Download ECMA04H - UTSC - University of Toronto

Fall 2008
INTRODUCTION TO
MICROECONOMICS:
A MATHEMATICAL APPROACH
•ECONOMICS A04H•
Prof. Gordon Cleveland
COURSE HANDBOOK
AND
STUDY AIDS
© Michael Krashinsky, Gordon Cleveland
2
TABLE OF CONTENTS
ECMA04H
(This entire handbook is downloadable, in sections,
from the UTSC Intranet)
BASIC COURSE INFORMATION
PAGE 2
SURVIVAL GUIDE
PAGE 7
SCHEDULE OF IMPORTANT DATES
PAGE 12
READING LIST AND COURSE OUTLINE
PAGE 13
TUTORIAL QUESTIONS
(ANSWERS HANDED OUT AT WEEKLY TUTORIALS)
PAGE 16
STUDY QUESTIONS AND STUDY OBJECTIVES FOR EACH
WEEK OF THE COURSE (ANSWERS INCLUDED)
PAGE 30
SUPPLEMENT A: ON ELASTICITY, TAX INCIDENCE
AND EXCESS BURDEN OF A TAX
SUPPLEMENT B: THE PRISONERS’ DILEMMA AND
APPLICATIONS TO DUOPOLY
University of Toronto at Scarborough
September 2008
ECOA04H
Introduction to Microeconomics: A Mathematical
Approach
There are two sections of this course taught by the same professor: Professor Gordon
Cleveland teaches the L01 section on Monday and Wednesday 2:00 p.m.– 3:30 p.m. in
AC223 (the big lecture theatre in the ARC). He teaches the L02 section on Monday and
Wednesday 3:30 p.m.– 5:00 p.m. in AC223.
Professor Cleveland’s office is on the 3rd floor of the Management Building MW364.
His office hours are on Mondays and Wednesdays from 1 p.m.- 2 p.m. and on Tuesdays
from 2 p.m. – 3 p.m. Materials related to this course are available in two different places
– on the intranet site for ECMA04 and on Prof. Cleveland’s website
(www.utsc.utoronto.ca/~cleveland) . All students should look carefully at both of these
sites. There are study aids and information (including tests from previous years)
relevant to students in both sections (L01 and L02) of this course. Prof. Cleveland’s
office phone is 416-287-7317, and he can be reached by e-mail at
[email protected]. E-mail is good for simple questions, but complex questions
requiring explanation should be asked in person (or try consulting one of the Teaching
Assistants during the TA office hours in MW369).
This handbook applies to both sections of the course. There will be common term exams
and final exams in this course.
The teaching assistants have regular office hours in the Economics TA Office which is
located on the third floor of the Management Building – MW369. Plan now to go and
talk about any problems you have with the course material. Their office hours can be
found on the door of the T.A. office, and on the course website and on the Intranet, and
you will meet them at the weekly tutorials held for this course.
This course is a half-credit course, which together with ECMA06H, makes up the
mathematical (i.e., using calculus) stream of introductory economics and is directed
primarily at students interested in specialist programs like the B.B.A. or specialist or
major programs in Economics. Before you take either ECMB02H or ECMB06H, (which
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are the intermediate level courses in microeconomics and macroeconomics), you must
complete both ECMA04H and ECMA06H and you must complete MATA32H and
MATA33H, or the equivalent material in other calculus courses at university level (for
instance, you could do MATA30H and one of MATA35H, MATA36H or MATA37H,
instead). If you are interested in a career in Economics, you should definitely do
MATA30H plus one of MATA35/A36/A37, plus several more math courses (more
calculus and matrix algebra, and perhaps real analysis) during your undergraduate
program, as well as taking advanced courses in economics and econometrics.
Note that the natural progression in the Management program would suggest that you
complete MATA32 and MATA33 at the same time that you are taking ECMA04 and
ECMA06 in first year (and preprogram students should be aware that they MUST
complete both half-courses in calculus before they can be admitted to the BBA).
The Canadian economy is relatively complex: this course gradually builds our
knowledge of concepts and tools of analysis that allow us to understand the economy,
as well as to pass the course. The course requires steady work on problems, reading and
thinking about concepts, and learning how to prepare for testing. It is not a course that
can be crammed into a couple of weeks of preparation before exams.
1. CLASSES: There are three hours of lectures each week. Because our text does
not use calculus and is not mathematically-oriented, we will be introducing extra
mathematical material in class that is not in your textbook. Problem-solving
concepts will also be introduced and discussed in your tutorial sessions. That
being the case, you should plan on attending all classes and tutorials,
concentrating in class, and taking proper notes. You are responsible for what is
discussed in class. If you miss a class, you are responsible for finding out what
was covered.
The classes are large - up to 500 students in a classroom - so noise in class can be a
serious problem. Please do not talk in class. If you want to talk to your
neighbour, the class and the professor would appreciate it if you both left the
class. Of course, you should turn off your cell phones and other noisy devices
while in the classroom.
2. VIDEO VERSION OF THE CLASS ON THE INTRANET: You can access
streaming video versions of the weekly lectures at the address:
www.utsc.utoronto.ca/~ECMA04/online.html. You can play the lectures s at
home or on the on-campus computers if you miss a class, if you wish to watch it
from home, or to review something you may not have fully understood.
3. EXAMS AND GRADING: Your grade is determined on the basis of two tests
during the term (each worth 25%) and a final exam in the final exam period
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worth 50%. Your marks will be posted on the intranet. If you miss either or both
of the two tests during the term, your marks will be adjusted to put the weight
on the final exam. You do not need to present a doctor’s note or excuse, and
there are no make-up tests for students who miss tests. On the other hand, if
you miss the final exam, you will have to petition to the Sub-Committee on
Standing (see the Registrar’s Office) for permission to write a makeup exam,
which will be written at the end of the following term.
We want to encourage you to write the term tests, so we will reward you for
doing so. If you write the term tests and the final exam and your mark on the
final is higher than on a term test, we will replace the lower term test mark (or
marks) with the mark you received on the final exam. This means that there is
no penalty for trying a term test, even if you think you are not fully ready. Our
intention is not to delay the point at which you begin to take this course
seriously. You should do that now. Our intention is, however, to provide a
small safety net for students in first year as they begin to learn how to do this
challenging subject.

The final exam for all students will be a three-hour exam and will take
place in the final exam period, between Friday, December 5th and Friday,
December 19th, 2008

The two mid-term tests will each be held in a 2 hour test period. Later in
the term, you can check the web site at www.utsc.utoronto.ca/~cleveland
for information on where to write these tests. The dates and times will
be announced in class and shown on the web site.
The mid-term tests will be made up entirely of "objective" questions
(mathematical problems or questions about economic concepts and graphs in the
multiple choice form). The final exam will include “objective” questions, but also
questions where you must provide a written or graphical answer. The exact
design of each test will be discussed in class prior to its taking place. Check the
web site www.utsc.utoronto.ca/~cleveland for sample tests from previous years.
