great um afternoon everyone
the plan today is twofold we're going to
finish up the the topic on market structures
we're going to do the kahoot and we'll
probably have 20 minutes left so what i'll do
is go over once again the idea of of
rationality specifically transitivity and completeness
if you're confident with that for monday's
exam you can get out of here early um
i mean you can get out of here anytime you
want attendance isn't compulsory after all
but i'll allow a little break for that to happen
so we've looked at um competitive markets
where everyone sells the same product
literally carrots so the same thing there are
many buyers many sellers everyone's a price
taker not a price maker so firms face the
horizontal demand curve which is price that's
their marginal revenue whereas with monopolies
there's only one seller no one else
could enter the market and they set the the
price um based on their output where marginal
revenue equals marginal cost they face this
downward slope of the market and the
last on a monopolistic competition has a
little bit of both so it exists if there are many
buyers and sellers each from the industry
produces a differentiated product so what this
means is overall the product is the same
but slightly different so we're thinking about
beer um beer um is like one thing but
there are hundreds of different beer
companies they're all differentiated in a little
way, whether it's like site differences in
taste or branding, you've got big companies, but
you also have small individual suppliers
as well. So if you go to a bar in Seattle
at some point, you'll see hundreds of different
local suppliers. And importantly, unlike
Monopoly, there's free entry and exit
into the industry. So because each firm
produces a product that is slightly
differentiated, the implication is products are
close to each other, but not perfect
substitute. therefore a firm's demand curve is
downward sloping under monopolistic competition
so downward sloping it has similarities
to monopoly so just like monopoly you can
see they're facing a downward sloping
demand curve as a result the marginal revenue
is also downward sloping and always below
the demand curve you maximize profit where
marginal cost equals marginal revenue so
at q star this is the demand curve here
so the price of the product will be p and
the profit is the price minus the average total
cost multiplied by the output. This is
the same as monopoly. And once again we
can do the exact same analysis of the profit
maximizing price quantity and the
maximum profits for a monopolistic
competitive firm. So can someone remind me
how we get started with these sort of
questions? What do we need to do? What's
our launching point? How do you figure
out what the profit maximizing price or
quantity is here. Okay, do you have
any intuition here? Profit maximizing. What's that profit
maximizing condition? The price is like
the cost is equal to. Kind of, kind of.
The marginal. Yeah. The marginal
cost. Equals what? The. We almost said it.
You've got this. Does anyone want to
jump in and help DKI out? What does the
marginal cost need to equal? Marginal revenue.
Exactly, exactly. Marginal revenue
equals marginal cost. No matter what the
firm structure is, this is what our profit
maximizing situation is. So we have our
marginal cost here. We can turn the
inverse demand function into our marginal
revenue curve by finding what the
total revenue is. And total revenue,
once again, is just price as a function
of Q multiplied by Q. That's our way to get
total revenue. so this is total revenue and
marginal revenue is just the derivative
of total revenue so we have our marginal revenue
marginal cost every time we increase output
by one cost increases by two so marginal
cost is just two equate them together you get
the profit maximizing output which is 24
.5 and like we just showed before if this
is 24.5 where it hits the demand curve is
going to be the profit maximizing price so we
want to plug 24.5 into the inverse demand
curve so here we find the profit maximizing
price is $51 and the exact same as monopoly
the price times the quantity minus the cost
you plug in 24.5 the Q gives you the profit
maximization outcome okay so what is the
long run equilibrium and what is the short
run equilibrium so in the short run you can see
that these monopolistic competitive firms
can make profits however similar to the
competitive market because there are no barriers
to entry anyone can enter these types of
markets so a new beer producer could come
in a new soda company could come in and make
a product and this is going to eat into
profits so even though things aren't exactly
the same imagine you're the only soda the
company out there, you sell Coca-Cola, then
Pepsi comes along, or what's that other one
that people sometimes drink, the weird one,
Dr. Pepper, that's the one I'm thinking of,
comes in as well. It's going to eat into the
profits, and this can keep happening until
we get a similar situation to the perfectly
competitive market. So if there are
short-run profits, economic profits,
additional firms have incentive to create a
similar type of product and enter the industry
to capture some of these profits. so they
produce similar but not the exact same product
and similarly if a firm experiences short
-run losses in this market once all their
things are variable so there's no longer fixed
cost they'll just exit they'll just exit so
we have that similar idea to perfectly
competitive markets so let's focus on the
situation where we're at D zero and thus the
marginal revenue zero so when demand curve is
zero and the marginal revenue curve is zero
where it intersects with marginal cost is here
so this is the point where firms will
