Great. So a couple of
housekeeping things. The next homework should
now be available on Sunday night. So I
said that's the night before the exam. It's
only 17 questions you can get done
any time this week. I've turned off the
ability to check your answers this time around.
But remember, it's only a 1% penalty to
like redo them. It's pretty low. Also, please
feel free to use my office hours if you've
got questions. the second thing is with
the exam so a couple of notes about that I
need to be quite frank I was hoping to have
practice questions ready for today when you
know teach a course for the first time and you
don't have material you're already pretty
far behind I will get one out there to you
I know it's important but it'll probably be
on on Wednesday but I'll make sure you do
have practice questions to look at the other
thing is I will have a formula shape but
with only certain formulas on it so things
like the present value and future value time
conversion I expect you to understand that
and the ideas behind it but for something
like cash flows of companies when it comes
to time value money I don't expect you to
know that if there is a question on that I
will give you the the formula, but given that,
I'll try and make sure there aren't questions
on things right, I wouldn't have given
the formula. So that, the expanded version of
cross-price elasticity, which was, yeah, if
this comes up, you're definitely getting a
formula, but for basic elasticities, I'm
not going to give you a formula. Once again,
I'm hoping the way we, you know, went over
it is enough to help you intuitively understand
what's going on. Any questions regarding
the homework or exam? Yeah? In other courses,
yes, I haven't taught this before,
so not for me. So this is the
first time I'm writing an exam
for this course. Yeah, unfortunately,
that's just the way it is. So I'll give
you practice exams, and I'll write
questions in like my style as well, because
the homework questions are the McGraw-Hill
style, and I want to at least give you
some understanding of how I conceive
questions, but yeah, it's just the way the
cookie crumbles here so i i do apologize for
that all right great so what we're going
to do today is finish off the topic of
elasticity and if you remember while we did
all this you know fancy math the reason why i
wanted to go over the math was to show you
where these sort of things came from and
importantly when we convert from total revenue
to marginal revenue which is a thing that
comes up over and over again this marginal
thinking i think it's important to understand
how we get there. However, I want to go back to the basics here. All elasticity is at
the end of the day is how a percentage change
in one thing results in a percentage change
in something else. That's all elasticity
is at the end of the day. That's what
I want to get back to. So at the end of the
first topic, we kind of looked at these
linear regressions where we can put a bunch
of data into this dysfunction, this
regression, and it spits out of prediction how a
one unit change in price will affect the
amount in quantity demanded essentially in
units. Will it increase or decrease it? What
we can actually do here is we can transform
this regression by the function log,
so log or ln, and what this will do is if we
do it to both sides it converts units
into percentages and this gives us the
elasticity. So if you remember from before
when we had our linear demand function we need
to take the slope of whichever variable
we're interested in and multiply it by the
price divided by the quantity. Once we
convert it into the percentages we don't
need to do that anymore. So for example if we
convert both sides of this formula by log
so we convert the y variable here would be
quantity demanded by the log function and the
price of good x by the log function and we
run a regression it will spit out something
like this and what this is is this is the
elasticity of demand so this kind of shows
that a one percent increase in price will
result in a 0.85 percent decrease in quantity
and as we know this is inverse law of demand
so it's negative for that reason and this is
inelastic the absolute value is less than
one so we get all that once we transform
it from logs and in fact every variable
here is the elasticities we're interested in
once we transform it all by the log function
so the own price elasticity of demand
is beta x cross
price elasticity is beta y and the
income elasticity is beta m so for example
an analyst for a major apparel company
estimates that the demand for its raincoats is
given by the log of the quantity demanded
of raincoats equals 10 minus 1.2 log price of
raincoats plus 3 log r which is the daily
amount of rainfall and minus 2 log the
advertising of another company now this is
positive because the the assumption here is
that more rainfall more people want raincoats
to not get drenched by the rain and the
negative sign in front of the advertising of the
other company It seems the more they advertise,
the more they'll buy of good Y, which
means less of good X, which is a competitor.