4. CALCULATORS: The following simple calculators are recommended (there
may be additional letters added at the end on the version you buy, but that does
not make any difference).
SHARP EL-531
SHARP EL-509
TEXAS INSTRUMENTS TI-30
TEXAS INSTRUMENTS TI-34II “Explorer Plus” or TI-32
CASIO fx-65 or fx-280
You may buy other types of calculators and use them for this course, but you
should avoid any that have considerable storage capacity for text, or those that
have large screens and sophisticated graphing capabilities, because these
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calculators can be confiscated during an exam or test.
5. TUTORIALS: Tutorials have been scheduled in this course, led by senior
undergraduate students, or graduate students. There are no tutorials in the first
week; these will begin in the second week of classes. We have prepared special
problems/questions which will be dealt with in these tutorials; these tutorial
questions are included in this Handbook, which you will download from the
intranet. The answers will be taken up by your teaching assistants (TA’s) at the
weekly tutorials; a paper copy version of the correct answers will be handed out
at the end of the tutorial. Tutorials will parallel the material which we are doing
in class, at about the same time. These tutorials are an excellent source of
supplemental help in this difficult course. There are tutorials held every week
except the first week of term.
6. DROPPING OUT OF ECMA04H : Sorry to bring up this painful subject so
early in your career in economics, but if you are not doing well in economics, you
may decide to drop out of ECMA04H. Dropping a course is unfortunate, but it is
not a shameful act; under certain circumstances, it is the wisest course of action.
The drop date is Sunday, November 16th. By that time, you will have written at
least one mid-term test and received 25% of your marks in this course (probably
more than that). If, at that stage, it is clear you cannot handle the material (given
the rest of your academic load), you are better to drop the course and take it
again another term, rather than see it through to the bitter end.
ECMA04H will be offered again in the summer term, so you can take it at that
time to catch up. You are permitted to take ECMA06H without having
previously taken ECMA04H, so dropping out of ECMA04 now does not mean
that you must drop ECMA06 from next term’s course schedule. Of course,
ECMA04H is also offered each fall, and ECMA06H is also offered in the summer
term.
7. OFFICE HOURS: My office hours have been provided above and will be
announced in class. I am happy to see you to talk about any problems you may
be having in the course. Although there are a lot more students than there are
office hours (there are close to 1000 students in the two sections of this course),
you will often find me available, especially if you are willing to wait a few
minutes. In fact, there are many office hours when there is no wait at all.
However, right before each test or exam, there is likely to be a line up. This
suggests the obvious: don't wait until right before tests to see me about problems
(and of course I am not likely to be sympathetic to a student who comes in a day
or two before the test to announce that he or she does not understand the past
two months worth of material!). If you find the line-ups too long, you may find it
easier to resolve some problems by speaking with the tutorial leaders (tutorials
are led by teaching assistants - TA’s - who are senior undergraduates or graduate
students). And, of course, e-mail is another possibility for relatively simple
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questions.
8. BOOKS: It is recommended that you purchase this textbook and follow the
recommended readings each week that are outlined in this Course Handbook.
This textbook cannot substitute for the lectures, the tutorials, and regular work
on the problems that are assigned in this Handbook. The textbook does not use
calculus. While it provides important discussion of the economic theory you are
expected to learn in this course, it is not sufficient to prepare you for writing the
“problem-based” questions on your tests and exams this year. Therefore,
purchase of this textbook is recommended, but not required.
The textbook is:
Christopher Ragan and Richard Lipsey, Microeconomics: 12th Canadian
Edition Pearson-Addison Wesley Publishers, Toronto. It is available in the
bookstore.
The rest of this handbook, available through the Intranet, is an absolutely vital
part of this course!! I strongly recommend that you download it and PRINT IT
immediately. Students in past years have also found past exams extremely
useful for review purposes. A (nearly) full set of tests, exams, and answers to the
tests and exam questions, is available on the course website at
www.utsc.utoronto.ca/~cleveland.
9. CHEATING: Cheating debases the learning process and is immoral.
Furthermore, it violates the rules of the University and, if detected, will have
serious consequences. Even more to the point, the Department of Management
takes it very seriously, and will pursue any case to the limit. I routinely take a
variety of measures calculated to make cheating difficult and to catch offenders
(some you will know about; others are kept secret). The point is simple: students
who do not cheat should know that they are not disadvantaged by their honesty.
Each year, a couple of students are caught cheating and get a mark of zero, and a
notation on their transcript. You have now been warned.
10. EXTRA HELP: Students who are having trouble should make sure that they
work through the problem set questions (and answers) and tutorial questions
and answers carefully. Teaching assistants are available at various hours during
the week to provide assistance in explaining these answers, and the appropriate
techniques for answering questions. Each T.A. will have three or four hours of
office hours per week, in the Economics T.A. office on the 3rd floor of the
Management Building (MW-369). Several independent operators have been
posting ads around campus offering special tutoring for which you are asked to
pay. These sessions are not sanctioned by the University and we have no
information about whether they are of any value. Caveat emptor – Let the buyer
beware.
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Survival Guide for Introductory Economics
(and your first year at Scarborough College)
Some advice from Professor Michael Krashinsky,
chair of the Department of Management
I have taught the introductory course at Scarborough at various times over the past 34
years. Certain patterns have emerged that make it possible to tell you about what
seems to produce success and failure in this course. Some of these observations will be
useful in your other courses. My suggestions apply to everyone, but might be
particularly useful to first year students.
1. Keep up: University courses tend to be cumulative, so that not falling behind is
critical. If you are up-to-date in your work, my lectures will make more sense and
reinforce what you are studying. On the other hand, if you fall behind, the lectures will
not make sense and you will fall further behind. The pace in university is likely a good
deal faster than what you have been used to, so your experience in high school (that you
can fall behind "x" weeks and be able to catch up) is probably misleading. To keep up.
you will have to ...
2. Expect to work regularly at home: In most university courses, you are expected to
work regularly on the course material outside the classroom. Again, this is likely quite
different from your high school experience. Quite aside from your problem set
assignments, you have an automatic assignment after each lecture. That is, I expect you
to go over your lecture notes and the related reading and get the material clear in your
head before the next lecture. Most students do not do this, which is one reason why ...
3. Marks tend to be significantly lower in university: The average first year student in
Management arrives from high school with an average mark of well over 80% (on the
best 6 courses, including English). Our experience over the past few years suggests that
about 15-20% of the students registering in this course will drop out of this course
before it ends. Another 20-25% will either fail the course or receive D’s. Since I regard
D as an unacceptable grade for a student, only slightly more that half the students
starting this course will receive good grades.
Clearly, many students do not do as well as their high school marks might suggest. The
median mark at the University for students tends to be around 70. If the average
student coming into Management has an 85% coming out of high school, then the
median student sees his or her mark drop by 15 percentage points. Of course, some
individuals (the ones who work very hard) find their marks do not fall at all, but clearly
more is expected of you here than in high school. This is not to scare you off university,
because...