maximize their output so as you can see this is
how much output they'll produce and then the
amount of profit is the difference between
where this hits the demand curve here the
average total cost and the amount of output
so this is going to be that here but if new
firms enter what this is going to do um due
to entry of new firms selling other brands
the demand curve that they face is going to
shift down and to the left there's just less
people now demanding from them in particular
because they're splitting with these
other companies so you can see this also shifts
the marginal revenue curve down into the
left so this intersects with marginal cost
at a lower point the quantity is going to be
lower and at this point here we have price when
it hits the new demand curve and as you can
see it's where average total cost is also
so there's going to be no economic profits
here no economic profits the key difference
between this and a competitive market is
remember in a competitive market the point is
going to be where they're at the lowest
average total cost this point isn't where the
average total cost is at its minimum so you
can still have a higher than usual average total
cost and still have zero economic profits
and this is the exact same thing here the
long run equilibrium so in the long run
the price is going to be above the marginal
cost remember in competitive markets
the price is the marginal revenue so
that will equal the marginal cost but here
the price is above the marginal revenue
which is equal to the marginal cost and
the price equals the average total cost
as you can see here but this is not the
minimum of the average total cost which
would be down here so the differentiated
nature of products in these monopolistically
competitive markets implies that
firms in these industries must continually
convince consumers that their products
are better than their competitors so
as a result they want to produce less than
optimal If they can, similar to monopoly,
and by optimal, I mean the competitive
equilibrium, that's how they can maximize
their profit as well, by capturing
more of the audience. So, for these types of
markets, you probably see more advertising
than any other type of market. You
don't see your local farmer's market person
putting TV ads out for their carrots or
something like that. It's a perfectly
competitive market, you shouldn't do that.
The famous one is Coke versus Pepsi. There's
something called the Cola Wars, where
they went back and forth. they still do.
In fact, I think Pepsi just released an ad,
going back to the original taste test
ads, trying to show people that Pepsi
tastes better than Coke. There's actually a couple of cool videos on that. Fast food is a really
big one. Fast food ads really try and
get you to go to their brand rather
than the other. And in fact, there's a
pretty funny version of this that happened
over the last few days. And I, rather
than just talking about I found a video
so people may have seen this oh I got
to put the volume up So I don't know if
anyone saw the original video but it's like
weird like Like, as they said, he calls it a
product, not a burger. He takes a little bite,
and he kind of looks disgusted with his
own burger. So Burger King and our Wendy's
have all, like, latched onto that. So with fast
food companies, they're always kind of having
a go at each other and trying to
differentiate themselves from the rest
through things like that. I mean, the
Happy Meal was something like this
as well, like these types of features
of these companies. Other ones are,
like, Apple versus, like, Samsung or
Android phones. That's monopolistic
competition. Also, in sports, NFL
and basketball, both playing Christmas Day,
there's only a certain amount of things
that we can watch, so they're competing for
eyeballs as well through their advertisements
and other things. So, are there
any marketing majors in here
by any chance? Anyone? Okay, great. So, no
one's going to know more than me on this topic.
This is more about the market in itself.
So, there are two main strategies firms
try and use when differentiating themselves
from the competition. So the first is
comparative advertising. So this is a form
of advertising where a firm
attempts to increase demand for its brand
by differentiating its product from
competing brands. So brand equity is
the additional value added to a product
because of its brand. And we're all very brand
conscious in terms of what we choose to
buy. And I've got a couple of videos that
try and show this brand differentiation on the
next page. The next is more niche marketing.
so this is instead of differentiating
your product this is kind of tying your
product to a type of identity to a type
of identity so green marketing for example
targets consumers who are concerned about
environmental issues so as you know like
with with how polarized politics
is in the u.s. a product will like kind
of advertise themselves as either left-leaning
or right-leaning leaving half the
population a boycott and half the population a
buyer so like products leaning into politics
is nothing new, this is ideas of niche
marketing, which you've probably seen countless
examples of recently. Finally, what we'll
talk about is that while there can
be successful differentiation and
branding strategies, this can make
managers brand myopic. So what that means
is they're so locked up in the brand's
identity of who they are and what they do,
they don't innovate or catch up with
modern times and the old product then
becomes redundant and you never hear of it
again. So I've got examples of all of
these that I'll show. Okay, so this is the
first one of comparative advertising, brand
differentiation. Hello, I'm a Mac.