So, I don't know if anyone saw the Claude
ad last night during the Super Bowl. Did
anyone see it? Is that a nod? Do you want to
remind us what it is? Oh, you? Yeah. Yeah, so there
was a guy doing a workout, and
he has this trainer who's
meant to be an AI, and he's giving him
advice, and all of a sudden he just rattles
off some ad, which is straight out of a
Black Mirror episode, and Claude's pretty
much saying, this is what open ai wants
to do so you can assume that that ad will
probably be relatively effective and if
someone's choosing between claude and jpt
they're more likely to choose claude now
so i think that's a great example of
this negative effect on demand from another
company advertising so what would be the
impact on demand of a 10 increase in the
daily amount of rainfall so we know when we
transform by log this is the elasticity of
rainfall on quantity demanded which is just
this the elasticity is 3 and we know that
equals the percentage change in quantity
demanded divided by the percentage change in
rainfall we've just been given the percentage
change in rainfall 10 increase here
just take it over and we see it's a 30 increase
in the demand for raincoats this is
fairly straightforward once you know this
represents the percentage change everything
falls out of that and yeah once again this
is just our regression table our intercept
the the parameters here on each one so the
slopes nothing's different than before
but what I really want to do today is to show
you briefly how easy and simple it is to run
your own regressions if you get a table
data so before what this is isn't a table
this is a this is an output but if someone
gives you, you know, a document with a bunch
of data with different variables, really
easy to run these regressions that allow
you to predict how one variable changes,
affects another variable, etc. So the two, I
guess, classical ways of doing it are Stata
and R. These are both statistical softwares.
Stata is what economists, like, tend
to use historically. I actually would recommend
not getting them as a Stata if you can
avoid it. I think it's too niche and going
to be a redundant technology soon as well
i put way too much effort in in learning stata
so i i use it um but i think there are
better ways to do things r is an open source
software so anyone can download it it's
used a lot in industry startups data scientists
etc use it and it's complemented well
by a bunch of coding like in python etc what
i'm going to show you today is how easy it
is to run these simple regressions in excel
and there will be a homework question
asking you to do this so this is like just
an ability to practice it and also as I'll
show you today really easy to prompt GPT or
CLAWT or something else actually get these
same answers so I am going to get up my
documents one second so here's a really simple
really simple Excel document here we have
three variables we have demand we have price
we have income and as per usual we want to
see the effect of a of it changing the price
of a good and the changing income, and
how that affects demand. So, given this, if
you're just given this, how do you come up
with these predictions? Pretty straightforward.
So, if you go, if you're
starting at home, if you go to the
data tab, let me just, can I make
this bigger even? Yeah, if you go to
the data tab here, you need to add a
plugin called data analysis. You can
Google how to do that. Gemini will, like,
list the steps for you. Then, you want to
click on data analysis, and you have a bunch
of things here. You just want to click on regression and OK. And then you've got
the input Y range and input X range. The
Y range is the left -hand side of the
equation, the dependent variable, the thing
you're interested in seeing how other things
affect. So that's our demand. It's already
highlighted here. So you can see I've
highlighted this. And for our input
X range here, these are our
independent variables. We're interested
in how one of these change. It
affects demand. So as you can see, I've highlighted both
these comments. and the important thing
here is you need to tick labels because
I've highlighted the first row if you don't
tick labels it's not going to run so it
takes that into account then you just click ok
and then yeah it spits out the regression
here you've got your intercept you've got
your price and income so what this means is a
one unit increase in price or a one dollar
increase in price will reduce demand by 12
units or 12.8 units and as you can see the p-value
here is statistically significant as a
correlation and with income you can see the
same thing but this one isn't statistically
significant i think more interesting than
just being able to do that in excel really
easy if you've got a simple data set but you
can prompt gpt as well here so what i did
here is i just uploaded the excel document
i said can you run a linear regression where
the dependent variable is demand and
independent variables of price and income so the
thing to to be cautious of here is your
languages like you've got to be very i think
um distinct in your instructions and also
make sure your your definitions are correct
for example when i was just doing this just
seeing if it worked i wrote um quantity instead
of demand and if you look here my variable
here is called demand, not quantity. And
it just sped out the wrong answer. So you've
got to be very careful when you're prompting
to make sure that your definitions and
your labels are correct. So as you can see, we get the exact same answer. Demand equals
67.2 minus 12 .82 price plus
0.53 income. So it's the exact
same answer as here. That's good. That's
validation. We have the p-values and
everything as well. The model fit,
you've got that up here as well. Same
thing as in Excel and it also gives you
an interpretation. So it gives you this
one unit increase in price, low is demand
by about 12.8 units. It talks about
the statistical significance as
well, which is great. However, it's really
easy to go even further. So I just said, can
you transform both sides of the regression
equation by lock? And this is exactly
what it did, as you can see.