4. Everyone we accept to university is capable of doing well: The work in this course is
not overwhelming or too hard. However you will have to work very seriously. As I
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have suggested, your experience in high school is likely to be a bad guide to how you
must work in university. You will have to work more on your own, you will have to
plan lots of time out of class to review your notes, to read your text, to do sample
problems. The bottom line is that you should ...
5. Expect to work harder than you did in high school: We expect a minimum of ten
hours a week of work in the course, including your time in class. If you are taking five
courses, all of which expect this work level, that amounts to 50 hours a week of work on
academic subjects. That is real work, not work while watching television or a party
going on in the background or while you are earning money at a job. In fact, ...
6. You should NOT go to school full time AND hold a demanding job: No one can work
30-40 hours a week at a job and 50 hours a week at learning university-level material.
Yet every year I meet large numbers of students trying to do just that. It may be that
their high school experience has taught them that combining work and school is quite
reasonable. It is a serious mistake to extend that experience to university. The work
here is at a higher level and the pace is such that what you did in high school is not
enough. You CANNOT work full time and go to school full time.
Several years ago, I had a student in a fourth year seminar who was earning an "A" in
the course. I was surprised, because his average mark over the previous three years had
been a "C+" (and my course was hard, so that a student earning an "A" in it could have
done as well in any other course). When I asked the student about this, he told me
frankly that he had a job that required 20 hours a week, and that he accepted the lower
marks because he needed the money to operate his car (he was, however, working
particularly hard in my course because he liked the material, and also because he liked
me and didn't want to let me down). I felt his choice was strange (in the long run, his
lower marks would cost him a lot more money than he was earning, not to mention the
fact that the extra money he would later earn could buy him a lot better car than he was
driving!), but at least he knew the choice he was making. Many first year students do
not know that working at a job during term will cost them marks, will mean their
income is lower in the future, and in many cases will result in them not surviving first
year.
If we believe that the student mentioned above is typical, then we can figure out what a
full time job will cost you. Working 30+ hours a week will mean that:
an excellent ("A") student will get average ("C" to "C+") grades
a bright ("B") student will get below-average ("D" to "C-") grades
a good ("C") student will fail or barely pass.
If you have such a job, I can hear your objections now. Let's deal with them in turn:
• "I'm not typical. I can work and still study, since my job is boring and doesn't take
that much out of me." - You're wrong. Boring work is the worst of all in terms of
destroying the urge to study (since, let's face it, studying for most people is not
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something we look forward to, so motivating ourselves to study is next to impossible
after a boring job). And you may not be typical, but don't kid yourself.
• "You're wrong about supporting a car. I work to support myself. Without the money
I earn, I couldn't stay in school." - This is a tougher objection. I don't know your
personal financial situation, nor can I judge what pressures you face. If you truly need
to work to stay in school, then you still have to face the cost of work in terms of your
grades. If you must work, then accept reality and go to school part time. Or work full
time and save up to go to school. Or borrow the money somehow, or apply for a
bursary, or cut your budget to the bone. But for goodness sake don't try to combine 30
hours a week of work with a full time course load. Because the inevitable result is the
worst of both worlds: wasted effort, low grades, and a year down the drain.
• "What about self-reliance and all those movies about kids working their way through
school." - Most people are not movie heroes! I admit that there are in this world some
fantastically motivated people who can manage it all. After all, there are 168 hours in a
week, and even subtracting 50 or so for sleep, there are enough hours for school and
even a full time job ... if you are Superman or Superwoman, that is. Most of us aren't,
which is why so many of the students who started the introductory course last year did
not finish it or, if they did finish it, did not receive acceptable grades. I don't doubt your
motivation at the beginning of the term. But the movie picture of the dedicated student
living in poverty and coping is not the story I see in my classes!
• "I'm different. It won't happen to me." - Yes it will.
7. High school economics is not university economics: Another reason for the lower
marks in university is that what you are expected to be able to do at the end of the
course, and what you are expected to know for exams, differs between high school and
university, even when the material covered is not much different. In past years, I have
had some students who even used the same economics text in their grade 13 economics
course as I used in first year. The students were sure they knew what they needed to
know even before the course started. Most of them were supremely surprised after the
first test. One student came to me and said: "I had seen all the material before, but you
really expected us to be able to solve problems and know what was going on. In high
school, the questions were more general. We never had to be able to solve problems
involving the detail that you expect." Precisely. I won't ask you, for example, vague
questions about why perfect competition works, but rather will ask detailed questions
about how it works. Your high school training won't hurt you, but don't expect it to
carry you any distance.
By the way, this same phenomenon applies in your other courses. The math people say
that their students do best when totally new material is introduced, since the students
work hard to overcome their lack of knowledge. When high school material is
reintroduced more rigorously, students relax, figuring that they know what is going on.
Inevitably, they don't. All this is a good reason why ...
8. A little bit of fear wouldn't hurt: The purpose of all these warnings is not to scare you
out of university. There is the classic story of the dean calling all the students together
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in a first assembly and saying "Look to your left; look to your right; one of you won't be
here in six months." That is not a bad summary of what happens in this course. But the
reason is not that one-third of the students can't handle the work. As mentioned earlier,
everyone accepted here is capable of doing the work. Thus the issue is how to get you
to do the work you are capable of. One way is to make you a little afraid at the
beginning so that you work hard and do not fail out before you discover just what is
required to do well in university. The key lies within yourself, because ...
9. University is a very impersonal place: You hardly need to be told this, as you sit in
classes with 300-500 students. But the anonymity means that if you don't do the "right"
amount of homework, if you skip classes, if you don't do the sample problems - in
summary, if you don't follow all my advice - it will seem that nothing bad happens. No
one yells at you, no note goes home to parents, no one, it seems, even notices. Even if
you fail the first exam, nothing seems to happen. You can drift (and party) for the entire
year failing all your courses and no one will say anything to you. How can they, when
they don't know your name?
The danger in first year is worsened by the fact that you will get little feedback on how
you are really doing in the course until it is too late to do much about it. That is because
there is a lot of weight on exams in university, with little for problem sets and nothing
(at least in this course) for class participation, oral presentations, and so on.
There is only one way to deal with this problem. Work hard, keep up-to-date, work
with other students, and ...
10. When you are having trouble, get help quickly: Your professor has office hours.
There are lots of students, but you will be amazed at how accessible they are in office
hours that are not right before an exam or a problem set due date. If you prepare for
seeing them (by writing down specific questions, and working on problems you are
having trouble with), they can make very effective use of your time and their time.
Also, there are teaching assistants (t.a.'s) who can help and who are even more
available. But you will have to take the vital first step by coming in to see us. Don't
worry that your professor will be angry if you are not understanding things. What
makes professors angry (and frustrated) is the students who drift along not
understanding things and then write exams that reflect that lack of understanding!
Finally,
11. Enjoy University! This sounds like the parent telling a teenager not to do this, not to
do that, not to do the other thing, and above all to have fun! But the point is that if you
work hard and keep up with your course work and avoid "part time" jobs that chew up
all your available time for thinking, university will be a very rewarding time for you.
