How to Build an Economic Model in Your Spare Time

                                            by

                                      Hal R. Varian
                                        UC Berkeley

                                      December 1994
                              Current version: June 11, 1997

Abstract.  This is  an essay for Passion  and Craft:  Economists at Work,  edited  by Michael
Szenberg, University of Michigan Press, 1997.

Keywords.

Address.     Hal  R.  Varian,  Dean,  School  of  Information  Mangement  and  Systems,  UC

                                                             ~
Berkeley. Web page http://www.sims.berkeley.eduhal
                    How to Build an Economic Model in Your Spare Time

                                            Hal R. Varian

Most of my work in economics involves constructing theoretical models. Over the years, I
have developed some ways of doing this that may be worth describing to those who aspire
to practice this art.  In reality the process is much more haphazard than my description
would suggest---the model of research that I describe is an idealization of reality, much
like  the economic  models  that  I create.    But  there is  probably enough connection  with
reality to make the description useful---which I hope is also true for my economic models.

1.  Getting ideas

The first step is to get an idea.  This is not all that hard to do.  The tricky part is to get a
good idea. The way you do this is to come up with lots and lots of ideas and throw out all
the ones that aren’t good.

    But  where to  get ideas,  that’s  the  question.  Most  graduate students  are convinced
that  the  way  you  get  ideas  is  to  read  journal  articles. But  in  my  experience  journals
really aren’t a very good source of original ideas. You can get lots of things from journal
articles---technique, insight, even truth.  But most of the time you will only get someone
else’s ideas. True, they may leave a few loose ends lying around that you can pick up
on, but the reason they are loose is probably that the author thought about them a while
and couldn’t figure out what to do with them or decided they were too tedious to bother
with---which means that it is likely that you will find yourself in the same situation.

    My suggestion is rather different: I think that you should look for your ideas outside
the academic journals---in newspapers, in magazines,  in conversations,  and in TV and
radio programs.     When you read the newspaper, look for the articles about economics
                                                                                             1
stimulating: there’s nothing like a fallacious argument to stimulate research.
    Conversations, especially with people in business, are often very fruitful. Commerce
is conducted  in many ways,  and  most of them have never been subjected to  a serious
economic analysis.  Of course you have to be careful not to believe everything you hear-
--people in  business usually  know a set of rules that  work well for running their own
business, but they often have no idea of where these rules come from or why they work,
and this is really what economists tend to find interesting.
    In many cases your ideas can come from your own life and experiences.  One of my
favorite pieces of my own work is the paper I wrote on ‘‘A Model of Sales’’. I had decided
to get a new TV so I followed the ads in the newspaper to get an idea of how much it
would cost. I noticed that the prices fluctuated quite a bit from week to week. It occurred
to me that the challenge to economics was not why the prices were sometimes low (i.e.,
during sales) but why they were ever high. Who would be so foolish as to buy when the
price was high since everyone knew that the item would be on sale in a few weeks? But
there must be such people, otherwise the stores would never find it profitable to charge
a high price.     Armed with this  insight,  I was able to  generate a model  of sales.              In my

model there were two kinds of consumers:  informed consumers who read the ads and

uninformed consumers who didn’t read the ads.                The stores had sales in order to price

discriminate between the informed and uninformed consumers.

    Once I developed the model I had a research assistant go through a couple of years’
worth of the Ann Arbor News  searching for the prices of color TVs.  Much to my delight
the general pattern of pricing was similar to that predicted by the model. And, yes, I did
manage to get a pretty good deal on the TV I eventually bought.

2.  Is your idea worth pursuing?

So let’s assume (a favorite word of economists) that you have an idea. How do you know
if it is any good? The first test is to try to phrase your idea in a way that a non-economist
can understand. If you can’t do this it’s probably not a very good idea. If you can phrase

  1
    But which sources to read?  I read the New York Times, the  Wall Street Journal and the Economist; these are
probably good places to start.

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it in a way that a noneconomist can understand, it still may be a lousy idea, but at least
there’s hope.
    Before you start trying to decide whether your idea is correct, you should stop to ask
whether it is interesting. If it isn’t interesting, no one will care whether it is correct or not.
So try it out on a few people---see if they think that it is worth pursuing.  What would
follow from this idea if it is correct? Would it have lots of implications or would it just be
a dead end?  Always remember that working on this particular idea has an opportunity
cost---you could be spending your time working on a different idea.  Make sure that the
expected benefits cover that opportunity cost. One of the primary purposes of economic
theory is to generate insight. The greatest compliment is ‘‘Ah! So that explains it!’’ That’s
what you should be looking for---forget about the ‘‘nice solid work’’ and try to become a

Wizard of Ahs.