This is the transformation that
we're interested in. And then it gives
us the elasticities. So now we can say
that a 1% increase in price leads to a
1.6% decrease in demand. And this is
elastic. We know that. The absolute value
of this is above 1. And a 1% increase
in income leads to a 0.84% increase in
demand. So we know it's a normal good,
positive effect. Inelastic, it's less
than 1. So this is pretty easy, you can
do a whole bunch of these things just using
AI, so whatever you prefer doing, feel
free to use it that way, but as you can see,
it's kind of validated whether you use
Excel, whether you use AI, you can use R
or State, or whatever software you want,
and this should work. Second. Great. Any questions on that? Yeah. So a confidence interval. I think that's
confidence level. Yeah. Yeah. So it's
the same thing. So in statistics we say what
a confidence level, a confidence interval
is, is we're 95% confident that the
true value lies in this range, essentially.
And when you have a zero in there, that's
usually when we say you can't find, like
you can't say that you found an effect or
something like that. Kind of beyond
this course, but yeah, that's
essentially what it is. about
distributions. Okay, great. So
that's all on that. We're gonna do the the
Kahoot now and then we'll get started
on the next topic. Any more questions
while we wait? Boilers today. One of the homework
questions you will then do the
data analysis. The others you don't need
to use any of that but I just want to
give you a little bit of practice
at least with it. Anyone still logging in? Hey, let's get started. Elasticity is the
percentage change in one variable
that arises due to a given percentage
change in another variable true or
false let's hopefully start off with a
relatively easy one great most people got
that right that's just what the definition
of elasticity is nice ah does this is a
thousand like a perfect score like you hit
it even before it came out like so
that's impressive okay next one if the own
price elasticity of demand is minus 0.99
it is elastic inelastic unitary elastic
cannot determine yeah this is inelastic
the absolute value of this is less than one
we know when it's less than one it's
inelastic equal to one unitary elastic above
one elastic nice yeah third question the
following demand curve is perfectly elastic
true or false this is false so this is
perfectly inelastic so when you've got the
vertical demand curve like that the quantity
is the same no matter what the price
is the price could be one cent fifty bucks
an infinite amount of money and demand is
the same so it doesn't respond at all to
price so this is perfectly inelastic
our perfectly elastic curve is the horizontal
one all right new leader cool frog or
cool toad yeah next one which of the following
is not a determinant of price elasticity
of demand substitutes share of budget
production costs time these is not like
the others okay so So, some wrong answers
here, so let's go over it again quickly.
So remember, we talked about the three
things that can affect whether something's
elastic or inelastic. The first was
substitutes. If a product has more substitutes,
there's more outside options, things
that you can switch to. If there are no
substitutes, even if prices rise, you can't
switch to anything. Share of budget. We
talked about if something is a huge part of your
budget, like 80% of your cost, if the
prices rise, you don't have much wiggle room
anywhere else. you have to change. So if your
rent increased by 10%, you're going to have
to do something about it. You can't afford
it out of other things. You might downsize,
get a smaller place, or you might get a house
to make. These things happen when your share
of budget is pretty high. Finally, with
time, in the short run, you can't make many
changes, but in the long run, you can. So if
gas prices rise, you kind of need gas today
to get home, you're still going to buy it.
But in the long run, you can make different
plans. You can decide you know to organize
getting a yearly bus pass and take the bus to
college or you can buy a bicycle so whether
you have little time or more time to adjust
changes how elastic a good is and production
cost is just wrong i just threw that in there
okay cool frog still in the lead with two
questions left second last question this
demand curve is elastic inelastic unitary elastic
none of the above. Okay, so the answer
is none of the above. I'll admit, I
didn't word this question in a great
way. Remember, it depends where you
are on the demand curve. So when
you're at the bottom, when price is really
low, it's inelastic. When price is really
high, so you're at the top left, it's elastic.