You'll learn more about yourself and about the world around you, and you may even
get a job at the end of it all. Maybe even more importantly, if you fall behind and do
badly in your courses, you won't enjoy university, and if you are not having much fun,
you are unlikely to stay here very long. And that would defeat the whole purpose of
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coming here in the first place.
Enjoying university also means that you should take courses because you are interested
in them and because they stimulate you. All too often, students take Economics even
though they don't like it and are bored in class, because they (or, even worse, their
parents) believe that "practical" courses like Economics are what lead to good jobs. This
is a bad strategy. For one thing, if you don't like what you are studying here, you are
unlikely to do very well. A's and B's in Political Science or Psychology or History on a
resume look far more impressive than C's, D's and F's in Economics. And in any case,
getting a job is, I hope, not all that university will be about for you.
On this last point, I rather like a quote from Thomas Jefferson's Principles of Education
for the American People:
"It is the objective of higher education
To form the statesmen, legislators, and judges upon whom public prosperity and
individual happiness are so much to depend;
To harmonize and promote the interests of agriculture, manufacturing and
commerce, and by well-informed views of political economy to give free scope to
the public industry;
To develop the reasoning faculties of our youth, enlarge their minds, cultivate
their morals, and instill in them precepts of virtue and order;
To enlighten them with mathematical and physical sciences, which advance the
arts and administer to the health, the subsistence, and the comforts of human life;
and, finally,
To form them to habits of reflection and correct action rendering them examples
of virtue to others and of happiness within themselves."
All that having been said, let's get down to the course!
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SCHEDULE OF IMPORTANT DATES
ECMA04H
Week 1
Week 2
Week 6
Week 7
Week 10
Week 10
Monday, September 8
Sunday, September 21
Monday, October 13
Saturday, October 25
Saturday, November 15
Sunday, November 16
Week 13
Monday, December 1
- first day of classes; no tutorials this week
- last day to add/change courses
- Thanksgiving, no classes
- possible day for first test
- possible day for second test.
- last day to drop course without academic
penalty
- last day of classes (replacement class for
Thanksgiving)
Friday, December 5 to Friday, December 19 - FINAL EXAM PERIOD - exam may come
at any time in the exam period.
Note - There will be tutorials in ECMA04Y in all weeks except week 1 (Note: there are
tutorials even on weeks when mid-term tests are scheduled)
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READING LIST AND COURSE OUTLINE
Week 1 (Sept 8, Sept 10)
Topics: The definition of economics; the role of scarcity of economic resources and of
choice. Opportunity cost defined and explained. The production possibilities model as
a way of thinking about scarcity, choice and opportunity cost. The role of markets.
Definition of microeconomics and macroeconomics. Supply and Demand introduced.
Recommended Reading: part of Chapter 1 “Economic Issues and Concepts” (pp. 1-22).
Also, there is much useful material about how economists use theory, data, functions
and graphs in Chapter 2 “How Economists Work” (pp. 23-46).
Week 2 (Sept 15, Sept 17)
Topics: The market model in general. How markets allocate resources through buying
and selling of goods and services. Shifts in demand and shifts in supply and how they
affect equilibrium price and quantity traded. The key role of prices in allocating
resources to different uses. How price floors and price ceilings can affect the allocation
of resources through markets. Judgement of the allocative function of free markets.
Recommended Reading: Chapter 3 “Demand, Supply and Price” (pp.47-72) and Chapter
5 “Markets in Action” (pp. 95-115).
Week 3 (Sept 22, Sept 24)
Topics: The theory of consumer demand for goods and services. Utility, total utility,
marginal utility, and the optimal purchase rule; how these concepts help us understand
the negative slope of demand curves. The Law of Demand. The Water-Diamond
Paradox. The concept of consumer surplus algebraically and graphically. Individual
and market demand; shifting of demand curves and moving along them.
Recommended Reading: Chapter 6 “Consumer Behaviour” (pp. 124-139)
Week 4 (Sept 29, Oct 1)
Topics: Measuring and understanding the elasticity of demand and of supply. How a
sales tax will affect a market. The importance of the elasticity of demand and supply in
determining the incidence and excess burden of a sales tax.
Recommended Reading: Chapter 4 “Elasticity” (pp. 73-94) and read Supplement A (on
the Intranet) on excise taxes and elasticity.
Week 5 (Oct 6, Oct 8)
Topics: Finish material from last week on demand, elasticity, tax incidence and tax
burden in preparation for first midterm test. Start discussion of material from Week 6,
especially material on cost functions and cost curves.
Recommended Reading: Chapter 7 “Producers in the Short Run” (pp. 145-168).
Week 6 (Oct 13 is Thanksgiving (holiday), Oct 15) No class on Monday
Topics: How a business firm makes its hiring and production decisions. Use of fixed
and variable inputs determine short run costs. Diminishing marginal product and
rising marginal cost. The distinction between the short run and long run. Total,
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average and marginal costs in the short run. The importance of marginal costs to
decision-making. The envelope theorem and the relationship between short-run and
long-run costs. The long run average cost curve (LAC or LRAC) as an envelope of the
short run average cost curves. Economies of scale, diseconomies of scale, and minimum
efficient scale.
Recommended Reading: Re-read Chapter 7 “Producers in the Short Run” (pp. 145-168)
and read Chapter 8 “Producers in the Long Run” (pp. 169-190).
Week 7 (Oct 20, Oct 22)
Topics: Economic models often assume that a market is "perfectly competitive". Perfect
competition is defined, the demand situation facing a perfectly competitive firm is
clarified, and we figure out how a perfectly competitive firm will make supply decisions
which will maximize its profit (in the short run). Assuming all firms have similar costs,
we derive the implications of perfect competition for the supply of goods to the market
as a whole (the industry supply curve in the short run). Demand and supply across the
whole market will determine the price, which then has feedback effects on the
behaviour of the individual firm.
Recommended Reading: the most important chapter of the entire term - Chapter 9
“Competitive Markets” (pp. 191-217)
Week 8 (Oct 27, Oct 29)
Topics: Finish discussion of competitive markets (short and long run adjustment
mechanisms) and proceed to discussion of monopoly industries. Entry and exit of firms
give us the long run supply curve of the perfectly competitive industry as a whole.
Long run equilibrium in a perfectly competitive market. How a perfectly competitive
market allocates resources in the short run and in the long run…the invisible hand at
work. The polar opposite of a perfectly competitive market is a monopolistic one.
Monopoly is defined, the demand situation facing a monopolistic firm is clarified, and
we examine how a monopoly will make price and output decisions to maximize profits.
Recommended Reading: part of Chapter 10 “Monopoly” (pp. 218-231)
Week 9 (Nov 3, Nov 5)
Topics: Taking the point of view of society as a whole, it is possible to compare the
results of business decisions made in perfectly competitive and monopolistic market
structures. This economic theory is the foundation of public policies towards a number
of important industries. Public policy may strive to regulate the behaviour of industries
that do not operate in the public interest; we discuss the pros and cons of these
regulatory efforts.
Recommended Reading: Chapter 12 “Economic Efficiency and Public Policy” (pp. 271296).