3.  Don’t look at the literature too soon

The  first  thing  that  most  graduate  students  do  is  they  rush  to  the  literature  to  see  if
someone else had this idea already. However, my advice is to wait a bit before you look
at the literature. Eventually you should do a thorough literature review, of course, but I
think that you will do much better if you work on your idea for a few weeks before doing
a systematic literature search. There are several reasons for delay.
    First, you need the practice of developing a model.  Even if you end up reproducing
exactly something that is in the literature already you will have learned a lot by doing
it---and you can feel awfully good about yourself for developing a publishable idea! (Even
if you didn’t get to publish it yourself
4.  Building your model

So let’s skip the literature part for now and try to get to the modeling. Lucky for you, all
economics models look pretty much the same.  There are some economic agents.                        They
make choices in  order to advance  their objectives.           The choices  have to satisfy various
constraints  so there’s something that adjusts to make all these choices  consistent.               This
basic structure suggests a plan of attack: Who are the people making the choices?  What
are the constraints they face?  How do they interact?  What adjusts if the choices aren’t
mutually consistent?
    Asking questions like this can help you to identify the pieces of a model. Once you’ve
got a pretty good idea of what the pieces look like, you can move on to the next stage.
Most students think that the next stage is to prove a theorem or run a regression.                   No!
The next stage is to work an example. Take the simplest example---one period, 2 goods, 2
people, linear utility---whatever it takes to get to something simple enough to see what is
going on.
    Once you’ve got an example, work another one, then another one. See what is common
to your examples. Is there something interesting happening here? When your examples
have given you an inkling of what is going on, then you can try to write down a model.
The critical advice here is KISS: keep it simple, stupid. Write down the simplest possible
model you can think of, and see if it still  exhibits some interesting behavior.  If it does,
then make it even simpler.
    Several years ago I gave a seminar about some of my research.  I started out with a
very simple example.  One of the faculty in the audience interrupted me to say that he
had worked on something like this  several years ago,  but his model  was ‘‘much more
complex’’. I replied ‘‘My model was complex when I started, too, but I just kept working
on it till it got simple!’’
    And that’s what you should  do:  keep at it till  it  gets simple.         The whole point  of a
model  is to  give a simplified  representation of reality.         Einstein  once said  ‘‘Everything
should be as simple as possible
    This takes a surprisingly long time---there are usually lots of false starts, frustrating
diversions, and general fumbling around.  But keep at it!  If it were easy to do, it would
have already been done.

5.  Generalizing your model

Suppose that you’ve finally made your model as simple as possible.  At this point your
model is probably too simple to be of much interest: it’s likely just an example or a special
case. But if you have made your model as simple as possible, it will now be much easier
to see how to generalize it since you know what the key pieces are that make the model

work.

    Here is where your education can be helpful. At last you can use all those techniques
you  learned  in  graduate  school.  Most  of  the  time  you  were  a  student  you  probably
studied  various  canonical  models:   things  like  consumer  choice,  and  producer  choice,
general equilibrium, game theory and so on. The professor probably told you that these
were very general models that could encompass lots of special cases.
    Well,  it was all true. Over the last fifty years economists  have come up with some
very general principles and models.     Most likely your model is a special case of one of
these general models.    If so you can immediately apply many of the results concerning
the general model to your special case, and all that technique you learned can help you
analyze your model.

6.  Making mistakes

This process---simplify to get the result, complexify to see how general it is---is a good
way to understand your model.  Most of the time that I spend modeling is involved  in
this back-and-forth process. Along the way, I make a lot of mistakes. As Piet Hein puts it:

    The road to wisdom? We’ll it’s plain
    and simple to express:
    Err
    and err
    and err again
    but less
    and less

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    and less.