And I'm a PC. You know, we use a lot
of the same kinds of programs. Yeah, like
Microsoft Office. But we retain a
lot of what makes us... You should see
what this guy can do with a spreadsheet.
It's insane. Yeah, and he knows
that I'm better at life stuff like music,
pictures, movies, stuff like that.
Whoa, whoa, whoa, what exactly do you mean
by better? By better, I mean making a
website or photo book is easy for me, and
for you, it's not. Oh, that kind of
better. I was thinking of
the other kind. What other kind? Okay, so there's a
few things going on here. From the photo
of the Mac that they show, you can tell
this is really old. Really old. So this
was in the 2000s when more people
were buying PCs. Like now, a lot of
people have Macs. If you ask people what the
most common computer is, I'd probably say a
Mac. So, if you remember, we talked about with
Monopoly, one of the reasons for Monopoly
is network effects. And Microsoft had
this kind of pseudo -monopoly in a way,
because all the software was written for
Microsoft, for Windows. And even in the ad, they
say, hey, this guy's really good at the
spreadsheet stuff. But the whole differentiation,
originally from Max's, lifestyle is
better. So iTunes was like the first kind of
streaming service for music, and that was
only accessible on Mac. So if you wanted to
like upload things onto your iPod in like 2006,
that's how you could do it. And they claim
it to be better at things like that and
movies as well. So that's originally how they
tried to differentiate themselves from Microsoft
and from Windows. And now, as you can
see today, they're probably, you know,
more popular in
both departments as well. So this is
a very famous ad, and they had a few
different versions of it. Okay, a more modern
one is what's going on with all
the AI companies at the moment. If you
remember, there was this Super Bowl
ad I discussed. This is a different
version of it. So this is an ad by
Anthropic trying to differentiate
itself from open AI. I feel like I'm just
going in circles. Is my essay making
a clear argument? Absolutely. Your point
of view is fresh, well thought out,
and rich in research. I didn't use
too many quotes. Absolutely not. Your quotes help build a thought-provoking peace. From our previous
conversation, I've noticed
that the deadline for this essay
is due today. So why not cherish
this unforgettable occasion with Luna
Memento Jewelry, with 10% off charms
this weekend? What? place your order
today for free personalized engraving
differentiation is clear here they're
trying to scare people into the idea that
their competitor here that also is AI
are going to have these ads built into it so
they're differentiating on that front mostly
might have noticed that the the professor
AI was like kind of psychophantic and
this was an issue with open AI and chat
GPT for a while you give it the worst
idea ever like hey I I want to start a business
where I sell fax machines. Is this a
good idea? And it'll be like, oh, this is the
best idea I've ever heard. You're really
smart. You're really intelligent. So the
beginning of that ad is definitely pointing
in front of that. So those are two
examples, one more old school and one
literally in the past few months of
comparative advertising. And here's an example
of niche marketing, trying to tie
your product to some brand
or identity. But we step in as a
body shop because we can show the will of our
customers and the general public by signing the
petition by getting 8 million signatures
to show this is what people want so get on
with it and ban animal testing in cosmetics
okay so the body shop didn't say one thing
in that ad about like what they actually sell
like what their products are they just tied it
up with an identity that if you care about
animal welfare you should buy from us
because we don't test on animals so that's the
idea of niche marketing and there's a ton of
that You know, like, this is like a big thing
for brands, especially over the past 10,
15 years. So you can probably think of countless
examples yourself. Finally, this is
the idea of brand myopia. You're so
locked up in what your product's brand is,
you don't adapt. And as a result,
these companies, like, barely exist anymore.
So the first is Kodak. Back in the day,
before you could take photos on your iPhone,
you have to get film, put it in the camera,
take your photos, print the film. and
Kodak was like the number one seller of cameras
that use film and printing film etc
etc but when digital cameras came along they
didn't adapt they're like this is what
our model is they're stating the the the
core idea of photo film and as a result no
one really uses Kodak today I'm sure there
are some stores that still exist but Kodak
was huge in the in the 90s and early 2000s.
One you're probably familiar with is the
idea of Blockbuster. So pre-streaming,
Blockbuster was the place to go for entertainment.