Week 10 (Nov 10, Nov 12)
Topics: Much of the Canadian economy is neither perfectly competitive, nor
monopolistic. The rest of the Canadian economy can be better understood with models
that emphasize strategic behaviour with uncertain outcomes. We briefly mention
15
monopolistic competition (product differentiation) and then focus our attention on
oligopolistic industries. Game theory, especially the prisoner’s dilemma, can be used to
understand decision-making of firms in an oligopoly. We compare the gain to society
from oligopoly, with the gain to society from monopoly and perfect competition, and
discuss public policy which can improve public results from oligopolistic industries.
Recommended Reading: Chapter 11 “Imperfect Competition and Strategic Behaviour”
(pp. 244-270). Also read Supplement B: “The Prisoners’ Dilemma and Applications to
Duopoly” which you can download from the Intranet.
LAST DATE TO DROP COURSE WITHOUT ACADEMIC PENALTY IS SUNDAY
NOVEMBER 16th
Week 11 (Nov 17, Nov 19)
Topics: So far in this course, it may seem that governments play a minor role in the
economy; in fact, the role of governments, through taxation, laws, regulations, and direct
expenditures is very large. All too briefly, we examine two major classes of arguments
that suggest that a market economy may not work well and that we may benefit from an
important degree of government intervention into the economy.
The first of these is the case of “public goods” – goods that are consumed collectively,
rather than individually, and where excluding additional consumers is infeasible. The
second of these is “externalities”; goods that are consumed by individuals, but where
there are effects on others. Pollution is one main example of an “externality” - a problem
that a purely private market economy may not be able to solve; we analyze this problem
in theory and look at alternative forms of government intervention which may help to
control pollution.
Recommended Reading: Chapter 16 “Market Failures and Government Intervention”
(pp. 375-406) and Chapter 17 “The Economics of Environmental Protection” (pp. 407425).
Week 12 (Nov 24, Nov 26)
Topics: The rationale for trade between countries is frequently misunderstood. We focus
on the importance of comparative advantage in determining what each country will
specialize in producing and trading with others. In simplified models, it is shown that
all countries can be made better off by international trade. In other models, we examine
the overall economic cost to a country that decides to ignore these benefits and protect
its own markets with tariffs or quotas. We also examine situations under which
protectionism makes good economic sense.
Recommended Reading: Chapter 33 “The Gains from International Trade” (pp. 802-822)
and Chapter 34 “Trade Policy” (pp. 823-846).
Week 13 (December 1)
Completion of material on microeconomics and review for Final Exam.
Recommended Reading: none
16
TUTORIALS
Your tutorials are scheduled on the same day each week (different days for different
students). Tutorial questions are printed below.
****************************************************************
ECM A04H
TUTORIAL #1 (WEEK 2)
1.
What is the opportunity cost to you of going to Economics class?
2.
What is the opportunity cost to you of getting a university education?
3.
What is the opportunity cost to you of taking a part-time job during the school
year?
4.
Assume that Jane lives in a single-person economy and is only able to produce
juice (Y) and nuts (X). Her Production Possibilities Frontier for one month's
production can be described by the function:
Y = 400 - 30X - X2
0 ≤X≤10
(a) What is the maximum amount of juice (in litres) that she could produce?
What is the maximum amount of nuts (in kilos) that she could produce?
(b) Why do we restrict X to lie in the interval (0,10) when we write the PPF as a
function?
(c) Is the point (5, 100) [i.e., X=5, Y=100] an efficient amount of production for
Jane? Why or why not?
(d) Sketch the PPF. Divide the diagram into three sets, as follows: points that are
attainable but inefficient; points that are attainable and efficient; points that
are unattainable.
(e) What is the opportunity cost of nuts at (4, 264)? What is the opportunity cost
of juice at the same point? Repeat both questions at (8,96). How are these
costs related to calculus concepts that you have learned? How are they related
to geometric properties of the graph that you have sketched?
(f) What is the value of the second derivative of the Production Possibilities
Frontier (i.e., d2Y/dX2)? What does the sign (i.e., positive or negative) of this
derivative imply, economically speaking? How do we interpret a PPF that is
17
linear, compared to one that is bowed (i.e., curved) outwards?
(g)
Imagine now that Jane has a utility function (a function that expresses her
evaluation of X and Y (nuts and juice). Let’s say that this utility function is: U
= 80X + 2Y. This utility function tells us that every kilo of nuts gives Jane 80
units of utility (joy or satisfaction), whereas each litre of juice gives her 2 units
of utility. (The odd thing about this utility function is that these valuations of
X and Y don’t depend on how much juice or nuts Jane already has, but we will
ignore this unrealistic feature and enjoy the simple mathematical form of a
linear utility function….). Given the PPF (which tells us how much juice and
nuts can be produced) and her utility function (which tells us the amount of
joy she will get from different combinations of juice and nuts), how much of
each do you think she will decide to consume?
18
ECMA04H
TUTORIAL #2 (WEEK 3)
QUESTIONS
1(a)
Draw a graph depicting supply and demand curves in the market for tomatoes.
What would happen to the prevailing price and quantity traded if family incomes
were suddenly to rise? Show the changes on the graph.
(b)
Does your answer to (a) depend on whether tomatoes are considered to be
"inferior"? Show the effect of a rise in incomes if tomatoes are an inferior good.
2.
The following changes will either cause (i) a change in quantity demanded, (ii) a
change in demand, (iii) a change in quantity supplied, or (iv) a change in supply.
Indicate which description applies to each of the following, and also whether the
equilibrium price and the equilibrium quantity will rise or fall:
(a)
the effect of a shift to the right of the supply curve of margarine on the margarine
market
(b)
the effect of a fall in the price of margarine on the butter market
(c)
the effect on the aluminum market of a subsidy which lowers the price of
electricity (note: aluminum smelters use a lot of electricity).
(d)
the effect of a shift to the left in the supply curve of oats on the oat market
(e)
the effect of a rise in autoworker wages on the market for cars.
3(a)
The demand for strawberries can be represented by:
P = 10 - .6Q, 0 ≤ Q ≤ 16.66
where P is the price in dollars per pint and Q is thousands of pints sold per week.
The supply of strawberries in the off-season can be represented by:
P = -2 + .4Q, Q ≥5
Determine the equilibrium price and quantity in the off-season. At this
equilibrium quantity, what is the extra cost (measured along the supply curve) of
supplying an extra unit of strawberries (i.e., the opportunity cost). At this same
quantity, what is the extra value to consumers of an extra unit of strawberries
(measured along the demand curve).
(b)
Assume that in the strawberry season, the supply curve shifts to:
P = -2 + .2Q, Q ≥ 10
Determine the new equilibrium price and quantity.
19
Draw the change in supply on a graph and show the new equilibrium price and
quantity.
4.
In the market for apartments in Prince George, British Columbia, demand is given
by:
P = 100 - Q
and supply is given by:
P = 20 + .25Q
where Q is the number of apartments rented and P is the rental price per day.
