______
Congratulations Chessies! You have solved problem #2 correctly. Pick up your song sheet, join hands and sing the appropriate verse. Then go on to the next problem.
Imagine that point G bisects line segment BC and that G represents the price of a slice of pizza.
Step 1: Using markers, drop a vertical line to the
horizontal axis from point G, connecting it to point K.
Step 2: Technically speaking, the elasticity of demand at point G equals line
segment AG divided by line segment GC, that is, (AG/GC)
but those results are also proportionally equal to line segment AK divided by
line segment KD, that is (AK/KD).
Step 3: How long is AK? Answer: ____12
- 3 = 9______
Step 4. How long is KD? Answer: _____3
- 0 = 3_____
Step 5. What is AK divided by KD? Answer: _____9 / 3 =
3_____
Step 6. If the number you calculated is “greater than 1,” yell out
“Demand is
Elastic and total revenue will be increased if we lower the price of a slice of
pizza.”
If not, ask the instructor for help.
Step 7. Prove that by multiplying the price times the quantity demanded for
each point and by calculating the result called total revenues in the chart
below and by plotting the total revenue for each quantity demanded on the graph
on the board. Ask the instructor for help if necessary, and to check your work.
Price X Quantity Demanded = Total Revenue Dollars
$1.00 0 ____$0.00_______
.75 3 ___ __2.25_______
.50
6 ______3.00______
.25 9
______2.25______
.00 12 ______0.00______
Congratulations Chessies! You have solved problem #3 correctly. Pick up
your song sheet, join hands and sing the appropriate verse. Then go on to the
synthesis, or to the next problem as directed by your instructor.
________________________________________________________________________
Appoint a time-keeper. Spend no more than 3 minutes on each task if possible. Ask your instructor for help if you need it.
Step 1: Read the following article that appeared in the St. Paul Pioneer on 12/12/91, regarding data on Wisconsin deer licences for 1990 and 1991.
Wisconsin
raised fee to $18, sold 50,000 fewer deer licenses
(Associate Press: Madison, WI)
The state of Wisconsin sold about 50,000 fewer deer
licenses this fall but collected about $4 million more in fees than a year ago
because the licenses cost more, the Department of Natural Resources says.
”The drop in license sales, from 700,000 to 650,000, reflects deer hunter
backlash to raising the gun license from $15.35 to $18,” said Ronald Semman,
administrator of the DNR’s Office of Planning and Analysis.
”We always have that when we increase fees,” he said. “There’s always a
rebound, generally the following year.”
Step 2: Using the numbers given, fill-in the prices, quantities, and total
revnue.
Use the total revenue test to determine if deer licenses were elastic,
inelastic, or of unitary elasticity.
|
Year |
Price |
Quantity |
Total Revenue |
|
1990 |
$15.35 |
700,000 |
10,745 |
|
1991 |
$18.00 |
650,000 |
11,700 |
Demand for deer licenses is characterized as _____Inelastic___________.
(Raise the price and total revenue rises)
Step 3: Calculate the elasticity of demand using either the midpoint formula or the natural logarithm formula. (Use one method or the other.)
|
|
Mid-Point Formula |
Log Formula |
|
(1) % change in Q |
(Q91 –Q90) / (Average Q) = ___________________ |
Ln (Q91 / Q90) |
|
(2) % change in P |
(P91 – P90) / (Average P) $18.00 - 15.35 =
$2.65 = .158 |
Ln (P91 – P90) |
|
E-sub-D = (1) / (2)
|
|
= __________________ |
Step 4: Considering the determinants of elasticity of
demand below, which in your opinion provide an explanation for the elasticity
that you derived?
A. availability of substitutes
B. proportion of the budget spend on the good or service
C. the length or passage of time.
(Because people use time to search for substitutes!)
Congratulations E-Speakers! You have solved problem #1 correctly. Pick up your
song sheet, join hands and chant the appropriate verse. Then go on to the next
problem.
Step 1: Read the following summary of “Lower-priced PCs Drove Stron Sales for Holiday Month,” The Wall Street Journal, by Gary McWilliams, January 8, 1999.
Nearly half of U.S. households now own a PC, yet
December 1998 turned out to be a strong sales period for computer retailers.
Unit sales rose 41 percent.
Average prices fell by 20 percent to barely more
than $1,000 as computer manufacturers increased their production of sub-$1,000
home-PC models to satisfy the demand for less affluent households.
The fortunes of different retailers varied. Best Buy
and Circuit City saw double-digit gains in revenue, but Comp USA and Tandy,
which did not focus on low-priced PCs, saw slower growth.
Step 2: Using the information given, calculate the price elasticity of
demand in the PC market.
E-sub-D = (+41%) / (-20%) = 2.05
Step 3: Answer the following questions.