And at some point in the middle, it's
unitary elastic. So the slope is the same throughout,
but the elasticity changes depending on
where you are on the demand curve. This
will definitely come up on the exam so so for
those of you that got it wrong here take the
l and make sure you get it right on the exam
okay who's cool frog you've been up there
for a while have you won one already okay
nice nice you think you're gonna hold on
for this one oh yeah i should imagine this
last question you've got 45 seconds for and it
involves some basic calculation but got 45
seconds for the following linear demand function
if price of x is two dollars and quantity
is four then own price elasticity is what
own price elasticity music so intense
i love it in seconds yeah the majority of people
i guess got that right was the most popular
answer so the way you calculate this is
remember the first part of elasticity is the
change in quantity given the change in
price and we have that in the function the number
outside of the price of X was minus 3 that
gives us that exact change. A one unit
change in P causes a negative 3 unit change
in Q. And the second part is just the price
divided by the quantity so 2 divided by 4 is
a half so just a half times minus 3 gives us
minus 1.5. Once again this is something
you'll definitely be seeing on the exam so
just remember this is because this is how it
goes with the formula. Alright, congratulations. This is the second win. You can choose
once again. I can't remember, did you choose this last time? No. That was brilliant. I think first
time someone's chosen a chocolate
this semester. Yeah. Can we give like
top three double prizes? Yeah. Top
three prizes? Yeah. I pay these prizes out
of my own pocket. I'll think about it. I'll think about
it. Top three? I've got three classes, top three, nine prizes. Okay, no, I'll
think about it. It's probably
a good idea. Yeah, okay. Thanks for the
feedback, guys. Yeah. So, okay, some caveats
with this next topic. So the
textbook's not going to help you much
with this next topic because I
have one page on it. But this is, once
again, where I diverge from the textbook. I
think the concept of rationality and rational
choice theory is so important, it's
worth spending time on. So understanding
why we do what we do matters a lot. I just
don't think this should be assumed knowledge.
So for those of you that will decide
to continue on with some sort of minor in
economics or anything to do with econ in
the future, This is the foundation of how
we do econ analysis. For those of you that
aren't, who are just here, yep, get this
out of the way, no more econ ever. When
you think about, you know, we make
evaluations in the world, like which policy
should we put in place? Should we do something
that makes one group of people
happier or the other? How do we compare things
between people? How do we compare levels
of happiness? Where does this idea of
utility come from? Under what circumstances can
we make comparisons? That's what this
is all about, this topic. And I think
it's too important to brush aside, so I'd
rather get rid of one of the lamer chapters
on some weird, firm definition stuff
later in the semester and spend time
on this. So notes are going to be
very valuable here, textbooks are not going
to be that helpful. So a term that is
thrown around a lot is rationality,
to act rationally. And the foundation of
econ, as I said before, is this idea of
rational choice theory. Thus, rationality plays
a really important role in economic modelling,
economic decision -making, and the econ
framework as a whole. But what does
rationality mean? So, what I want you
to do now is take a minute to yourself
to think about and discuss with the
people next to you what you think it
means to act rational. Come up with an example
of acting rationally. And more importantly,
if someone's not acting rationally, they
are acting irrationally. What does it mean
to act irrationally, and what's an example
of irrational action? So take a minute to
yourself and just think about it, and
then I'll let you converse with others,
and we can, you know, crowdsource and see what people come up with. Thank you. Okay, let's bring
about, before we talk about what it means
to act rationally or irrationally, I want
to see if anyone came up with any fun
examples, even if they're right or wrong,
that doesn't matter, just tell me what
you came up with. Yeah. like really like
something yeah so they buy a car even though
they're a college student not earning any
income right now would that be the example
yeah and i figured it's okay cool um
do people agree or disagree with that example
just out of curiosity this is actually
a great moment to actually show you something
because i i disagree with that actually
um so there's There's a thing called
consumption smoothing. And this is the
idea, if I can show it here,
this is, shh, does this work, yeah, so this is the
idea that when making purchasing decisions,
you shouldn't just take into account your
income right now, you should take into account
your whole life's income and smooth your
consumption across that. So right now, you're all
in university, unless any of you have
incredible side hustles. I think it's fair
to assume you're not earning that
much. But given you're at university,
all doing either eng degrees, business
degrees, degrees that have high
earnings potential, even though there's
a lot of uncertainty in the future right
now with work, with AI, etc., I think
you can still believe that you will have
higher salaries in the future. So what Milton
Friedman said is that you should take
this into account in your spending patterns.
