and this is for
the level of code. Right? So this is, this is, you cannot say,
you are not missing, this,
this, or this. So, you cannot
say, you cannot say, this, this, this, this, this. Yeah, can I say this? It's not all right.
So, hold the other. Thank you. sorry okay great so
I uploaded a lot of information about the
midterm last night and I just want to go over
it make sure we're all on the same page here
so on the the syllabus that says it's in two
rooms the exam it's just going to be in
WAUC 1055 the reason why is I usually like people
to not sit next to anyone in the exam
when I was an undergrad I'd try and get every
edge I could so if I could shade and get
away with it I probably would so I know a very
easy thing to do especially a multiple-choice
exam is just look at what the person next
to you is doing even if you don't mean to do
it it's very easy to do but I have two versions
of the exam with the order switch so
it's a bit harder not impossible but a bit
harder to do that and I'd rather everyone be in
the same room then have half the class been
in another room where I'm not present in case
someone has questions. This won't be a problem
for the other exams but they put us in
in this situation for this one. I've already
discussed what's going to be on the exam so
the stuff we're doing now on rationality,
utility and then consumer preferences isn't on
this exam. So it's just the basic concepts,
chapter one, market forces, chapter two,
so supply demand, equilibrium, consumer
producer surplus, taxes and government intervention,
so price falls and ceilings then market
failures which is module group b module six
in the in the ebook really is buried at the
back of the book and then finally elasticity
so there's not going to be a formula sheet
i've decided against it um for two reasons
and i know it may seem harsh but there is a
leniency reason to it anything that i believe
would require formula i didn't write a
question for that on the exam so anything that
involves like this crazy you know cross price
elasticity revenue equation where you have
to like figure out you know the burgers and
fries and there's one plus elasticity etc
etc you don't need to know that one um i i
showed where in the ebook those formulas are
and also the present value of the firm that
involves both growth and interest rates you
won't be asked anything about that you will
be asked questions on future value and present
value conversion in fact if you go to content
i have uploaded so down the bottom there's
a practice exams tab i've uploaded a
formulas to know tab so knowing how to convert
between present value and future value just
in general is a really good skill to have you
should understand the intuition behind it
hence why there's no formula for that basic
total revenue profit equations as well
understanding that marginal revenue is just the
change in total revenue given the change in
quantity we've gone over that through intuition
then with the elasticity so the the basic
form of elasticity of demand as we as we
showed is the percentage change in quantity demanded
given the percentage change in price and
then we can break that down into these two
components where this is just if you have
the equation where quantity is on the left
hand side it's just the slope in front of the
price that's the first part here multiplied
by price divided by quantity which we give
you when we ask these questions or if you
get the inverse demand function so you get
price on the left hand side of quantity on
the right this is just inverted so it would be
one over the slope and we've gone over that
a number of times so i do expect you to know
this and finally just knowing the equations
for producer surplus and consumer surplus
the the difference in underneath the demand
curve that that hits where the price of at
equilibrium is multiplied by by by 5 and same
for the producer but it's just above the
supply curve so those are the ones you need to
know the others you don't okay what to bring
scientific calculator make sure the
calculator you bring the scientific one can compute
like exponential so if you have like 1.4
to the power of 3 or whatever make sure
you can do that on the calculator there's got to
be future value present value conversion questions
that involve this type of thing this
is just a warning to make sure you can do
that so you don't get tripped up we're using
scantron you probably know more about that
than i do if i'm being honest so i've been told
you need a number two pencil but i'm sure
there are others that work just as well so
don't let that restrict you if you know it
works for something else okay so i've put on
some extra office hours No one actually came
to my office hour today, so I'm thinking
maybe I should strip it back and spend
more time to myself, but I'll keep this on
in case people want to come. So tomorrow
between 2 and 4.20, I'll be holding office
hours in my office, CRAN 339. Also, this should
be 339, but Friday morning, 10.30 to
11.30 as well. I'll have an extra office
hour, and I'll have my usual one
on Friday as well. On the day of the
exam, after I finish my class after this for
the two hours after I'll be posted up in rule
3082 and I'll just be there if they want to
come ask me questions use it as a base for
study there are 200 people in this course
so I know there's not enough room for everyone
but I assume a lot of people will want to
do other things instead so that resource is
there to you and as we discussed Monday's
class is just going to be a revision just
going over the the main concepts you need to
know for these topics. Finally, I spent the
last few days writing up the exam and
getting practice exam questions organized.
