run into a few issues
so i put up that link regarding like support
i noticed that they helped some people solve
it the biggest issue i think people face
is um they'll buy the textbook they'll get
to the course they'll click on it and it'll
say like access denied or something like that i
see too many nods in the head for my liking
i'm pretty sure they're able to resolve it but
don't worry it does register you've bought
the book and part of the course so if
you're still having issues with it let me know
and i'll get in touch with them and yeah tell
them that you know a few people are having
this problem but it should be able to work
itself out in the end so we finished up the
last class by spending a good like half an
hour talking about incentives even though
there's probably like one line in the textbook
about it I think this is so important and
something that may stick with you after the
course I wanted to focus on it so is this about
the the textbook or no so I put a date on
it 25th as soon as we're finished the second
chapter though I'm happy to allow people to
do the homework and it'll be due Feb second
so I might put it up earlier if we do the
content in time I'm just not going to open it
up if we haven't done any everything because
people might do it they'll get something
wrong and it's because I haven't taught it yet
yeah no worries but I'll let you know I'm
just keep you know posted of the announcements
on Brightspace and the emails you get I'll
be transparent about when everything opens
and the due dates are all accessible in the
syllabus already for a bit late on a topic
I'll you know extend the due date for that as
well so yeah just keep up to date with that
yeah so with incentives we looked at the fun
video of the office for like five minutes then
we look at some you know I think really
fascinating studies of incentive structure I
put those studies up on Brightspace not for
any like examinable reasons it's not core
reading it's just for your own interest if you
want to take a look into that and finally
we're going to look at a few examples of these
perverse incentives. So clearly incentives
matter and how you design it matters
towards whether you get the outcome you want
or whether it backfires completely. You
can crowd out other motivations or you
might not take something into account and this
is known as perverse incentives. So in
other words introducing this incentive
actually makes the problem worse than
before you introduced it. So here are a few famous
example so this is the window tax example
so in 1696 in England they implemented
a window tax where landlords were taxed two
shillings which was a lot back then for
having a certain number of windows in the building
and this incentive this tax was put
in place to reflect prosperity so wealthier
people were the ones who lived in houses with
like a lot of windows however because it
was the landlords and not though the renters
who paid the tax the landlords responded
by even boarding up the existing windows
or when properties were built they built the
properties without windows so what this
meant is it exasperated inequality because the
wealthier people were like fine whatever
will pay the tax but the poor people would
now live in places with no natural sunlight
and I can't imagine living here in Indiana
with no natural sunlight during winter there's
not enough light as there is and this
can't be good for physical and mental
health so this exasperated inequality compared
to what the tax was trying to do, which was
reducing the quality. Is anyone here from
South America by any chance? Has
anyone traveled to South America before
in here? Anyone? Where in South America
did you go? I went to Brazil. You went
to Brazil. So I don't think this is the case
in Brazil, but when I was backpacking
around Peru in 2017, I noticed something
really weird. Every like house and every building
looked like this. So you have the
building and then on top of the building you
can see all these like concrete pillars with
wires out of it and this wasn't just one
building this was like literally 95 of
the buildings in peru and look art is probably
a subjective thing but objectively i felt
this is quite ugly and i was so curious
about why this was the case i went and
i found out about it and things like this
don't happen for a reason there's always a
reason behind people acting in certain
ways can anyone take a guess or does anyone
have any intuition why all the buildings look
like this in Peru? You're in the Texans
jumper. Do you have any intuitions about
why they all look like this? What do
you think is going on? That's exactly right
actually. This is the whole point. This
is still by definition in construction
and as you'll see there's a reason why
they look like this. So a problem historically
in Peru was that constructing homes was
difficult as halfway through based on the
law at the time they had to pay property taxes
which meant a lot of these houses like the
the builders ran out of the budget they were
too costly to complete they weren't able
to sell them and it was a waste of resources
so in 1990 the president of Peru Fujimori
introduced a new policy that did away with
property taxes while homes are being constructed
he was like I don't want you know these
homes to not be completed so you only have to
start paying property taxes once it's