You would rent a video and then a DVD
or whether it's a TV show or movie, you
could be able to get video games there as
well. They were huge all over the world. But
then the streaming services came along
and they didn't adapt because they're like,
this is our core model. Blockbuster could
have easily adapted. They had like the capital
they had the networks they had the
established name but it was stubborn about
their model and as a result I think the
last blockbuster store closed last year or
something like that so they're dead they're
gone because they didn't adapt finally
Nokia I had my first mobile phone like 99
it was you know that brick like the I don't
know if you see the photo or be like this
huge phone actually I want to see if I
can get it up it's pretty funny in
hindsight um so nokia had really good hardware
um nokia brick phone no this one's smaller
let's see if there's the og one yeah so the
the like like these here these were like
the og nokias these here and you could play
snake on it the game snaker this was like
revolutionary for us as like 10 or 11 year olds
like we thought this was the coolest thing
ever which is so funny in hindsight so
nokia was all obsessed about their hardware
um and when uh the iphone came around they
could have switched to more of a touch based
phone and there's other companies that did
so like android samsung qa they all did this
nokia could have done this but they were
locked up in the idea that we produce these
like hardware phones not the the touch screen
ones and as a result they're they're not
in this industry anymore so this is the
thing like you You get so locked up in what
your brand is, you can't adapt the changes.
And there's going to be a lot of this
happening to firms in the next few years as well,
for obvious reasons. Alright, any questions regarding any of that? Brilliant, let's
get to the cahoot. So I should say,
I'm going to cancel class on Wednesday
as well. So there's going to be no class
Wednesday, Friday. Reason being, I
don't want to just start on game
theory, then have like a week and a
half break and no one's going to
remember anything. So I just felt best
to give you all a break, enjoy a longer
mid-sent break. And yeah, we can get to
it after all of that. Some new ones
that I haven't seen the overset before. Anyone still logging in? No worries. Is that you? Oh, I still know. Okay, you can
let me know. You good now? Okay,
let's get started, everyone. Six
questions, as per usual. Which of the following
is not a condition of a perfectly
competitive market? Firms produce differentiated
products, free entry and exit, many
buyers and sellers, perfect information.
what's not a condition of a perfectly
competitive market most people got that
right so this is what separates a perfectly
competitive market from a monocularistically
competitive market nice most people
got that right doing better than the
previous class next question under perfect
competition the firm's demand curve
is horizontal because it is perfectly
elastic true or false I think I chose this
photo because the tug of war rope is horizontal
but i made this at like 1am a week
ago i don't remember what i was doing okay
no it's true yeah this is just the definition
of it this is the demand curve they
face which is just a price they're price
takers not price makers cool we've got
judge duck in the league judge duck
okay next one in the long run
perfectly competitive firms earned
zero econ profit because free entry
and exit drives profits to zero
true or false most people got that right
remember the difference between economic
profits and accounting profits there's zero
econ profits there's still positive accounting
profits it's just that with econ profits
you also take into account the outside
option the implicit cost what you're giving
up by running this company so as long as
there's positive econ profits people are
incentivized to join the industry because they
can do better off and if there are people
making losses they're incentivized to leave
the industry so in the long run when everyone
can enter and exit we get to zero economic
profits judge duck still in the lead
kind of like these new ones the apple pie's
interesting all right fourth question a
monopolist has unlimited market power because
it is the only seller okay so this one was
a little tricky so um the majority of you
you got it wrong so remember they only have
unlimited market power if they're facing a
perfectly inelastic demand curve that means
you raise your price and no one's gonna
change their demand but when they face a
normal demand curve as we showed then their
market power depends on the elasticity of
that demand curve at some point they can't
raise or lower their prices anymore because
they start losing profit essentially so
when they're up in the top left when they're
in the elastic zone they want to reduce
their price so more people flock to them
and they make more money so this constrains
their market power essentially they can't
do whatever they want there are situations
where they'll earn less profit if they don't
do the right thing okay so the same leader
i'm gonna call you out on the next
question if you're still in the lead i mean
you're only up by 37 points but yeah we'll
see all right penultimate question for a monopolist
marginal revenue is positive when
the elasticity of demand satisfies
elasticity is zero it's inelastic unit elastic
or elastic where is marginal revenue positive
for a monopolist oh not great i should say
most people got that wrong i got confused