    This back-and-forth iteration in building a model is like sculpting:  you are chipping
away a little bit here, and a little bit there, hoping to find what’s really inside that stubborn
block of marble. I choose the analogy with sculpting purposely: like sculpture most of the
work in building a model doesn’t consist of adding things, it consists of subtracting them.
    This is the most fun part of modeling, and it can be very exciting when the form of the
idea really begins to take shape.  I normally walk around in a bit of a daze at this stage;
and I try not to get too far away from a yellow pad. Eventually, if you’re lucky, the inner
workings of your model will reveal itself:  you’ll see the simple core of what’s going on
and you’ll also understand how general the phenomenon really is.

7.  Searching the literature

At this point you can start doing your literature search. Tell your professors about what
you’ve discovered---nine times out of ten they’ll tell  you to look in the ‘‘1983 AER ’’ or
‘‘Econometrica 77’’ or some textbook (maybe even one of mine). And lots of the time they’ll
be right. You’ll look there and find ‘‘your’’ model---but it will be much better done, much
more fully developed, and much clearer.
    Hey, no one said research would be easy. But this is a point where you really have a
chance to learn something---read the article(s) carefully and ask yourself ‘‘Why didn’t I
do that?’’ If someone started with the same idea as you and carried it further, you want
to see what you missed.
    On  the  other  hand,  if  you  really  followed  the  advice  I  gave  you  above  to  keep  it
simple,  you  may have  come  up  with  something  that  is  much  clearer than  the  current
treatments. Or, maybe you’ve found something that is more general. If so, you may have
a worthwhile insight. Go back to your advisor and tell him or her what you have found.
Maybe you’ve got a new angle on an old  idea that is worth further exploration.              If so,
congratulations---you would never have found this if you did the literature search right

away.

                                                 6
    Maybe what you’ve figured out is not already in the literature. The next possibility is
that you are wrong.  Maybe your analysis isn’t right, maybe the idea is just off the wall.
This is where your advisor can play a big role.       If you’ve really made your analysis as
simple as possible, it is a) less likely to contain an error, and b) any errors that remain will

be easier to find.

    This  brings me  to  another  common  problem.      When you’ve  worked  on  a  topic  for
several months---or even several weeks---you tend to lose a lot of perspective
on it.  But most people don’t have to listen to you.  They don’t have to read your paper.
They won’t even have to glance at the abstract unless they have a reason to.
    This comes as a big shock to most graduate students.            They think that just because
they’ve put a lot of work and a lot of thought into their paper that the rest of the world
is  obliged  to  pay  attention  to  them.  Alas,  it  isn’t  so. Herb  Simon  once  said  that  the
fundamental scarcity in the modern world was scarcity of attention---and brother, is that
the truth. There are demands for everybody’s attention, and if you want someone to pay
attention to you, you have to give them a reason to do so. A seminar is a way to get them
to pay attention, so be sure to exploit this opportunity to get people to listen to you.
    The useful thing about a seminar is that you get immediate feedback from the audience.
An audience won’t put up with a lot  of the things  that authors try to write in papers:
turgid prose, complex notation, and tedious details. And, believe it or not, readers won’t
put up with these things either! The trick is to use the seminar to get all those things out
of your paper---that way, it may actually get read.

Controlling the audience

I’ve seen it claimed that one of the greatest fears that most people have is speaking before
a group. I imagine that most assistant professors have this problem, but after many years
of giving lectures before several hundred students it goes away.
    In fact, lecturing can become downright addictive (as my family often reminds me.)
As the mathematician R. H. Bing once said:  ‘‘When I was young, I would rather give a

lecture on mathematics than listen to one. Now that I am older and more mature I would

rather give two lectures on mathematics than listen to one.’’  Giving lectures is a bit like
eating oysters.   Your first one requires some courage,  but after you develop a taste for
them, it can be hard to stop.
    There are three parts to a seminar: the introduction, the content, and the conclusion.
My advice  about introductions  is  simple:  don’t  have one.       I have seen many seminars
ruined by long, pretentious,  contentless introductions.        My advise:  say a few sentences
about the big picture and then get down to business:  show them what you’ve got and
why it’s important.  The primary reason to get down to business right away is that your

                                                  8
 audience will only remember about twenty minutes of your talk---and that is usually the
first twenty minutes.    So make sure that you get some useful information into that first
twenty minutes.
    As  for  conclusions,  the  most  common  problem  is  letting  the  seminar  trail  off  into
 silence.  This  can  ruin  a  good  talk. I  always  like  to  spend  the  last  couple  of  minutes
 summarizing  what  I  accomplished  and  why  the  audience  should  care.          After  all,  this
 is  what  they  will  walk  away  with,  so  you  might  as  well  tell  them  what  they  should
remember rather than make them figure this out for themselves.
    Nowadays everyone seems to use overheads for their lectures.  The downside of this
 is that the seminar isn’t very spontaneous---but the upside is that the seminar is usually
better organized.    My advice is to limit  yourself to one or two slides for a introduction
 and one for a conclusion. That way you will be forced to get to your  contribution sooner
rather than later.  And make your overheads big; use large type and don’t try to say too

much on each one.