and actually borrow and spend big when
you're young because you know you'll be
earning this in the future. So rather
than consuming little now, a lot, you know,
when you're older, you should consume
at an optimal amount where you're happy
now. So this was just a great opportunity
to bring this idea of consumption smoothing
up. As you can see, income's low here.
It's low here. It's high during your
work periods, but you should consume the
same amount every time. But that's a little
bit of a tangent there, but that's still a
pretty... One second. Still a really good point. Any
other examples? What was your
name at the back? Amelia? Yeah. If you choose an
option, that's not the best of you. Not like
a fun example like over here, but like
a great example as well. Just choosing
what you don't prefer seems pretty
irrational. And we will come back to that.
That's a really good one. What about
definitions of rationality? What does it mean
to be rational? What about over
here, Brooke, what did you discuss
over here? Do you have an example of an extreme decision?
Not really. Okay, what about a
tame decision? Um, I don't know. Fair enough. Okay, not coming up
with an example is a tame decision. Okay,
let's go with that. Extreme decision would
be to sell all your earthly possessions and
move to the middle of South America. That's
an extreme decision. Is that irrational?
That's a good question. so these things are
relatively hard to think about once you
try and pin down the definitions as i said
it's really important in economics what
to what rationality is and i'm going to
kind of disappoint you all a little
bit here because in economics rationality
simply means that a person's preferences
what they like what they prefer satisfy
two things two axioms the preferences
are complete and the preferences
are transitive it's all they require
these two things so as you know economics
is all about making choices do you choose
option A do you choose option B how do you
make that decision we want a framework
where we can compare the choices that people
make and we're really interested in this
thing called revealed preference what people
choose must be the best thing for them as
Amelia said someone shouldn't choose what
they don't prefer that doesn't make any sense
so this idea of revealed preferences a person
who chooses x instead of y must prefer x to
y so how do we model these preferences so
formally speaking what a preference is is
just a relation between two objects x and y how
do you relate between them you prefer x
over y but relations can be more abstract
than just preferences. For example, Alf is older than Betsy. France is bigger
than Luxembourg. Sue is the mother
of Franklin. John is worried
he may not do as well in this
course as Jennifer. So each of these
sentences expresses some sort of binary relation
between two entities. So in the first one,
we have Alf and Betsy, our two entities,
and is older than is the relation between
them france luxembourg is bigger than sue
franklin is the mother of this is just some
sentence that relates the two objects together
for example something that's not a binary
relation is bruce stands between clark
and diana this is one person in between
two this is a ternary relation in economics
with preferences we're only interested in
these binary relations and this is just how
we write it out so alpha is older than
betsy as you can see the first entity and
the second entity are on either side
of the relation in lowercase and the
relation is the capital r here that's just
how we write it up so it's important to
consider who and what are we comparing what
have these relations Sometimes this matters. Is this set or this
group just humans? Is it just dogs? Is it
all humans and dogs? Is it current humans
or every human who's ever lived?