(a) What is the equilibrium price and equilibrium quantity of apartments traded?
(b) If the city council of Prince George decides to enforce a price ceiling of $30 per
day, and this price ceiling is effective, how many apartments will be rented?
(c) Given the number of apartments from answer (b), what price would renters be
willing to pay, at the margin, for apartments? If price/rent controls forbid renters
from paying the price they are willing to pay, what form might these extra
payments take?
(d) What is the amount of excess demand or excess supply of apartments at the
controlled price?
20
ECONOMICS A04H
TUTORIAL #3 (WEEK 4)
QUESTIONS
1.
You have the following utility function for roller coaster rides (where utility is
measured in dollars, and X refers to the quantity of roller coaster rides):
U = 10X1/2
a) Derive the demand curve for roller coaster rides and determine how many
rides are purchased when the price per ride is $1. What is the marginal utility of
an extra ride when X = 25, when X = 16, when X = 9, when X = 4?
b) What is the consumer surplus when the price per ride is $1? Explain what
consumer surplus is, in plain English. How does the amount of consumer surplus
you receive affect your decision to buy a certain quantity of rides if the price
rises?
c) Suppose that the amusement park operator offers a day pass for $40 which
allows you to take all the rides you can manage for the entry fee of $40. You
determine that there is enough time during the day for 50 rides. Should you buy
the pass, or continue to pay by the ride? What is the most you would pay for the
pass?
d) Ignore the day pass. If the price per ride rises to $1.25, how many rides are
purchased and what is the consumer surplus. What impact has the price increase
had on the amount spent on rides?
e) Elasticity of demand measures the sensitivity of quantity demanded to changes
in price along a demand curve (e.g., when the supply curve shifts but demand
remains the same). When the price per ride is $1, determine the elasticity of
demand. Is your result consistent with the answer to the final question in part d?
21
ECOA04H
TUTORIAL #4 (WEEK 5)
QUESTIONS
1.
The demand and supply of gazebos are given by the following equations:
demand: P = 110 - 0.5Q
supply: p = 54 + 0.2Q
where Q = quantity and P = price in dollars.
(a)
Compute equilibrium price and quantity.
(b)
Suppose that a tax of $7 per gazebo is placed on consumers. How are demand
and supply affected? Determine the new equilibrium price paid by buyers and
equilibrium quantity. Who bears the burden of the tax? Draw this graph.
(c)
Now suppose that the government removes the tax on consumers and replaces it
with a $7 gazebo tax on the sellers of gazebos. How are the curves affected?
Draw the graph for this new situation. Demonstrate that there is no change in the
economic incidence of the tax (even though the statutory incidence of the tax has
changed).
(d)
Determine the elasticities of supply and demand at the initial equilibrium point
(prior to the tax). How are these elasticities related to the economic incidence of
the tax?
2.
Now the demand for gazebos changes to P= 82 - 0.15Q. Repeat parts (a), (b) and
(d) of the previous question.
22
ECMA04H
TUTORIAL #5 (WEEK 6)
QUESTIONS
1.
An industry has the following demand curve: P = 500 - 10Q. Any amount of
output can be supplied at a price of $100 per unit. A $50 tax is placed on the sale
of this output. Compute government revenue, excess burden, the cost to
taxpayers of the tax, and the cost to taxpayers per dollar of revenue raised.
2.
A firm employs 34 units of capital (fixed in the short run) and has the following
short run production function:
Units of labour used per
day
Output per day
11.3
12.0
12.8
13.7
14.7
15.8
15
16
17
18
19
20
The price of capital is $2 per unit and the price of labour is $20 per unit. The
production function can also be written as
L = 0.05Q2 - 0.85Q + 12.8 for Q ≥ 15
a)
Derive a table for the AP (average product) and MP (marginal product) of labour,
without calculus. What is the relationship between the maximum AP and the
MP? Is the pattern of (eventually) declining average product and marginal
product normal or abnormal in the production of goods and services?
b)
Without calculus, construct a table showing TVC (total variable cost), TFC (total
fixed cost), TC (total cost), AVC (average variable cost), AFC (average fixed cost),
AC (average cost), and MC (marginal cost). Is AVC minimized where AP is
maximized? Explain.
c)
Derive an expression for AVC, AC, and MC, using calculus where appropriate.
Find the minimum value of AVC and AC. Show that MC passes through both
minimum points. Explain why this happens.
23
ECMA04H
TUTORIAL #6 (WEEK 7)
QUESTIONS
1.
A firm in a perfectly competitive constant cost industry in the short run has fixed
costs of $240, and total costs given by:
TC = 3q2 + 10q + 432 q ≥ 4
where q is output of the firm.
Demand for the output of this industry is given by:
P = 154 - 0.06Q
where Q is industry output.
a)
Form an expression for AC, AVC, and MC for this firm. Where is AC minimized?
Where is AVC minimized?
b)
In a perfectly competitive industry, it is assumed there are so many firms that no
individual firm has any control over the price; price is a constant from the point of
view of the individual firm. Form an expression for the profits earned by this firm if
the price in the short run is P0. Maximize this expression, and show that the result is
the same as setting price = marginal cost. Form an expression for the supply curve of
this firm.
c)
Suppose in the short run that there are 60 identical firms in the industry. The
industry supply curve is the sum of the quantities supplied by each individual firm.
Find the industry supply curve and then calculate the equilibrium price and output
in this industry in the short run. How much profit does each firm earn?
d)
Repeat part (c) when the number of firms in the industry is 100, 200, and 300.
24
ECONOMICS A04H
TUTORIAL #7 (WEEK 8)
QUESTIONS
1.
A constant cost industry is one that has a horizontal long run industry supply curve.
We continue to use the firm in the perfectly competitive constant cost industry from
last week's tutorial. This firm had fixed costs of $240, and total costs of:
TC = 3q² + 10q + 432 q ≥ 4
where q is output of the firm.
Demand for the output of this industry is given by:
P = 154 - 0.06Q
where Q is industry output.
Initially there are 100 firms, each producing 12 units of output, and price is $82 and
profits are zero. Assume that this size of plant generates the minimum long run
average costs, so that this situation is also a long run equilibrium.
a)
Explain why this is a long run equilibrium.
b)
Suppose that demand increases to P = 178 - 0.06Q. What will happen in the long
run and the short run?
c)
Return demand to the original level and return to the initial equilibrium. Now
suppose that the government imposes a tax of $12 per unit sold on every firm in the
industry. What will happen in the short and long run and who will bear the tax in
each case?
d)
Return demand to the original level and remove the tax. Now a new technology is
developed which can produce output at a minimum AC of $64 when the firm
produces 25 units (this is the new minimum LRAC [or LAC]). What will happen in
the long run?
25
ECMA04H
TUTORIAL #8 (WEEK 9)
QUESTIONS
1.
We continue to use the cost data from the firm in the previous tutorials. Now,
however, there is a single (monopoly) firm in the industry. This firm had fixed costs
of $240, and total costs of:
TC = 3q² + 10q + 432 q ≥ 4
a)
where q is output of the firm.