1. Does the value indicate that demand is price elastic or price inelastic?
Answer: Demand is _____Elastic________________.
2. Given the elasticity and the fact that prices fell, what happened to the
total revenue in the market for PCs?
Answer: ____Total Revenue Rose______________
Congratulations E-Speakers! You have solved problem #2 correctly. Pick up your song sheet, join hands and chant the appropriate verse. Then go on to the next problem.
Step 1: Read the following case study by Schiller, The Micro Economy Today, 6th edition.
“Like many local governments, the District of Columbia is perennially short of revenues. In an effort t to rais additional revenue, Mayor Marion Barry of Washington, D. C., decided in early 1980 to increase the city’s tax on gasoline. On August 6, 1980, the city government raised the gas tax… The higher tax raised the retail price of gasoline by 8 cents, to $1.60 per gallon.”
“The mayor and city council thought the higher gas tax would be an easy way to increase city revenue. Unfortunately, the District’s projections were grossly in error. In August 1980, gasoline sales in the nation’s capital fell from 16 million gallons per month to only 11 million. Ten gas stations closed down, and more than 300 service-station workers were laid off.”
Step 2: Fill-in the chart below about gasoline sales in Washington, D.C.:
|
|
Price |
Quantity (million gallons per month) |
Total Revenue (in millions of dollars) |
|
Before the tax increase |
$1.52 |
16 |
$24.32 |
|
After the tax increase |
$1.60 |
11 |
$17.60 |
Step 3: Answer the following questions:
2. Now calculate
the price elasticity of demand for “gasoline in D.C.”
Answer:
E-sub-D calculates to % change in quantity =
difference/average quantity = 5/13.5
= .3704 = 7.22
% change in price difference/average price
.08/1.56 .0513
Congratulations E-Speakers! You have solved problem #3 correctly. Pick up your
song sheet, join hands and sing the appropriate verse. Then go on to the
synthesis, or to the next problem as directed by your instructor.
Dear Colleagues and Friends of Mine in Education,
My teaching style makes intensive use of these six characteristics:
1. Empathic Teaching
Recognizes Different Learning Styles and Capabilities
Many students have initial difficulties with graphics (as the Chessies may have
experienced) and many more students bring a lingering fear of problem solving
into the classroom with them. The E-Speakers might have frightened the more
timid students, and were therefore given tasks commensurate with their level of
experience.
2. Advantages of
Cooperative Learning
Cooperative learning introduces students to shared, inter-dependent problem
solving.
Cooperative learning prepares students to work on team projects as is expected
by many employers in today’s business world.
Cooperative learning can help dilute the risk of failure, provide supportive
roles, and build solidarity, confidence, and self-esteem through relational
experiences.
3. Incentivising the
Learning Community
Every one likes to be rewarded. Learning should provide its own incentive so
that it leads to further stimulation and interest in higher levels of learning.
While the verses might have been fun to sing, and provided some psychological
reward internal to each team, they also had a more subtle purpose. The verses
were written to show the other team that real progress was being made. It was
as though there were two learning levels that were valid, and I intended that
each team member silently ask him or herself if he or she were really capable
of, and now becoming more interested in the level of learning being accomplished
on the other team.
4. Measurable Learning
Outcomes
Achievement is best documented by use of measurable learning outcomes. None of
my lesson plans contain more than three measurable learning outcomes.
Students progress satisfactorily when they know how much they've learned, and
when they know what skills they have yet to master.
5. Use of Real World
Examples
Education is self-reinforcing when it helps explain, improve control of, and
prophesy about the real world. Theory that is not usefully employed fails to
inculcate a love for learning. So this we learn from Tom our colonel, “Love for
Econ Springs Eternal!”
6. Globalizing the
economy, and creating empathy for foreign cultures
The shrinking globe (via rapid communications) creates the need
to see that foreign cultures require our respect. China, Russia, Japan,
and India now each create as many engineers as we do in the United States.
The German people attend school 51 more days per year than we do. The
Japanese study even more intensively than that! We will not be competitive
unless we train our students (human capital), harness our strength in technology
(material capital), and utilize the strength resulting from the sheer size of
our free market economy to create a universally level playing field.
Two years ago, I wrote a graduate studies paper about
"Internationalizing Education" and Tidewater Community College was one of the
colleges I cited as a pillar of strength in that endeavor. I therefore
hope and look forward to working with your dynamic instructor force!
At this point in my career, I believe in putting personal achievement ahead of personal security. It is worth more to me to "dance into class" each day, than it is to earn a paycheck. I want an audience that can be receptive to ideas that loom large on our national agenda. For these reasons, I seek and embrace the wider world, with all its challenges.