This group will make a difference
to our comparisons. So when we want to
be careful, we can define a set or
universe U as the set of all things
that can be related. So suppose the universe
is just Ed, Ed and Eddie. we write it
this way where the universal set equals
ed ed and eddy order doesn't matter it could
be eddy ed ed it's the same thing here and
a quick note here more of a mathematical
note these sets these universes can be
infinite like the set of real numbers points
of time between 7am and 8pm points of time
between 7.59am and 8pm any two points on
these number lines are going to be infinite
and for those of you who are studying
some mathematics will know about the differences
between infinite sets if you don't i
recommend looking up a youtube video called
the hilbert hotel which is a classic
thought experiment on different sizes of
infinity it's pretty cool okay so when it comes
to preferences in economics a relation we
care about is at least as good as or at least
as preferred as and the symbol we use for
this is kind of like the greater than or
equals to sign but in this way this is our
preference relation this is known as the weak
preference relation and the weak word in
here is really important and you'll see shortly
why we say at least as good as or at least
as preferred as and not better than or
preferred than it will actually result in um
one of our axioms being violated so simple
examples for me ben coffee is at least as
preferred as T and we can write it in this way
coffee at least as preferred as T for Ben
or B and then my brother Adam T is at least as
preferred as coffee or at least as good
as coffee we write it in the the the opposite
way here so once again what makes
preferences rational we only need two properties and
this is why economists kind of like this
and why the model is so appealing because
we don't put many restrictions on it. This
allows people to believe all sorts of things
that we'll get into. But one example
would be is in the other class
when we're giving examples of
what's irrational. Someone said if
you know your house is on fire and
your family's inside and you have
time to save them and you don't,
that's irrational. And yeah, like it
would be pretty screwed up not to save them,
but what if you really hate your family? Like
it could be irrational, a screwed up, but
a rational action. Ultimately, going back
to what Amelia said it depends on what you
actually want that's how we can describe
behavior so completeness x is either at least
as preferred as to y or y is at least as
preferred as to x or both and transitivity
if x is related to y y is related to z
then x is related to z so transitivity is
the more intuitive one so let's start off
with that so once again transitivity is if
x is related to y y is related to z then
x is related to z so let's say the universal
set is all people currently alive is
the binary relation is taller than transitive
if x is taller than y and y is taller than
z is x taller than z yeah eric you're
nodding you're confident in this one yeah
well you're you're you're correct eric so
this is mark Zack and Broden. They're my
favorite comedy trio. They're Australian.
It's called Auntie Donna. They do absurdist
comedy sketches. They're pretty funny
if you're into that sort of thing. And as
you can see from the photo here, it can
empirically validate their hearts. Broden's
the tallest, Mark's the shortest, and
Zack's in the middle. So according to
transitivity, if Broden is
taller than Zach. And Zach is taller
than Mark. Then by transitivity, Brodin
is taller than Mark. And that's correct
here. And you can take any
three people in the world and
this will be true. So proving something
is is kind of like hard in, well not
hard, but proving a theory to be true
is much different than falsifying a
theory. I'm not going to teach you how
to prove something is true, but to prove
something is false, you just need one
counter example. But this is true here. Okay, what about the binary
relation for the set of all people in the
world is in love with? Is that transitive?
Is in love with? No, why not? No, I said it. Oh, you
said it? Sorry. Yeah, why not? Can you
think of an example? Does it mean that
you love them at the same time?
Yeah, exactly. So let's say you
love me. What was it, DK loves it?
So DK loves me? What's your name
again, sir? Daniel. I love Daniel.
That doesn't mean DK loves Daniel. DK could hate Daniel.
I mean, that's probably closer to
love than indifference. But yes, clearly this
is not a transitive relation. So I
came up with this example before the
final season of Stranger Things came out,
where Steve Harrington was clearly still
in love with Nancy, but Nancy was in
love with Jonathan. And if transitivity
held in this case, that would mean that
Steve was in love with Jonathan, which
is clearly not true. So in love with is not a transitive relation. Here are some
other examples of relations that
are transitive. Is siblings with
is transitive. So if Ron is
siblings with Ginny, and Ginny is
siblings with Fred, then Ron is
siblings with Fred, is an ancestor of. So if a grandparent is the ancestor of a parent, and the parent is
the ancestor of a son, then the
grandparent is the ancestor of the son.
That makes sense in the logical flow,
and I have the example here with
the Manning family. If Usain Bolt runs
faster than me, I run faster than DK, then Usain Bolt
runs faster than DK. I feel like
DK's like, nah, I got you covered
in 100 metres. Okay, and here are
some examples of things that aren't transitive.
So going back to this example of family,
instead of saying ancestor of, parent of, isn't
transitive. If a grandparent is the parent
of a parent, and the parent is the parent
of a son or daughter, this doesn't mean
the grandparent is the parent of the
son or daughter. That's not transitivity. Is friends with?