So as you can see, there's 55 questions.
The actual exam is only 30. And when I say
only 30, you only have 90 minutes. So it's
one every three minutes. So in terms
of exam strategy, don't get bogged down on a
question. You'll pay for it later on if
you don't finish so by coming to class
and going over the concepts you should be
able to do things in time relatively easy
easily it's not like the homework questions
that are a lot of reading and a lot of
figuring out a lot of these are just short
and sharp questions but just keep that in
mind but i did um ask a lot more in terms
of the practice exam to give you extra practice
the answers are up there as well so if
you go back here you have the solutions i
highly recommend not opening the solutions
until you finish with the practice exam what
tends to happen i do this all the time as
well it's a very human thing you won't be
sure you'll glance at the answer and you'll
be like oh yeah i knew that you didn't and
you'll pay for it on the actual exam so better
to get it wrong when there's zero stakes
figure out why you got it wrong and some of
these concepts will obviously be coming up
again on the exam so i shouldn't be giving
this advice because i don't follow it myself
but um yeah it definitely is a better way to
go about studying and yeah if you don't
know anything come to the office hours i'm
happy to help with your misunderstandings and
to get you ready for monday any questions
regarding the exam great fantastic okay so we
finished up last class talking about what is
rational behavior and economics and we said
it only required a satisfaction of two
axioms transitivity and completeness transitivity
is fairly straightforward it's this idea that
if you prefer a to b and you prefer b to
c then you must prefer a to c we showed
what happens if your preferences violate
transitivity you get into this um situation called
the money pump which just isn't a good thing
for rational behavior then we discussed
completeness which doesn't have the same, I
think, intuitive notion to it as transitivity,
but it's the simple idea that if X is related
to Y, or Y is related to X, or both, then
it's complete. So when we talk about preferences,
we essentially want to just be able
to compare everything. If we can't compare
everything, then that's bad. We can't actually
build a numerical scale to measure the
utility people get from certain decisions if we
can't compare absolutely everything so we gave
this example of for all the people in the
universe is taller than complete and we said
it's not so the check is you take the binary
relation in this case is taller than and
you take two objects in the universe in this
case chris paul and steph curry and we said
chris paul is taller than steph curry that's
not true steph curry is taller than Chris
Paul, also not true. Both are true.
That's also not true. Therefore, we haven't
checked any of these three boxes, so this is
not a complete relation. And we talked about
this is why the idea of weak preferences
are really important. It allows for the
concept of the same height or the same
number. In the case of preferences, this
idea of indifference. So at least as tall
as is a complete relation. It takes
into account this situation where people
are the same height. So to finish off this
idea of completeness, I've got four more
examples here. So, siblings with. Remember, siblings
with was transitive. If Ron was siblings
with Guinea, Guinea is siblings
with Fred, then Ron is
siblings with Fred. But is siblings
with, is that a complete or
incomplete relation? Yeah. let's go for an example
what's your name Kevin Kevin are you
and I siblings just just so everyone knows
yes or no no we are not siblings okay
so we can check this now is Ben siblings
with Kevin that's not true is Kevin siblings
with Ben that's not true are both true
no we don't take any of those boxes
it's not a complete relation so big mistake
people make is when they're doing that
check They'll be like, is Ben siblings with
Kevin? Then they'll be like, is Ben not
siblings with Kevin? That's not what the
relation is. The relation of is siblings
with is different to the relation of
is not siblings with. So while that
may have sounded a bit strange,
that's how we actually check
for completeness. We want the same
binary relation and just switch the order
of the two objects that we're comparing.
So is siblings with a complete
relation? No, it's not. okay what about at
least as good as in the universe of all
basketball players any nba fans in here by
any chance okay lebron or jordan lebron okay
so if i asked you every comparison you
would be able to rank them someone's at least
as good as the other correct fantastic yes
like before because we have this weak
preference and we have this definition at
least as good as we're talking about
basketball here then it is a complete relation
technically yes but it's a joke here like
good luck getting an agreement on lebron
jordan jordan lebron okay this next one's
a bit weird but it's important for a
certain reason at least it's good at in the
universe of all people it's a little
bit strange but roll with the
stranger so what's your intuition
telling you Eric, what do you reckon? Why not? Tell me what
you're thinking. Sorry? I just guessed. Just tell me what's
going on in your brain right now. Tell me
what's weird about it. You have no
specific subject. Exactly. What are we comparing?