    There are two things to avoid in your presentation: don’t let your audience go to sleep,
 and don’t let them get too lively.  You want the audience to hear what you have to say.
 They won’t hear your message if they are sleeping, and they won’t hear your message if
they are talking more than you are. So don’t loose control of your seminar!
    The key to maintaining control is to establish credibility early on.  The way to do is
to go into great detail in the presentation of your first result---a theorem, a regression, a
 diagram, whatever.  Spell out each aspect of your result in excruciating detail so no one
 can possibly misunderstand. When you do this you will certainly get questions like ‘‘Will
this generalize to n agents?’’ or ‘‘Have you corrected for heteroskedasticity?’’
    If you know the answer to the question, go ahead and answer it. If you don’t know the
 answer---or the questions is totally off the wall---say ‘‘That’s a good question; let me come
back to that at the end of the seminar.’’ (Of course you never will.) Don’t get sidetracked:
the point of going through the initial result in great detail is to establish credibility.
    Once you’ve presented your result and you see that the audience has understood the
point---their heads are nodding but not nodding off---you can go on to the generalizations
 and elaborations. If you’ve done a good job at establishing your credibility initially now

                                                  9
 audience will only remember about twenty minutes of your talk---and that is usually the
first twenty minutes.    So make sure that you get some useful information into that first
twenty minutes.
    As  for  conclusions,  the  most  common  problem  is  letting  the  seminar  trail  off  into
 silence.  This  can  ruin  a  good  talk. I  always  like  to  spend  the  last  couple  of  minutes
 summarizing  what  I  accomplished  and  why  the  audience  should  care.          After  all,  this
 is  what  they  will  walk  away  with,  so  you  might  as  well  tell  them  what  they  should
remember rather than make them figure this out for themselves.
    Nowadays everyone seems to use overheads for their lectures.  The downside of this
 is that the seminar isn’t very spontaneous---but the upside is that the seminar is usually
better organized.    My advice is to limit  yourself to one or two slides for a introduction
 and one for a conclusion. That way you will be forced to get to your  contribution sooner
rather than later.  And make your overheads big; use large type and don’t try to say too

much on each one.

    There are two things to avoid in your presentation: don’t let your audience go to sleep,
 and don’t let them get too lively.  You want the audience to hear what you have to say.
 They won’t hear your message if they are sleeping, and they won’t hear your message if
they are talking more than you are. So don’t loose control of your seminar!
    The key to maintaining control is to establish credibility early on.  The way to do is
to go into great detail in the presentation of your first result---a theorem, a regression, a
 diagram, whatever.  Spell out each aspect of your result in excruciating detail so no one
 can possibly misunderstand. When you do this you will certainly get questions like ‘‘Will
this generalize to n agents?’’ or ‘‘Have you corrected for heteroskedasticity?’’
    If you know the answer to the question, go ahead and answer it. If you don’t know the
 answer---or the questions is totally off the wall---say ‘‘That’s a good question; let me come
back to that at the end of the seminar.’’ (Of course you never will.) Don’t get sidetracked:
the point of going through the initial result in great detail is to establish credibility.
    Once you’ve presented your result and you see that the audience has understood the
point---their heads are nodding but not nodding off---you can go on to the generalizations
 and elaborations. If you’ve done a good job at establishing your credibility initially now