by the colors there yeah so if you remember
when we looked at the graph we had the demand
curve and the marginal revenue curve just
sits below the demand curve so in the region
where the prices are high this is positive
and in that region where we're in the
elastic zone the elastic zone what this means
is if you lower your price by one percent
more than one percent of consumers will flock
to buy your product so as you decrease your
price you're making more money all the way
up until the unitary elastic point that's
when marginal revenue intersects with zero
and after that as prices are low it's inelastic
and as you lower your prices further less
than one percent of people are going to flock
towards your product and you make a loss
so it's the top left region where marginal
revenue is positive and this is where we're
in the elastic region as well so i mean it's
going to be a while but questions like this
will be on the third exam so this is important
to know now well not now it's important
to know later so if you know it now that's
great okay um it's still 27 point lead here
who's our judge duck who's judge duck right
have you you've won one already oh yeah
great so who's in second place as well who's
penguin in love penguin in love okay great do
you reckon you have a shot at catching
no I like setting low expectations is the
secret to happiness so I like that yeah great
last question what is the key difference
between monopolistic competition and perfect
competition firms are price takers in monopolistic
competition there are barriers to
entry in monopolistic competition each firm
produces a differentiated product in monopolistic
competition there are fewer sellers in
monopolistic competition yeah i feel like the
the photo may have given away what
the answer is here yeah so so um remember
in monopolistic competition there
are no barriers to entry anyone can
answer you can come up with your own soda
if you want, if you want to compete
with Coke and Pepsi. So it's H-Verb has
something different about their product, whether
it's taste, whether it's the brand style,
anything really. Great. Okay. Great. Congratulations. What do you
want? Oh, you can choose. You can
pick your prize. Okay, so we have 20
minutes left. I'm happy to go over completeness
and transitivity for those who want.
If you don't want to go over it, you're more
than welcome to get out of here and enjoy
this well the sun's kind of gone now and
enjoy the rest of the day so I'll give you
a moment to do what you want to do and
then I'll continue on. I know this trips
a few people up so I'd like to just
go over it again. So before we get
into rationality, completeness and
transitivity I wanted to go over just
how we think about riding our preferences.
So we're going to have some sort of set
which is just a giant circle it could be
anything the set of all people the set
of all cars anything like that and for all
people for example every person who's ever
lived millions of them are all in this set
we can take any two of them out and relate
them depending on what our binary relations
the relation could be anything from is
taller than to is just as heavy as to
unlocks the same color is siblings it could
be anything remember this is how we write
it up so the first person related to the
second person or the first car related to
the second car And we can do this for any
two items in our set. So in this case here,
where the relation is older than, we have
our first entity, alph, is older than Betsy.
And this is important for what we're going
to talk about now. So we have this
definition of rationality. In economics, we see
simply you've got to satisfy completeness
and transitivity. So your preferences
need to be well -ordered. You can
compare everything, and you can't have
cyclical preferences. so you can have weird
preferences that are rational like you could
prefer less money to more and that's
rational it's consistent it's weird but it's
consistent you could prefer to get hit in
the leg with a crowbar than eat a really tasty
sandwich that can still be consistent that's
the thing it could be really weird as
long as it's consistent it's rational so let's
start again with with transitivity so what
transitivity is saying is if x is related
to y and y is related to z then x is related
to c for all x y and z in this set so a simple
heuristic is whenever we're talking about
real numbers so 1 2 3 4 5 6 however many
it's always going to be transitive it's always
going to be transit so for example let's
go taller than so um remind me your name
again sorry clay clay so let's say that clay
is taller than me and i'm let's say taller
than then then brook by transitivity that
implies clay is taller brook and just think
about if you put any three numbers on our
heights if it's in that order that has to
hold it has to hold so when it comes to real
numbers it's always got to be transitive
now transitivity becomes a little bit more
difficult when we talk about weirder things
so let's speak about um an example is let's go
um biological siblings biological siblings
so the example i gave is we need so so for
transitivity to work we can't take clay and
i clay and i aren't siblings so we can't
say clay is siblings with Ben because that's
just not true. We need to set up X is
related to Y, Y is related to Z and then check
if X is related to Z. So using our example
from the Harry Potter universe we
said if Ron is siblings with Ginny and
Ginny is siblings with Fred, by
transitivity Ron is siblings with Fred.