Suppose that the demand for the output of this industry is given by:
P = 120 - 2Q
where Q is industry output.
How much output will the firm produce and what price will it charge? What profits
will the firm earn?
b)
Now the firm faces demand of
P = 90 - 2Q. Repeat part a.
c)
Now the firm faces demand of
P = 70 - 2Q. Repeat part a.
d)
For each of the answers to (a), (b), and (c), what is the elasticity of demand at the
equilibrium quantity? Is demand elastic, inelastic or unit elastic? Are you
surprised?
2.
Imagine that a tax of $10 per unit is levied on the monopoly firm in each of the three
cases from Question 1.
By how much will the market price paid by buyers (including the consumers’ share
of the tax) rise in each case?
(a)
(b)
How much is the buyers’ share and the sellers’ share of the tax in each case?
26
ECMA04H
TUTORIAL #9 (WEEK 10)
QUESTIONS
1.
Output in an industry can be produced most efficiently in plants producing q = 5
with LRAC (also known as LAC) = $12. Demand in the industry is given by P = 32 0.1Q.
a)
Determine long run output and price and number of firms in a competitive industry
(assume that each firm operates only one plant). What is the overall benefit to
society from the production of the good? What is the overall cost to society from the
production of the good? What is the (net) gain to society (G.T.S.) from the
production of this good?
b)
Now a single firm monopolizes the industry and bars entry by other firms.
Determine long run price and output, the number of plants operated by the firm, and
the firm's profits. What is the gain to society (G.T.S.) from the production of the
good? What is the efficiency loss due to monopoly?
27
ECMA04H
TUTORIAL #10 (WEEK 11)
QUESTIONS
1. There are two bus companies in the Land of Narnia; these are the only emitters of
carbon monoxide pollution. Both bus companies have buses that produce
considerable amounts of pollution; in fact, with no government intervention, each
bus company will produce 200 tonnes of carbon monoxide emissions. Because one
company has old buses and one company has newer buses, the marginal cost of
reducing (i.e., abating) this pollution is different for these two companies. For Firm
#1, the marginal cost of abatement is given by MCA1 = 5A1. For the company with
the newer buses (Firm #2), the marginal cost of abatement is given by MCA2 = 2.5A2.
In each case, MCA is measured in dollars per tonne of pollution and A measures the
amount of abatement of pollution. You may assume there are no “fixed” costs of
abatement, so the marginal costs can be summed to find total costs of abatement.
The marginal benefit of abatement measures the social costs avoided when pollution
is abated. Normally, the marginal benefit of abatement is assumed to fall as
abatement increases. In this case, for simplicity, we assume that MBA = $250,
measured in dollars per tonne.
(a) What is the optimal number of tonnes by which emissions of carbon monoxide
should be reduced in the Land of Narnia? How much will pollution be reduced
by each of these companies?
(b) If the Land of Narnia passes a law ordering each of these two firms to reduce its
pollution by half of the optimal amount of pollution reduction calculated in part
(a) (i.e., each company does its “fair” share of total pollution reduction), what will
be the total cost of reducing (i.e., abating) pollution to this level in Narnia?
(c) Imagine that instead of passing a law that dictates the amount of pollution that
should be reduced, the land of Narnia sets a fine (or fee) for polluting. What
would be the optimal fee per tonne of pollution? What would be the cost of
reducing pollution using this fee?
(d) What would happen if the government issued tradeable emissions permits to the
two companies? Assume that the government gives these permits away for free,
and that it issues permits allowing each of these firms to emit 125 tonnes of
carbon monoxide.
2.
In a small and isolated community, there are 20 consumers, each of whom have the
following utility for mosquito control during the summer:
U = 20X - 0.5X2
where X is the amount of mosquito control purchased in aggregate by members of
the community, and U is the utility measured in dollars for each individual when X
units of mosquito control are purchased (that is, all members of the community
derive benefit from mosquito control, whether or not they actually purchase it
themselves). Mosquito control costs $100 per unit.
28
(a) Explain why no individual acting alone will purchase any units of mosquito
control.
(b) Add up the individual utilities to obtain the aggregate utility obtained by the
community from the purchase of mosquito control. If the community acts together,
how much mosquito control will the community demand at a price of $100? If each
individual pays 1/20 of the cost per unit for mosquito control, show that each
individual will be made better off by acting collectively, rather than individually.
(c) Explain in words why the market fails to come up with the optimal solution in
this case.
(d) In real life, will the community ever act to overcome this market failure? When is
this likely to occur? When is this unlikely to occur?
29
ECMA04H
TUTORIAL #11 (WEEK 12)
QUESTIONS
1.
In Canada, the production of 1 unit of both grain and clothing each require 1 unit of
labour; in the U.S.S.R., 1 unit of grain is produced by 10 units of labour and 1 unit of
clothing by 4 units of labour. Canada has 20 units of labour; the U.S.S.R. has 160
units of labour.
a)
Derive the PPF of each country and indicate what each will produce and consume
given autarchy. What is the relative price of the goods in each country under
autarchy?
b)
Which country has an absolute and comparative advantage in each good? Under
free trade, who will export what? If both economies are decentralized, what
mechanism will lead to this result? If we call PG/C the number of units of C that trade
internationally for 1 unit of G (thus PG/C is the relative price of G), what can we say in
general about the value of PG/C after trade begins?
c)
Show that each country is made better off by trade. Do this by means of an invented
example, and by drawing Production Possibilities Frontiers and Consumption
Possibilities Frontiers for each country. (Can you also show this indirectly by
showing that there are efficiency losses due to imposing tariffs on trade?)
2.
A country consumes wheat, some of which is produced domestically and some of
which is imported. The domestic Demand and Supply curves are given by:
domestic Demand: P = 100 - Q
domestic Supply: P = 10 + ½Q
Wheat is also available for unlimited import at a price of $20 per unit.
a.
In the absence of any government interference, how much wheat will be
produced, imported and consumed in the country?
b.
Suppose now that a 50% tariff is placed on the importing of wheat. How much
wheat will be produced, imported and consumed in the country?
c.
We want to measure the inefficiency of the tariff. To do this, we must compare
the net benefit to society with and without the tariff. Without the tariff, the net
benefit is just the sum of producers' and consumers' surpluses. With the tariff, we
must also include any revenues earned by the government from tariff revenue
(which could be used to benefit residents of the country). In each case, derive net
benefit. What is the loss associated with the tariff?
30
STUDY OBJECTIVES AND STUDY QUESTIONS
WEEK 1 (CLASSES ON SEPT 8, SEPT 10)
Topics: The definition of economics; the role of scarcity, of economic resources and of
choice. Opportunity cost defined and explained. The production possibilities
model as a way of thinking about scarcity, choice and opportunity cost. The role
of markets. Definition of microeconomics and macroeconomics.
Recommended Reading: part of Chapter 1 “Economic Issues and Concepts” (pp. 2-12).
Also, there is much useful material about how economists use theory, data,
functions and graphs in Chapter 2 “How Economists Work” (pp. 24-44).