                                                  9
    **if you don’t grab them in the first page, they won’t read it

    I  create  a  notes  file  like  this  when  I  first  start  to  work  on  a  topic---I  jot  down  the
initial ideas I have, which are usually pretty sketchy.  In the following days and weeks
I occasionally  take a look at this outline.         When I look at it I move things around,  add
material and so on. I rarely take anything out completely---I just move material to the end
of the file. After all, I might want those notes again.
    After organizing these ideas for several weeks or months I am ready to write the first
draft of the paper. I usually try to do this in a day or two, to keep it all fresh. I normally
put the notes in one window and the paper in the other and write the paper while I refer
back and update the notes to keep them in sync with the paper.
    Once the paper is written I put it aside for a couple of weeks. Papers need to age like
fine cheese---it’s true that mold might develop,  but the flavor is often enhanced.                  More
importantly,  it gives your subconscious  mind a chance to work on the idea---maybe it
will come up with something your conscious mind has missed.
    When I come back to the paper I try to read it with a fresh mind, like someone who
has never seen it before.3       On rare occasions I like what I read,  but usually I have lots

of criticisms.  Whenever I have to pause and think ‘‘what does that mean?’’  I rewrite---I
add more explanation, change the notation, or whatever is necessary to make the paper
clearer. When I’m done with this process I have a first draft.
    I next check this draft into a revision control system.  This is a piece of software that
keeps track of the revisions of a paper.          It documents all of the changes you make and
allows you to restore any previous version of a paper.                I use the Unix utility  rcsbut I
know there are many other systems available.                Revision  control  systems are especially
valuable if you are working with a coauthor since they keep track of which person made
which changes when.
    I then repeat the process: let the paper sit for a few more weeks or months, then come
back to it, read it with a fresh mind and revise it accordingly.

  3
    This is much easier once you reach middle age.

                                                     11
    It is  particularly  useful to do  a revision  right after you give  a seminar.         Remember
those notes I told you to write after your seminar ended?  Sit down with the paper and
go over the questions the audience had and the suggestions they made. Can you answer
their questions in your paper? Can you incorporate their suggestions? Be sure to modify
the notes/outline/slides for your talk when you incorporate the audience’s suggestions.

Bibliographic software

One  very  useful  computer  tool  is  a  bibliographic  system.        This  is  a  piece  of  software
designed  to  managed  a  list  of  references.       There  is  a  master  database  of  references
that  is  stored  on  your  computer.      You  assign  a  key  to  each  article  like  Arrow70 or
ArrowRisk.  When you want to refer to a paper you use the key, by saying something
like
10.  The structure of the paper

There’s an old joke about academic papers.  They are all supposed to have three parts.
The  first  part,  everyone  can  understand.     The  second,  only  a  handful  of  readers  can
understand.    The last  part no one  can understand---that’s how the readers know it’s  a
serious piece of work!

    The big mistake that authors make these days is to leave out the first part of the paper-
--that part that everyone can understand. But the introduction is the most important part
of the paper. You’ve got to grab the reader on the first page. No matter how brilliant the
rest of the paper is, it won’t be noticed if no one reads it.  And no one will read it if you
don’t get their interest in the first few paragraphs. If you really know what your paper is
about, you shouldn’t find it hard to explain this to your readers in a couple of paragraphs.

    My  basic  advice  is  to  make  your  paper look  like  your  talk.   Get  to  the  point. Use
examples.    Keep  it  simple.   Tell  people  why  what  you  did  is  important  after  you’ve
done it.  Put the tedious stuff in the appendix.       End with a summary of what you have
accomplished.     If you have really written a good paper, people won’t have to listen  to
your seminar to find out what you have done: they can just read it in your paper.

11.  When to stop

You  can  tell  when  your  work  is  getting  ready  for  publication  by  the  reactions  in  the
seminars:   people  stop  asking  questions.    (Or  at  least,  the  people  who  have  read  your
paper stop asking questions.)  If you’ve followed my advice, you’ve already asked their
questions---and answered them---in your paper.

    Once you’ve made your point,  stop.       Lots of papers drag on too long.      I said earlier
that people only remember about 20 minutes of your seminar (if you’re lucky), and they
only remember about 10 pages of your paper.  You should be able to say most of what
you want to say in that length.

    Once your paper is written, you can submit it to a journal.  I don’t have too much to
say about this;  Dan Hamermesh has written a nice article that describes the procedure

                                                 13
better than I can.    4  All I can say is to echo his advice that you go over the article with a

fine tooth comb before sending it in. Nothing turns off an editor or a referee more than to
find typos, missing references and sloppy editing in the articles they deal with.