Same thing as in love with. I don't know
if any of you have ever thrown an event
or a party where you've invited
multiple friend groups, maybe your school
friends and your college friends and get along.
That's an example of this transitivity
falling apart. Finally, a very common
one is in sporting events, there isn't
this principle of transitivity where
the wins or losses. So an example
here is the Raven this season
beat the Bears. The Bears beat
the Steelers. But the Ravens
didn't defeat the Steelers. Transitivity
would imply the Ravens would
win. This property doesn't exist in
sporting contests. Now someone said,
hey, could you say the Ravens are better
than the Steelers? And yeah,
technically you could just put a number
on every team of how good they are. And
then you can say, that is, yeah, a
transitive relation. But an important
note here is, just because something's
not transitive, sorry, just
because something's not transitive,
it's not necessarily a bad thing. It
just has this property of not
being transitive. However, this is a
problem for rationality and rational choice.
And I'll show you now why we need to have
transitive preferences. Why does it matter
for economics and for choice? So without
it, preferences can become unstable
and it leads to a paradox called the
money pump scenario. So it's necessary for
meaningful utility representations
and ideal of the types of choices we
want people to have. So imagine you
have three choices, an apple, an orange
and a banana. If you prefer apples
to oranges and oranges to bananas,
according to transitivity, you prefer
apples to bananas. but what if we don't
have the axiom of transitivity and you say
actually i prefer bananas to apples why is this
bad and this is why this is called the
money pump so here we have z oranges we have
apples which are y and bananas which are
x and we have the intransitive preferences
here so with transitivity apples should be
preferred to bananas but you can say bananas
are preferred to apples so you start with your
intransitive preferences you start with an
orange and I come up to you and say you
have an orange I have an apple I'll give
you the apple for the orange and you give me
one penny and you're like okay I prefer apples
to oranges so that's good for me that's
worth at least a penny I'll make the try
so now you have the apple and you've given
me a penny now I offer you a banana for the
apple and the penny. And you're like, okay, I prefer bananas to apples. So that trade is
worth it for me. So I'll give you
the apple and a penny for the banana
I'm better off. So now you have
the banana. So the banana X, you're
over here now. And then I
have an orange. And I tell you, hey,
I'll give you an orange for the banana and
a penny. And you're like, hey, yep, I prefer
oranges to bananas. So I will make
that trade. I'll give you the banana and a penny, you give
me the orange. So each trade you
made makes you better off based on your
preferences. But now look, you're back at Z,
you were where you started, but there's one
thing that's different. You've lost three
pennies. And now three pennies might
not seem like much, but you can see with the
nature of the money part, it's cyclical.
This is never ending. You can take someone's
wealth for, for, for, like you can
essentially make them zero if they have these
preferences. So this isn't stable. This
isn't a good thing. We want people to have
stable preferences. So the idea of being
money pumped is something we want
to avoid when constructing this
idea of rationality. Any questions? And to finish off,
we're going to start looking into this
idea of completeness, which is a little
bit less intuitive. It requires a little
bit more thought. So either X is
related to Y, Y is related to X, or
both for all X and Y. for any x and y in
a universe either x relates to y y relates
to x or both okay so for every human
alive is the binary relation taller than
a complete relation someone want to take
a guess I see some nodding there do you
think it is yeah you think it is complete okay
great so this is something that everyone
gets wrong the first time around this is
not a complete relation and i'll give
you an example why this is the
counter example chris paul and
steph curry are both six foot two we cannot say chris paul is taller than
steph curry we can't say that
they're the same height we can't say that steph
curry is taller than chris paul they're
the same height and we cannot say both this
doesn't satisfy completeness we need one of these
three things to hold at least for it to
be complete so taller than is not a complete
relation for every person alive and this
is kind of the trick and going back to
before this idea of weak preference relations
if we said at least as tall as it's got to
be a complete relation but just say taller
than or better than you run into this
problem with completeness so there's an
important link between indifference and this weak
preference relation so remember indifference
is orange apple you are indifferent between
you get the exact same amount of happiness