Study Objectives
1.
To learn and comprehend the definition of economics.
2.
To learn the meaning of opportunity cost and to be able to apply this analytical
concept in explaining economic behaviour.
3.
To determine the specific meaning of the opportunity cost concept in the context
of a Production Possibilities model of an economy; to be able to calculate
opportunity cost mathematically.
4.
To understand the meaning of concepts such as scarcity, efficiency, inefficiency,
growth, opportunity cost tradeoffs, attainable and unattainable regions, within
the context of a simple Production Possibilities model of the economy.
5.
To begin to grasp the role of markets in making economic decisions in a market
economy.
6.
To distinguish clearly between the types of questions and issues addressed by
microeconomics and macroeconomics.
31
Study Questions
1-3
An economy can produce two goods, X and Y. The equation of the Production
Possibilities Frontier for this economy is given by:
Y = 144 - 10X - X2, 0 ≤ X ≤ 8, Y ≥ 0
Questions 1, 2 and 3 concern this economy.
1.
When the economy is producing 8 units of X and 0 units of Y, what is the
opportunity cost of Y?
(A) 0 units of Y per unit of X.
(B) 14 units of Y per unit of X.
(C) 26 units of Y per unit of X.
(D) 69 units of Y per unit of X.
(E) 90 units of Y per unit of X.
(F) 100 units of Y per unit of X.
(G) 102 units of Y per unit of X. (H) 130 units of Y per unit of X.
(I) 144 units of Y per unit of X.
(J) 1/144 units of X per unit of Y.
(K) 1/102 units of X per unit of Y. (L) 1/90 units of X per unit of Y.
(M) 1/69 units of X per unit of Y. (N) 1/36 units of X per unit of Y.
(O) 1/26 units of X per unit of Y. (P) 1/14 units of X per unit of Y.
(Q) 0 units of X per unit of Y.
(R) none of the above
2.
When the economy is producing 7 units of X and 20 units of Y, what is the
opportunity cost of X?
(A) 0 units of Y per unit of X.
(B) 14 units of Y per unit of X.
(C) 26 units of Y per unit of X.
(D) 69 units of Y per unit of X.
(E) 90 units of Y per unit of X.
(F) 100 units of Y per unit of X.
(G) 102 units of Y per unit of X. (H) 130 units of Y per unit of X.
(I) 144 units of Y per unit of X.
(J) 1/144 units of X per unit of Y.
(K) 1/102 units of X per unit of Y. (L) 1/90 units of X per unit of Y.
(M) 1/69 units of X per unit of Y. (N) 1/36 units of X per unit of Y.
(O) 1/26 units of X per unit of Y. (P) 1/14 units of X per unit of Y.
(Q) 0 units of X per unit of Y.
(R) none of the above
3.
We can tell that this economy has increasing opportunity costs because:
(A) d2Y/dX2 > 0
(B) dY/dX < 0
(C) d2Y/dX2 < 0
(D) dY/dX > 0
(E) all of the above
(F) none of the above
(G) this economy does not have increasing costs.
32
4. An economy can produce two goods, X and Y. The equation of the production
possibilities frontier for this economy is given by the following equation:
Y = 36 - 0.25(X+1)2
for 0≤X≤11
a)
a government official tells you that he hopes that the economy will produce 4
units of X and 31 units of Y. Is this a reasonable or unreasonable estimate, and
why?
b)
when the economy is producing 9 units of X efficiently, what is the opportunity
cost (measured in units of Y given up) of getting a small amount more of X?
c)
What is the general formula for measuring the opportunity cost of X in this
economy?
d)
Calculate the opportunity cost of X, when X = 1.
e)
Calculate the opportunity cost of X when X = 10.
f)
Explain, in an economic sense, why there is a difference in the opportunity cost
measured at different places along the PPF.
g)
How would you determine using calculus whether or not a PPF demonstrated
increasing costs?
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ANSWERS TO STUDY QUESTIONS: WEEK 1
1.
The correct multiple choice answer is (O). If Y = 144 - 10X - X2, then dy/dx = -10 2X. By the inverse function rule, dx/dy = 1/(-10 -2X). The opportunity cost of Y
is -dx/dy, which is 1/(10 + 2X). The point X=8, Y=0 is on the production
possibilities frontier, because it satisfies the equation of the PPF. Therefore, the
opportunity cost of Y is 1/(10 + 16) = 1/26 units of X per unit of Y.
2.
The correct answer is (A). Normally, the opportunity cost of X is given as -dy/dx.
However, the point X=7, Y=20 lies inside the PPF, which we can confirm by
substituting for X in the equation Y = 144 - 10X - X2. Along the PPF, when X = 7,
Y = 25. Inside the PPF, the opportunity cost of X is zero, because no units of Y
need be given up to obtain more X.
3.
The correct answer is (C). When the second derivative is negative, the PPF curve
has a bowed-out shape (concave to the origin). In this case, the opportunity cost
of X increases as more X is produced, or the opportunity cost of Y increases as
more Y is produced. This kind of economy is said to have increasing costs.
4. (a) If X = 4, then the maximum amount of Y that can be produced is
Y = 36 - 0.25(4 + 1)2 = 29.75. The estimate by the government official is therefore
in the unattainable region and therefore unreasonable.
(b)
The opportunity cost of X is -(dY/dX). Call Z = (X + 1), then use the chain rule to
find opportunity cost: -(dY/dX) = -(dY/dZ x dZ/dX). Since dY/dZ = -0.5Z and
dZ/dX = 1, -(dY/dX) = -[-0.5(X + 1)] = 0.5X + 0.5. When we evaluate this
expression at X = 9, we find the opportunity cost of X is 0.5(9) + 0.5 = 5.
(c)
The general formula for measuring the opportunity cost of X is -(dY/dX).
(d)
When X = 1, the opportunity cost of X is 0.5(1) + 0.5 = 1.
(e)
When X = 10, the opportunity cost of X is 0.5(10) + 0.5 = 5.5.
(f)
If the second derivative is negative, it tells us that opportunity costs vary along
the PPF because there are increasing costs of producing X as more of it is
produced (and increasing costs of producing Y, as more of Y is produced). In
other words, more units of Y have to be given up to get an extra unit of X as the
amount of X produced increases. Increasing costs are a reflection of the imperfect
substitutability of resources in different uses (resources are somewhat specialized,
rather than being all-purpose). A linear PPF would imply that resources are
perfectly substitutable for one another at some rate.
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(g)
Check the second derivative of the PPF function. The second derivative
(d2Y/dX2) tells us how the slope of the PPF changes as X increases. To show that
the opportunity cost of X is increasing, we must show that the second derivative
of the PPF function is negative. For the particular PPF analyzed in this question,
dY/dX = -0.5X - 0.5. Therefore, d2Y/dX2 = -0.5, which is negative for all values of
X. Therefore costs are increasing in X. (We could, of course, look at dX/dY [the
opportunity cost of Y] and d2X/dY2 [the second derivative of X, with respect to Y]
to show that costs are also increasing in Y).
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