That's transitivity. But let's think about
rather than biological siblings we can think
about all siblings so it includes half
siblings as well this isn't a transitive
relation this isn't a transitive relation
for example clay and i could be you know um
half brothers and clay and and and and and
brook would be half brothers but we could
be half brothers from my dad's side and
that could be um half siblings sorry half
siblings through the mom's side so that means we
wouldn't be related at all but if we're
using the same transitive relation is i'm
siblings with clay clay siblings with brooke
by transitivity i'm siblings with brooke
so that is a transit that is not transit
that's not true and in the um uh practice
questions i have a couple of more more not
difficult but like the different ones we talk
about car brands so think about every car
that's ever existed so if you've got
three cars of the same brand so let's say
toyota corolla a toyota prius and a toyota
camry this is going to hold so a toyota camry
is related to a prius sorry not related the
toyota camry is the same brand as the prius
the prius is the same brand as the camry
so the corolla is the same brand as the
camry so that holds but then i have another
one there as well which is not the same brand
as and this one's a little bit different
we can say a Toyota Camry is not the same
brand as a Chevrolet Imperium or whatever
the Chevrolet Imperium is not the same brand
as a Toyota Prius by transitivity they were
to comply the Toyota Camry is not the same
brand as a Toyota Prius so that's not
true so you can just do that basic check to
see if something's transitive or not the
simple heuristic is we're talking about real
numbers for relations that will be translated
completeness is a little bit more difficult
so um with completeness um one second let's
go to completeness and if you have time
i'll get back to the money pump we want
to say either x is related to y y is related
to x or both so what this means is we want
to put at least one tick next to them for
all x and y in the set for all x and y of
the set. Essentially, we want to be able to
compare everything. So the trick here to
think about it is if we're talking about
real numbers, so height, weight, age, there
are two situations. One, where one number
is bigger than the other, or two, if both
numbers are the same. So if the binary
relation can't count for both
of those things, it's not going
to be complete. So a classic example of incompleteness
is taller than. so for example going
back to clay and i clay could be taller
than me so we could check if clay's um
if i'm x and clay's y we go is ben taller
than clay no is clay taller than ben yes
that's true we're done with that check
but now we've got to check the situation
for two people who are the same height so
let's go with um uh clay and brooke let's
say they're the same height is clay taller
than Brooke? No. Is Brooke taller
than Clay? No. Are both true? No. That
violates completeness. So that's a check
you need to do. Now, this is why
we care about the weak preference
relation, at least as
preferred as, because that accounts
for when one number is bigger
than the other, or when two numbers are
the same. So at least as tall as, at least
as old as, at least as preferred that. All
those are going to be complete. All those are
going to be complete. So that's the simple
check with real numbers. When we talk
about other things, is siblings with, this is
pretty straightforward. Is Ron siblings with
Fred? Yes. But the other situation is when
people aren't siblings. So is Ron siblings
with Harry Potter? No. Is Harry Potter siblings
with Ron? No. Are both true? No. So is
siblings a complete relation? No, it's not.
So what you need to think about when you get
given a choice set and a relation you need
to think about what possibilities are there
with real numbers one number is bigger than
the other or they're the same and for things
like siblings people are either siblings or
not siblings so that's how you can check all
situations of complete preference relations
pretty easily now just a bit of an aside
like properties of transitivity and
completeness in general like aren't necessarily
a good thing but for preferences in economics
we need transitivity. I'll get back to the
money pump in a second but there's a one other
thing that I really wanted to talk about
this idea of of utility so um if you
remember quickly actually I want to just briefly
go over there's a ton of examples here
this idea of of expected value and expected
utility so yeah so expected value is you
have possible outcomes that each have
probabilities of occurring. So expected value is
just us finding out what the average is of that
outcome. So you want to take each outcome
multiplied by the probability of that
outcome occurring and add it all together. And that
gives you the average or the expected
value. And the only difference between
expected value and expected utility is with expected
utility we want to transform the outcome
in some way. So we gave a bunch of reasons
why and we did some we did some push-ups in
class so for example someone could have a
utility function that's the square root of x or
x to the power 0.5 so for expected utility
all you do is you take each outcome you transform
it by the utility function so in this case
we'll take the square root of the outcome
multiply it by the probability of that
outcome occurring add it all together and that
gives you the expected utility so that allows
us to take into account things like people's
risk preferences and also this idea of
diminishing marginal utility as well so we
have these conditions for utility functions that
i won't go into now but the key thing to
to think about is what the utility functions
are doing is allows us to map preferences