you can't choose and indifference falls out
of this property of the weak preference
relation so the technical definition is you are
indifferent between the apple and the
orange if and only if you weakly prefer the
apple to the orange and you weakly prefer the
orange to the apple and this that's a
little bit of a weird statement isn't it i'm
indifferent between x and y if and only
if, you weakly prefer x to y and you weakly
prefer y to x. So I want to finish this
class with a quick tangent into the realm
of logic, because there's a phrase in here
which seems meaningless, but it packs a ton
of information into it. Has anyone here
taken any logic classes before or any set
theory? Which sentence or phrase am I
talking about in here? I don't think it's a screen like this. Okay, no worries. So the phrase if
and only if. If and only if packs a
ton of information into it. You'll
see this all the time, and I just
wanted to take the opportunity to tell
you what it means. So what this means, sometimes in philosophy, just pronounce
if with two Fs, this means that
something is both a necessary and a
sufficient condition. So a necessary condition
is simply y cannot happen without x x
is necessary for y to happen in this form x
is necessary for y to happen example air is
a necessary condition for human life human
life cannot exist without oxygen without air
on the other hand a sufficient condition is
if x occurs then y if x then y and it's drawn
in this way in logic form don't worry about
the logical forms it's the intuition
here that matters more. An example, owning
a Labrador is a sufficient
condition for owning a dog. If
Labrador, then dog. And yeah, they're
logical counterparts, if you notice. If X is a
necessary condition of Y, then Y is a sufficient
condition of X. So if there's human
life, it's sufficient condition for there
to be oxygen or air. So a few more examples,
having gas is a necessary condition to
drive a car or maybe not so much anymore
with electric cars but it used to be having
a valid password is necessary to log into
my email account and then the oxygen one
sufficient conditions being divisible by four
is sufficient for a number being even if
you can divide it by four it's an even
number done this one scoring 100 on an exam
is sufficient to pass the exam you hope
would be some kind of screwed up subject if
you still failed even if you got a hundred
percent and if and only if is when something's
both necessary and sufficient so an
integer is even if and only if so it's necessary
and sufficient if it is divisible by two
so something can be divisible by four but
it's not a necessary condition because two
is an even number. However, under this
definition here, a number, if it is
divisible by 2, is an even number and it's
necessary that they can be divided by 2
to be an even number. And the classic
philosophy example, DK, you might be
familiar with this if you took this years
ago, someone is a bachelor if and
only if they are an unmarried adult male.
So a lot of these language games play
a part in logic. But this is why
we have this weird definition that for
someone to be indifferent between two things
is necessary and sufficient for that
if you weakly prefer x to y and you
weakly prefer y to x. There's no other
possible outcome except you're indifferent
between the two. So let's finish
off going back to is at least as
tall as complete. Yes, it is. So, taller
than is not complete, is at least as tall
as is complete. So, going back
to our Chris Paul and Steph Curry
example, Chris Paul is at least
as tall as Steph. Steph Curry is at
least as tall as Chris Paul. In this case,
we can say both. This is his property
of indifference. Wemby, who's 7'4",
and Messi, who's 5 '7". Wemby is at least
as tall as Messi. So, we've ticked
off completeness. One of the three
things has to tick. And finally,
Socrates and Julius Caesar. we don't
know their heights however even if you
don't know what two people's heights are,
if our relation is at least as tall as we
can say it's complete, because we can say
Socrates was at least as tall as Caesar or
Caesar was at least as tall as Socrates or both,
there's no other way you can say that
this is false, one of these has to be true
or both have to be true and when we come back
to the next class, we'll bring this back
and continue on with completeness to show
why it's important for preferences and then
we'll build upon that and discuss utility and
rationality as a whole. Homework's available.
Have a good afternoon everyone and I'll see
you all on Wednesday. I don't want
to close that. Yeah. That makes sense
that the preferences don't change but
what if you add time aspect of
it? This is really interesting. So I'll
give you an example. Let's say you can choose between two options. One in 11 months and
one in 12 months. So in 11 months you
can choose $100, or in 12 months you
can choose $150. What do you prefer? $250. Yeah, and $150. Okay. Now let's say 11
months goes by and you can make the
same choice, but now it's $100 today, or
$150 in one month.