We're not talking about basketball anymore.
as I show you here at least as good
as at what can we compare Lionel
Messi to Lebron Ronaldo to Magnus Carlsen
Tom Brady to Sabrina Carpenter there's
no context here and this is what's really
important we want to be able to compare things
and when you can't compare something
because the domains are so different it's not
commensurable it's not comparable as a result
we can't rank them in any way therefore
I would argue that at least as good as in
this case is incomplete Finally, at the
same university as, this is
very similar to the idea of is
siblings with. So, for example,
my friend Alex goes to UChicago, so if
you wanted to check if it's complete
for me and Alex, Ben goes to the
same university as Alex, that's not true. Alex is at the
same university as Ben, that's not true. Both are not true,
that's not complete. So it's the same sort
of idea as siblings with, and I want to
drive that point home, because completeness
does have this weird factor to it which isn't
the most intuitive. So an important note
is indifference is not the same as
incompleteness. We're still able to
compare and say that someone prefers two
things the exact same. And two ways we can
break the tie of indifference is through
the following two ways. So the first is if
you flip a coin, whatever outcome it
lands on, you'd be happy to choose, essentially,
if you're indifferent. that should be a
way to break the tie now something that i
i find kind of like interesting is a lot
of the time when you're making hard decisions
you'll flip a coin and all land on the outcome
you're like actually i want to do the other
so that's that's a good way of knowing if
you're truly indifferent or if you actually
prefer one thing over the other it was just
a bit murky to begin with the other thing
and the more technical way to break indifference
is if i offered you one dollar along with
either option you would select the option
with one dollar if you're truly indifferent, a
little bit of a good should separate the
tie. So if you're completely indifferent
between an apple and a banana, and I offered
you $1 to pick the apple, you'd pick the apple.
Because you're $1 better off than you would
be if you picked the banana, if you value
them the exact same. So why do we care
about completeness? If we want to
be able to make inferences about
people's preferences, this means that for every
two possible options that they can decide
between they must either prefer one of the
two or being different between them you
must know what their rankings are I must
either prefer apples to oranges prefer oranges
to apples or being different between them
I cannot say that we can't compare them
literally the saying you know apples to oranges
doesn't exist here we want to be able
to compare and rank everything when it comes
to preferences when preferences is irrational,
we can literally create a ranking of all
options from most at least preferred. So
in this world, there are only three options
a person can choose. What we can
construct is called this preference
ordering, a simple ranking of what
a person prefers. The axiom of completeness
guarantees that there will be only
one ordering, and there are no gaps or
ambiguous comparisons. We can literally rank
every option. They could all be even,
but we can rank them. and transitivity
guarantees there'll be no cycles of strict
preferences no money pumps that's kind of
important to economists but as i think i
mentioned one of my other classes some
philosophers actually disagree with that but
way beyond this course so going back to before
we we started last class by asking what
is rational behavior and as we said
these two axioms economists like them
as a definition of rationality because
it doesn't impose anything on what
you have to believe. So, for example, Bob always chooses
the option that results in him
being paid less. Is this rational
behavior? It's very weird, but
it's rational, according to this definition.
As long as he has this consistent ordering
or ranking of the least paid job, second
least paid job, so on and so forth, and
he doesn't violate transitivity, this is
a rational preference. So the definition
of rationality, as I said before, provides
little constraint on preferences
while allowing for diverse preferences
and behaviours. We don't imbue anyone
with any values. People can believe
and like whatever they want as long as
they're consistent. So weird preferences
can still be rational. As Bob, preferring
less money to more, preferring money
amounts that end in three to any other
amount. You can't have that preference
in a rational way. More for someone
else than yourself. This is actually
quite common. These are known as
social preferences. You might get $10,
give your friend $6, and keep $4
for yourself. As long as these
are consistent, that can be rational.