12.  Writing textbooks

Most of what I’ve had to say so far has to do with writing articles. But I suppose I really

                                                                                         5
should say a bit about the other kind of writing I’ve done: textbooks.
     My first text, Microeconomic Analysis  really wasn’t planned;  it just happened.  When
I first started my professional career at MIT in 1973 I was asked to teach the first year
graduate  micro  course.         The text,  such  as  it  was,  consisted  of about  20  pages of  notes
written by Bob Hall, maybe 40 pages of notes from Dan McFadden and Sid Winter, and a
few journal articles. The notes were awfully sketchy, and the journal articles were much
too advanced for first year students. So I had to write my own notes for the students.
     The first year I wrote about 50 pages; the next year another 50, and the year after that
another 50. The students who used them were great. They read them carefully and told
me what was wrong:  where the obscurities were, where the errors were, what was too
advanced, and what was too simple. I owe much of the success of that book to the fact it
was class tested before a highly critical audience.
     During this period I happened to meet Richard Hamming, an electrical engineer who
had written several texts. He gave me a key piece of advice: ‘‘Get together the problems
that you want your students to be able to solve after they’ve read your book---and then

write the book that will teach them how to solve them.’’

     This was great advice.  I followed it to some degree with the graduate text, but later,
when  I  wrote  the  undergraduate  text,  I  followed  it  religiously---but  more  about  that
below.6

  4
    Daniel  S.  Hamermesh,  ‘‘The Young  Economist’s  Guide  to  Professional  Etiquette’’,  Journal  of  Economic
Perspectives, 6: 1, 169--180.

  5
     The reader may recall Disraeli’s warning: ‘‘An author who speaks about his own books is almost as bad as
a mother who talks about her own children.’’

  6
     The  general  principle that  I followed  (and  still follow) with  the graduate  text is  that  it should give the
student the information they need to know to read a microeconomics paper in the American Economic Review.

                                                        14
    One  day  a  publisher  came  into  my  office  and  asked  (as  they  often  do)  ‘‘Are  you
writing a book?’’ I said that would be a silly thing for an assistant professor to do---but as
a matter of fact, I did have some class notes that I had been working on for a few years.
    Next thing I knew, I had several publishers interested in my notes. I spent a semester
at Berkeley in 1977 and used that opportunity to hammer them into shape. Much to my
surprise the notes eventually become a book and ended up being very widely used. I did

a second edition in 1983 and I should have done a revision in 1987 or so---but instead I

decided to write an undergraduate text.
    I wanted to write an undergraduate book because I was fed up with the books I had
been  using.    I  had  tried  several  different  ones,  but  couldn’t  find  any  I  really  liked.       I

remember one semester I sat down and tried to write a midterm exam---but the book I

had been using was so vapid that I couldn’t think of any problems that the students could
solve using the tools that had been presented in the book! At that point I figured I could
produce something better.
    About the same time one of my undergraduates had picked up a workbook by Marcia
Stigum called, I believe, Problems in Microeconomics.  The student found this very helpful
in understanding the concepts of economics, and I remembered what Hamming had told
me about how to write a textbook.  So I asked my colleague Ted Bergstrom if he would
like to work with me to  create a serious  workbook.7               Ted created problems as the text

was being written, and I had to make sure that the text contained everything necessary
to solve the problems he created.  I created problems too, but those were automatically
coordinated  with the textbook---the external stimulus imposed  by Ted’s problems was
much more important in shaping the content of the book.                    If the students weren’t able
to solve the problems, I had to add explanations to the text until they could---and if we
couldn’t create a problem to illustrate some point, the point probably wasn’t important
enough to put in the text.

Every now and then I go through a few issues of the AER and note topics that should go in the next edition of
the book.

  7
    As it turned out, it wasn’t quite as serious as I had expected---in fact, I think that it is quite funny, but that
is due to Ted’s unique sense of humor rather than my intentions.

                                                     15
    It’s a pity that most workbooks are created as afterthoughts.  Creating the workbook
really should be an integral part of the writing process, as Hamming suggested. You want
the students to be able to use the material you teach them, so the first order of business
is to figure out what it is that you want them to be able to do.  The latest buzzword in
education is ‘‘learning by doing’’ but as far as I’m concerned that’s always been the only

way to go.

    The undergraduate text turned out to be pretty successful as well. And the workbook
has ended up selling two or three times as much as any of its competitors---which goes to
show that there still is a market for a quality product in the textbook market.

13.  Summary

I said  that every talk should  have a summary---so I suppose I have to follow my own
advice. Here are the points to take away:

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