into real numbers so if i prefer an apple to
an orange we can put a utility of apple as
eight and orange as five and that's going to
map from the utility to the preferences
however it's important to know what they can
and can't tell us so here you can see I
have a utility of a banana is one utility
of pairs three all we can say is that I
prefer pairs to bananas that's the only
thing we can say here this gives us an ordinal
ranking so imagine a list one two three
four five six one eight nine ten is just
put in, in this case, banana at two and
pair at one in that ranking. You prefer
pairs. We can't say that I prefer pairs by
two utils to bananas. It's a meaningless
statement here. Nor can you say that
you prefer pairs three times more than
bananas. There's no meaning to that
statement. So all you can say with utility and
the number to it is if one thing's ranked
higher than another. All right. any questions about
any of that before I go back into
the to the idea of money pumps just to
bring the point home okay let's go back
to money pumps so transitivity isn't
always a good thing so for example imagine
is in love with is a transitive
statement that would be if Clay isn't
in love with me and I'm in love with
Brooke then Clay is in love with books. There
would be problems if that was a
transitive statement. So transitivity isn't
always a good thing. Completeness isn't
always necessary. We gave that example of
is better than as a relation. What does
it mean to say Sabrina Carpenter is better
than Magnus Carlson? What do we
compare? What do we compare? But we need
this in economics. So for transitivity,
if you don't have transitive preferences,
you get money pumped. so if you prefer apples
to oranges and oranges to bananas by transitivity
you should prefer apples to bananas but
this person doesn't have transitive
preferences they prefer bananas to apples and
this is what happens they start with Z and
orange and I know they prefer apples to oranges
so I can offer them an apple for their
orange and one penny and I'll make that trade
because they prefer the apples now they
have an apple which is why so they now have
why and I can say I know they prefer bananas to
apples saving transit preferences so I offer
them a banana for an apple in the penny
and they make the truck now they have apples
so now they have bananas and I know they
prefer oranges to bananas so I make the same
offer so they give me the banana and a at a
penny for the orange so now they're back
where they started they started with the orange
and now they also have an orange they
just have three pennies less so if i ask you
what do you prefer an orange or an orange and
three pennies i think the the answer is
obvious that it should be an orange and three
pennies so that's the intuition behind it
but with a money pump it doesn't stop there
we can keep doing this forever and ever and
ever until the person's lost their entire
world so that's why transitivity is important
for preferences and completeness is important
because we want to be able to have one
ordered ranking of everything and if you
can't compare apples and oranges we can't have
a ranking so finally with the last four
minutes i just want to go into the basics of of
of indifference curves again so we have these
four properties of indifference curves so
here are our indifference curves and the four
properties are as the name says at any
point along the curve any of these combinations
gives you the same utility you are
indifferent between them. The next one is, as
you move up and to the right, the high curve
means high utility. Third one is, indifference curves
cannot intersect. Does anyone
remember why they can't intersect?
What happens? Right, it's good that
you all say then. So what happens is, you
violate transitivity, and we can show you
this. If you draw two indifference curves
crossing, put a point up here of a and b and the
point where they intersect c then we can show
there's a proof by contradiction we can
give two statements that can't be true together
so first you see that a and c both lie on a
difference curve one so a we're indifferent
between a and c by definition we can see
that b and c both lie on a difference curve
two so you must be indifferent between b
and c and because you're indifferent between
a and c and you're indifferent between b and
c you must be indifferent between A and B. Must
be indifferent. But as you can see from
indifference curve 2, A would be up and
to the right. So A must be more
preferred to B. So we're simultaneously
saying that A must be more preferred
than B, and you must be indifferent
between A and B. That's a contradiction.
You can't have that. As a
result, this violates transitivity. And we
need transitivity, so this is why
they can't cross. Finally, we have this
idea of indifference curves being convex to
the origin. So that's this shape here. If
they were like that, that would be concave
to the origin. So if you flipped it around
and downward sloping. So this gives us
the idea of the diminishing marginal
rate of substitution. So when you have very
little x and a lot of y, you're willing to give
up a lot of y originally to get one more unit
of x. But as you keep moving along
you're willing to give up less and less and
less of y to get one more of x so this is
just the idea of scarcity in a way as well
when you've got a lot of x to get an extra
unit of x you're not willing to give up much
y but when you have little x you're willing
to give up a lot of y all right great
that's all i have for you um let me know
if you've got any questions otherwise i'll
see you all on monday yeah okay thank
you no worries To everyone who
values Tradition, what does Tradition mean? Friskay here, with you. That's a bit of video. Have a good day. See ya. You too, enjoy.