And finally, getting hit in
a leg with a crowbar can be
considered rational. A lot of people have
weird preferences. They're masochistic,
they're sadistic. We don't say they're
irrational because their preferences
differ from us. As long as they're
consistent and their preferences are
complete and transitive, we consider that
rational behavior. so this is the foundation
of rational choice theory in economics
however as you see there's a lot of
room for weird things like we probably
don't want a system of rationality when we're
modeling where people prefer less of a good
thing to more of a good thing so there's
other things that we're going to add so
before adding these extra components i want
to go through a couple of ways we look at
analyzing decisions okay so does anyone
want to play this game with me right now i'm
going to flip a coin if it's heads i'll
give you five bucks if it's tails you give
me a dollar anyone want to literally play
this right now yep what's your you up
first what's your name do you have one
dollar on you i've got a tenner
on me so if you've got a five that
would be that would be great if you
win otherwise i can zell you or we'll
figure out a way yeah oh good we'll
figure it out okay coin toss so you're happy with
the rules shog if it lands on heads
i owe you five dollars if it lands
on tails you owe me one dollar yeah
okay great got your consent brilliant
let's flip it you owe me a buck sorry
about that i would much rather owe you
five dollars actually than you owe me a buck
which is funny but yeah okay so i'm going
to pick on you a little bit more here sorry
about that outcome why why did you decide
to take this bet okay yeah the payoff is
attractive you're not just a degenerate
that enjoys gambling there's something nice
about this this bet correct so how do we
analyze it this does look like a good bet but
can we put it in terms of a framework to
actually calculate it. So in other words
if you accept this gamble what is the
expected value or the expected payoff of
accepting this gamble? So expected value is a
really important tool in decision-making
especially when there's uncertainty. All it
is at the end of the day is the mean or the
average of a random outcome. We calculate
this by taking a weighting average of the outcomes
so this is what expected value looks
like it's just each outcome how much you
get from it multiplied by the probability of
that outcome occurring adding it all together
so going back to our coin flip example
we have two outcomes win $5 lose one each
with 50% chance so to calculate the expected
value of this we take the first outcome win
5 multiplied by the probability of it
occurring, 0.5, and we add the second outcome,
minus 1, multiplied by the probability of
that occurring, and the expected value of
playing this game is $2. So I offered you all
the ability to play this game for $0, so
you made a positive expected value decision
here of plus 2 by accepting this bet. Once
again, it didn't turn out in your favour in
the end, but this was a good thing. if I
said you have to pay me one dollar to play
this game from an expected value perspective
it would still be worth it you've got
positive expected value another example
if you roll a die and I paid you
the number you rolled multiplied
by one what is the expected value
of rolling a die we do the same
calculations here there are six possible outcomes
one two three 3456 and the probability of
each of these events occurring is the same 1
over 6 or 16.7 percent once again we just use
the same formula it's the sum of each outcome
multiplied by the probability of that
outcome occurring adding it all together so
here the first outcome is rolling a one if
that happens you get one dollar multiplied
by the probability of rolling a one which
is one divided by 6, the second outcome you
roll a 2, you get $2 multiply by the
probability that an outcome occurring, 1 over 6,
so on and so forth, you add it all
together and it's $3.5 does this 3.5
mean anything to anyone in
regards to a die? anyone got any
observations or insights about 3.5? yeah yeah, exactly all it is,
is the mean it's the numerical average,
and this is why I set it up in this
way. If I ask you what is the average
number you roll when rolling a die in the
long run, it's 3.5. It's just each face
multiplied by the probability of that
face occurring added all together. So that's
all expected value is. So before I go on, if
anyone here is a sports fan or an NFL fan,
they talk a lot about things like expected
points added and also on fourth down decisions
do you like kick the field goal or do you
like go for a fourth down and these are
essentially just expected value calculations
once you know what the outcome is in terms of the
value you can calculate which decision is
better for you in terms of winning the game
so this is everywhere all right so i'm
not made of money so i'm not going to
offer this for for real but um i'm just
curious what people hypothetically would
choose here first option you receive
330 for certain 330 times 1 is 330
that's the expected value or do our die
roll but instead of receiving the
face times 1 you get the face times
100 which will give you an expected
value for anything. So hands up if you would choose option 1 again. With people
option 2 the more popular option,
fantastic. So can you remind
me hands up if you chose
option 1 again? Okay, brilliant. So does that
mean preferring 1 over 2 is irrational? You picked 1 over 2.