Thank you for inviting me to Tidewater Community College on the Chesapeake Campus! It was lots of fun to meet and interact with each of you.
Tom Meyer
Tom Meyer - A man with the golden shovel
Here is the same problem for both Chessies and E-Speakers.
For the Chessies:
What direction should price take (be raised, lowered, or remain about the same)
if the seller wishes to maximize total revenue in each of the following real
world markets for which these elasticities of demand have been published?
For the E-speakers:
Given that the availability of substitutes, the proportion of one’s income spent on the item, and the passage of time all influence elasticity, which factor may best explain the nature of the coefficient in each example.
(The more
substitutes there are for a good, the greater is its elasticity.)
(The greater the price for a good relative to one’s income, the greater is its
elasticity.)
(The greater the passage of time, the greater is a good’s elasticity.)
Good or Service Elasticity of Demand
Fresh vegetables : Tomatoes 4.6
Peas 2.8
Canned vegetable: Tomatoes 2.5
Peas 1.6
(Circle the correct answer)
With the previous goods, econometricians tell us that to maximize total revenue
we should
A. Raise the price;
B. Lower the price;
C. Hold the price constant
Good or Service Elasticity of Demand
Radio and TV 1.2
China and Tableware 1.1
(Circle the correct answer)
With the previous goods, econometricians tell us that to maximize total revenue
we should
A. Raise the price;
B. Lower the price;
C. Hold the price constant
Good or Service Elasticity of Demand
Physician’s services .6
Legal services .5
Kitchen appliances .6
Gas and oil in the long run .5
Gas and oil in the short run .2
Jewlery and watches .4
(Circle the correct answer)
With the previous goods, econometricians tell us that to maximize total revenue
we should
A. Raise the price;
B. Lower the price;
C. Hold the price constant
Tantalizers – (Follow-on Problems)
Here is an interesting set suggesting that for luxury
items, and with time to shop for substitutes, elasticities can change!
Airline travel in the short run .06
Airline travel in the long run 2.40
Foreign travel in the short run .70
Foreign travel in the long run 4.00
Demand for JP-4 fuel
by fighter pilots in
Southeast Asia conflict 0.00
(inelastic, a necessity, with no substitutes
and not responsive to
price)
From Paul T. Heyne of
Southern Methodist University
Characterize the market as having elastic or inelastic demand based upon the
following real world statements:
1. People won’t buy much more, no matter how far we cut the price.
(Clue – Draw a very steep demand curve, change the price and note the
response in quantity demanded.)
2. This is a competitive business. We’d lose half our customers if we raised
prices by as little as 2 per cent!
(Clue – Draw a nearly horizontal demand curve, and note
what happens to quantity demanded and to price when the quantity demanded is
halved.)
3. Tuition receipts would increase it they lowered the price of a credit hour
by 20%.
(Clue – This question requires that you create the correct relation between the
total-revenue and the price of a credit hour.)
(Clue – Use a steep demand curve and reduce the quantity by 25%, and note what happens to the product of price and quantity demanded.)
From Tom Meyer of Patrick Henry Community College
In Martinsville, I eat lunch at Subway. Across the street is one of two Valero
gas stations. They are only one block apart, on the same side of the road. One
gas station consistently sells gas for one penny less than the other.
1. Do you think some customers are price-sensitive enough
to purchase their gas one block further down the road? Are there other
customers for whom a penny per gallon seems not to make a difference?
2. Given the different prices occurring and the quantities of gas pumped, could
you calculate the price elasticity of demand?
These gas stations tend to be the price leaders Martinsville – Collinsville neighborhoods.
One More Tantalizer From Tom Meyer:
Examine the following columns of
numbers. Notice that in each case
quantity demanded increases when price declines, which is consistent with the
law of demand.
Multiply the price times the quantity demanded placing the result in the total
revenue column. Check your answers
Case I
Price Quantity Total Revenue Answers
20 10 ___________ 200
18 12 ___________ 216
16 15 ___________ 240
14 20 ___________ 280
Case II
Price Quantity Total Revenue Answers
20 10 ___________ 200
18 11 ___________ 198
16 12 ___________ 192
14 13 ___________ 182
Case III
Price Quantity Total Revenue Answers
20 10 ___________ 200
18 11 1/9 ___________ 200
16 12 ½ ___________ 200
14 14 2/7 ___________ 200
Which cases demonstrates Elastic Demand, (E-sub-D greater
than 1)?
Which cases demonstrates Inelastic Demand, (E-sub-D less than 1)?
Which cases demonstrates Unitary Elasticity of Demand, (E-sub-D equal to 1)?
(Hint: Use the total revenue test to find your answer. If you have never heard of the total revenue test for elasticity, ask someone in class who has.)