Do you want to give us your reasoning and
then tell us if you think it's rational
or rational? I got it. Exactly. You're
worried about the bad outcome. And
this is really important. This is
rational behavior. This is actually
really important and we'll get to
that in a moment. Alright, so let's
talk about this strange gamble. We've
talked about some simple 50-50 or
die rolling ones. Let's get a little
bit weird with it. So consider the
following game. I will toss a coin until
it lands on tails. So if it lands on
heads, we continue. If tails happens
on the nth toss, you get 2 to the
power of n dollars. So for example, if it
happens on the first toss, you get 2 to
the power of 1, $2. If tails happens
for the first time on the
second toss, you get 2 to the
power of 2, $4. Third toss, 2 to
the power of 3, $8, dollars, so on
and so forth. How much would you pay
to play this game? So imagine I offered
you the ability to play this game right now,
how much would you be willing to pay me
for this opportunity? This is a very
common answer, 4 bucks, why did
you land on 4? Clayton with 4 bucks,
gave really good reasons for it. Would
anyone go higher than 4 bucks to play this
we're not actually going to apply it
and i'll show you why in a second um would
anyone offer higher than four bucks to
play this game no we all don't like the
gamble which is which is very common no
one usually pays more than like ten dollars
for this opportunity the next question
is though what is the expected value
of this gamble does anyone want to
take a guess at this our engineers in the
room may know the answer I feel like it's a
really large value. What's the largest
value you can think of? Around infinite. It's not around
infinite, it is infinite. So the expected value of this gamble is infinite. So we can actually play it here if you want. This is so annoying.
I've got to do it the old-fashioned
way. Here we go. Control C. Get rid of this. so i yeah i um vibe
coded this a while ago so this these these
are the rules and you can i'll get the qr
code back in a second and it tracks your
total winnings your highest when your
average payout the game is played etc so we're
not doing that well are we to start with
will ever land on heads this is insane
i'm not stopping until we get ahead okay
so yeah you can you can play around with
that so I'll give you an opportunity to get
the QR code out if you want to play around
with it yourself. But the reason why
it's infinite is remember our expected
value calculation is the actual outcome
multiplied by the probability of the
outcome occurring. So how many possible
outcomes are there? So we know the first
outcome occurs when you toss tails on the
first flip, that's a 50 chance you get
two dollars second outcome is when you
toss a head then a tails you get four dollars
that's a 25 chance of occurring and as you
notice the probability decreases by a half
each time and the the amount you get
doubles each time this doesn't end this
goes on forever so there's still some
positive amount of probability where you
get an infinite amount of money at the
outcome and because of the weirdness of
infinity the probability i'm sorry not the
probability the expected value of this
gamble when you add everything up is going to
be infinite so according to expected value
theory if you want to maximize expected
value you should pay an infinite amount
of money to accept this gamble obviously
no one is willing to do that we didn't
get higher than four dollars in this class
why is that the case so this is known as the
the the st petersburg paradox the paradox
being the the values of the the gamble
is infinite but no one wants to pay like
more than ten dollars for it what's up
with that and it was um created and kind
of like solved in a way by daniel bernoulli
who we've got a nice photo of here so
people don't maximize money they maximize
utility happiness well-being an expected
value does not count for a few really
important things that we care about when it
comes to happiness. One is risk
preferences. People have different appetites
for risk as we saw before. The exact
reason you gave was I worry about getting
these bad outcomes. I'd rather just
take the safe bet. The second is diminishing marginal utility
of money. The idea behind this
is each extra dollar you get is worth
slightly less than before and on a similar
note, we care about our total wealth,
not just the marginal wealth from the gamble.
So, in the situation with Schlott, if he
had $0 in his bank account, he might
not have taken the gamble because he can't
afford to actually give up a dollar in
that case. And as I show, the total amount
of wealth matters. Okay, so let's do
one more hypothetical here. Would you rather
$1,000 for certain, or $0 with a 60%
chance or $3,000 with a 40% chance.
The expected value of the first one
is $1,000. The expected value of
the second is $1,200. Hands up if
you would take the $1,000 for
certain here. I feel like there's
quite a few more hands than before. I assume
everyone else is taking the second.
So just by changing how bad the bad outcome
is and how good the good outcome is, I can
show that there are people that care about
risk a lot more here. If you maximize an
expected value, you choose Gamble 2 here.
but just showing that a lot of people don't have
an appetite for risk so the expected value
of two is more than one but it's not
irrational in fact it can be perfectly rational
to prefer gamble on gamble too so as i said
before is five hundred dollars always five
hundred dollars who would value five hundred
dollars more person a has zero dollars
in their bank account person b has one million
in their bank account i could ask someone
to answer this but i think this one's hopefully
fairly intuitive. If someone has nothing
in their bank account, $500 is life-changing.
You can bring them so much happiness and
utility. Whereas if you have a million in
the bank account, yeah, $500 is going to make
you better off than you were, but it's
literally a drop in the ocean, a drop in the
bucket for you. It's not going to change my
bunch. And this is the idea about your starting
wealth mattering. So here we have
our classic utility function. So on the x
-axis is the amount of money you have. The
y-axis is utility. And we have this shape
of utility function. It's always increasing, but it's increasing
at a decreasing rate. This is
really important. And as you can see, one of the
consequences of this is $10 is worth
different amounts of utility depending
on where you are. So if we start at
someone who only has $10, giving them $10 moves
them from $10 to $20. and we can see
on the utility scale this gives them five
units of utility whereas someone
who has $70 if we give them
the same $10 the difference in
utility between $70 and $80 is only one
unit of utility so the amount of happiness
someone gets from $10 or in our example
$500 will be different depending on their
starting wealth okay so this is a bit
more technical but the idea essentially is
if marginal utility is decreasing so that
means if your utility is increasing at a decreasing
right each extra dollar gives you
slightly less happiness than before then your
expected value is going to be higher than your
expected utility so there's diminishing
marginal utility for most goods so here the
way you can think about it is when you get
the tenth dollar you get a certain amount
of happiness, when you get one extra dollar,
the 11th, it's slightly less happiness than
before, the 12th is slightly less, so on and
so forth. Your happiness diminishes slightly
with each extra dollar. We've kind of
talked about this example before with eating
pizza or burgers. The first burger or the
first pizza gives you a lot of happiness. The
second one probably gives you like happiness
in some regard, but less than before. At
some point you're going to resource the
happiness you get and you actually start getting
negative utility um unhappiness for i think
another example is and i was actually just
listening to a podcast about it is like winning
sporting competitions so the podcast i was
just listening to the guy said he was in
the change rooms when the chiefs won their
third um super bowl in like five years or
four years whatever it was and he said like
they were pretty calm in the locker room it's
like okay yeah we've already run you know
two this is our third like yeah we're still
happy but we're not over the moon about it,
whereas if a team went in for the first time,
in a long time like the Seahawks yesterday,
they were probably over the moon about
it in the locker room. So what matters is the utility of
prizes in total. So if a person's
utility function is increasing and concave,
like we saw here, which you can get
with a log x function, a person who has $1
,000 in their bank account should pay at
most $11 to play the St. Peterburg's Gamble.
So just by imposing these risk preferences,
this decrease in utility function,
we're able to kind of solve this St.
Petersburg paradox. There's math here.
Don't stress about it. I'm just trying to
show what's going on. So a common utility
function that we have is x to the power of
y, where y is between 0 and 1. We want it
to be less than 1. If it's more than
1, think about your parabola. we get that
exponential kind of shape whereas if it's
less than one we get this concave shape
instead and this is important because utility
is always increasing when you get more
money but we have this diminishing utility
aspect of it as well that is increasing
at a decreasing rate so if we have x to
the power of 0.5 that's our utility
function if we take the first derivative
derivative. So how does utility change
if we get one more unit of money? We
take the 0.5 out the front, reduce
this by minus 1, and we get 0.5x to the
power of minus 0.5. This sign out the
front is positive. So what this means
is if x increases, u increases.
So utility is always increasing
as money increases. However, when we take
the second derivative, so once again we
take the derivative here, take the minus 0
.5 out the front, reduce this by minus 1, we
get minus 0.25x to the power of minus 1
.5. This is negative. What this means is
as we know utilities increases, x increases,
but it increases at what we say
decreasing rate. So as you get the first
unit of money, you might get one unit
of happiness, then you get the second
unit, you only get 0 .99, 30 units, 0.98,
so on and so forth. Okay, does that make
sense to everyone? Hey, let's hammer it home with one more example. I'm going to ask for
a couple of volunteers here, and there's
going to be a prize just for volunteering.
So if you think you are the strongest in
this class, or one of the strongest,
also relative for your gender as well, I'm
going to make adjustments on that. you can
volunteer and you'll get a prize but you
have to do the task for me as well so I
have any volunteers we have one brilliant
does anyone else want to volunteer to great
come on down guys what's your name again? Ivan and? Christian Christian with an M or N at the end? Christian Christian
and Ivan our lovely volunteers here and
I'm hoping to show that Diminishing marginal
utility and diminishing returns occurs in all
aspects of life Okay, so what we're gonna do
this is how it's gonna work also you're both
gonna get a point of extra credit by the
way for volunteering regardless of how you
do so you're gonna have one minute and you
have to do as many sit -ups as you can in one
minute I'm gonna need two more people just
to help me count every 15 seconds how many
they do what's your name again sorry Logan
so can you count for Ivan every 15 seconds
I have a timer up how many he does in those
increments and can you Daniel can you do
it for Christian as well so I put it up so make
yourselves comfortable fellas I'll get I'll
get a timer up on the floor in front of
everyone I know it's um not an ideal situation
but you're literally getting a point of
extra credit for this I think it's a good
trade-off you know what I'll let you guys
decide if you want to switch the push-ups
I'll let you switch the footy okay yeah okay
let's do push-ups and and um the reason why
I was a little bit reluctant that's one
second you've got one minute is someone in
the last class like ruined my example
because he was too strong so it's a little bit
of pressure there okay hmm the guy in
the previous class i'll tell you i'll
tell you after you guys perform
okay ready set go all right let's go guys
good start solid so after 15
seconds i'll let you know when
it's 15 seconds hey it's good Ivan
keep going mate keep going let's go come on
let's cheer them on a bit 15 seconds come on
push it push it this is Peloton come on
don't slow down Ivan you got this mate
Christian you're a monster right now keep going
you got it one minute is crazy I know but
you've keep going fellas keep going come on
come on 15 seconds left 15 let's try and
get a few more out okay brilliant keep going
yes good good I've got we done we done thank
you so much brilliant incredible effort
okay so Logan how many did Ivan do in total
48 and did you break it down into the 15
second increments oh good Daniel did
you did you count how many Christian
did so 74 total that's insane
congratulations did you count by 15 second
increments how many he did in each one
I did like the first increment okay then it
got too much and then it dropped like
around 30 something approximately okay no
worries but I think we could all see what was
happening they both came out the gates farm
you can sit down by the way guys come up
to me at the end of class give me your
last time so I can give you a point of extra
credit. Thanks guys. So I think that
demonstration worked pretty well. They both came
out of the gates firing, they were able
to do many pushups in the first 15 seconds.
In the next 15 seconds they were still going
at a pretty good pace but a little slower
than before. The third one was when it really
hit. And Ivan, yeah you were really slowing
down and the last one was just a complete
ride off. And this is the idea of
diminishing returns. It's not just with utility,
it's not just with enjoyment of things it's
in so many aspects of our lives any of you
that have been to the gym will know the
feeling that Ivan and Christian just had that
first set on the way you can smash through
the second one's hard third one you are
failing early on a lot of the time as well so
that's a demonstration for you of diminishing
marginal utility Arnie would be proud
okay so in the past there are people that
have done this rather than doing push-ups
they got people up the front and saw how many
brownies or debbie rolls or whatever they
could eat in a minute. I feel like that's
kind of crude, reminds me a little
bit of Matilda, if anyone's seen that
movie or musical and I didn't want to do
that, but the idea behind it is, for the first
one you eat, you get 25 units of utility,
and as you're smashing them down, you're
slowly getting less and less units of utility
each time, still positive, and at some
point, each one you'll eat will probably
increase the likelihood you're going to send
the rest back up so you start getting negative
utility from it so after h1 you get less
and less utility so marginal utility is
always decreasing in our models so we've talked
about expected value but we want to incorporate
these things that we talked about to ensure
that our preferences can still be rational
taking things into account like risk
preferences diminishing utility and where
you start in terms of wealth. So expected
utility is just the sum of the utility of each
outcome multiplied by the probability of
that outcome occurring. Sounds very
familiar. This is our expected value
formula. Each outcome multiplied by the
probability that outcome occurring, adding
it all together. Expected utility is
the exact same except we transform the
outcome by the utility, the happiness it
gives you. Remember, $50 will give someone
who has nothing a lot of happiness, but
it will give someone who has a billion
dollars like little happiness. So we
transform that outcome into the utility
based on your utility function, multiply
by the probability of that outcome, and
add it all together. So the utility
function can take many forms. We've talked
about log x, x to the power of 0.5. This
is a famous function called the Cobb-Douglas
function. if any of you continue on with
economics you'll see this one a few times
as well but what this means is we use
utility functions and the utility function
is the key construct in economic theory
this is why we obsessed over transitivity
and completeness so what the assumption
of rational choice allows us is to use
a utility function to represent the preferences
of individuals they must be complete
and transitive in other words, utility
maximization is equivalent to the
maximization of a complete and transitive preference
that people hold so a utility function assigns a numerical value to each element in
x so x is all the choices that you can
make and ux just gives it a numerical value
that's all it does, that's what the utility
function is doing and what this means
is If the utility function spits out the
following, the utility of x is at least as
high as the utility of y, then you at
least prefer x to y. It's at least as good as. If the utility of x,
option x, is greater than the utility of
option y, there's a numerical, this means
you prefer x to y. You strictly prefer it.
And if the utility of option X gives you
the same utility in numerical terms as
option Y, then you're indifferent between X
and Y. So this whole point and things that
we're coming to is this mapping between
preferences and utility. And in the next
class when we talk about indifference
curves, a lot of people get confused
because I think indifference curves
are utility functions. They're not. They're
just preferences and we can map
those towards utility functions.
So this is why I spent a lot of time
focusing on this. I'm actually going
to finish up here. This is where I
finish up with the other class, and I
will need to reinforce a couple of
things in the next class anyway. So
let's finish up here. I'm here for another,
I guess, 10 minutes if you want to ask
questions, and otherwise I'll see you on
Friday where we'll maybe finish this up,
maybe not, we'll see. How many more
do we have left? Yeah, Ivan, Christian, come to me and, yeah. Why did I do that? What's up, Eric? I have a question.
so one of the homeworks and all the
questions are like you know yeah yeah
someone written a regression and then
the coefficient of the price it's on
the price it's some should it be negative
always i mean theoretically yes but a lot of
dimension that's kind of weird let me let
me double check that for you like good
intuition yeah i mean it's possible that the data
that gave you does that but like yeah no no
like it like according to the law I mean
this is weird things that can happen but
there's something called a giffin good yeah you
know about that yeah yeah so like it's
technically possible but it's weird that they
have that in the day so before submit in
let me double check can you send me yeah send
me which state it is yeah and I can look at
it as well yeah thank you well I'm fellas
that was that was an amazing effort in your
track using yeah so Christian what's your
last name Salazar S-A-L -A-Z-A-R yeah and Ivan
what's your last name? Latinovich L-A-T-I-N
-O-V-I-C oh brilliant so I have an extra credit
thing in Brightspace tonight you should be
able to see it thanks for thanks for volunteering
really appreciate it So what happened
in your last class? I made it 45 seconds
instead of a minute. And this guy just
kept getting faster and faster. He
popped out 79 in 45 seconds. And it kept
getting faster in increments. And I
asked him after like... I think he's a roller or something like that. So that's why I
made it more good on you. I wanted to get
the failure in there just to make my
point. Because he ruined my point. I
was going to say 45 out of it. I kept
going at the end too. Maybe I was closer.
Yeah, yeah, yeah, yeah, yeah, thanks
for volunteering, and I guess you guys will
never forget about diminishing returns
now, as well as I was going to ask
the question. All right, brilliant
fellas, have a good one. I'm just curious
what your thoughts are on why people
continue chasing money after a certain
amount of fire. Because at that point
you're getting almost a marginal utility, but
people will continue, so is it just an
economic inefficiency? So this is a big thing in
behavioural economics. We treat gains and
losses very differently, which violates
rationality. So I should have, I probably mentioned
this in this class or the other class, I
can't even remember. The whole behavioural
econ course that I teach takes these
foundations and it shows people violate these
axioms all the time. So people are much more
risk-loving for the exact same decision if you
frame it as a loss rather than as a gain.
So you can easily in casinos do this all the
time, of course, and you can find gangers,
et cetera. And there's this idea called mental
accounting that...