completed so this created a strong incentive
to find a way to live in a place without
ever ever finishing the building or the house
so a lot of peruvians would almost finish
their homes just enough to be comfortable to
live in so as you can see like this is like
a two-story place you can live in both stories
like completely fine but like hey we're
building a third story on this house it's
clearly not completed it's still in construction
so as a result they could live in their
homes but by putting that on top they were able
to avoid the property taxes by claiming that
their place wasn't you know completed and
this was the case in a lot of places across
Peru I don't know if they fix that or not
but if you travel to Peru in the near future
you can let me know if the building still
look like that finally there's a few examples
like this but this is the one I picked
out called the Great Hanoi Rat Massacre so
in 1902 in Hanoi Vietnam there was a plague of
rats and as any good government should do
they try to incentivize you know the citizens
to help get rid of the rats so they created
a bounty program that paid reward of one cent
for each rat killed and one cent was worth
a lot more back then than it is now and
to prove that people had killed the rat so
they can't just lie they said bring us the
rat's tail then we'll pay you the one cent
bounty however officials noticed that the the
population of rats didn't decrease at all
but a large subset of these rats and now
we're scurrying around without their tails. So
what happened was the rat catchers would
catch the rats, cut off the tails, use the
tails for the bounty but release the rats back
into the city so the rats could reproduce
and create more rats so they could have more
bounties by catching the new rats. Because if
they caught them all then this program would
cease and they could no longer claim the
bounty. So you're putting in this incentive to
stop the rats from being in the city but
what you're actually doing is incentivizing
in people to create more rats so they can
increase their income. So a better way to
have gone about this incentive scheme
would have been to say bring the head of the
rat rather than the tail of the rat. So
be very careful even in the minuscule
details because people will do what's better
for them and the benefit of letting
the rats procreate is greater than the cost
of not doing that. Finally there's
I think a bunch of different
miscellaneous ones. So physician bonuses
and this actually also applies to professors
as well. For a lot of physicians they
get rated and promoted based on their successes
so with a surgeon how what percentage of
your surgeries go well so if a surgeon is
meeting with a with a patient who they think
is high risk of the surgery not working
even though the surgery is probably the best
way for the patient to proceed a lot of
surgeons will refuse to operate on them
because it could lower their stats and anyone
who's seen a medical show will be like no
it will ruin my stats type of episode they
like to focus on that and with professors a
lot of professors in the first two weeks
before the drop date will try and make their
course seem a lot harder than it actually is
because they want to weed out students that
they think have a low work ethic or who aren't
as talented so they don't do poorly in the
course and thus don't give them a poor rating
because the evaluations are part of the
promotion and bonus process here at Purdue
and other places so I don't know if you've ever
been in a class where the professor seems
more off-putting than usual in the first two
weeks but they have an incentive to do
this which I think goes against like pedagogy in
general but yeah that's what incentives do
also the wells fargo scandal for those of
you who've seen the big short this might seem
familiar when people get commissioned to do
something they'll do it even if they know
it's like objectively bad so in the big short
these people working at these firms were
commissioned for giving out loans so they'd give
house loans to people who clearly couldn't
pay them back they knew they would default
on the loan but they get a commission for it
so they gave out tons of these loans the
same thing happened at Wells Fargo the bankers
were incentivized to open new customer
accounts and to meet these unrealistic goals
they began opening unauthorized accounts and
this caused you know a whole whole concern
finally the one we're all probably familiar with
is is rage baiting on social media so before
Elon bought Twitter people were just posting
the only incentive for post is the dopamine
hit you get from the likes and reposts
but once Elon took over they put in a
monitorization system where the higher engagement
the more like income you'd get and the way to
get a lot of engagement isn't by posting the
most accurate or you know educational content
it's to post like really like things
that make people either really angry a lot of
false information and things that probably
aren't good for you know progressing civilization
but this is what incentivizes people in
terms of the income so if you care about you
know that then the best thing to do is to
I mean like post like really hot political
takes misinformation all sorts of things so
rage baiting as you'll see on other platforms
as well is probably the best way to get
engagement even though we'd probably not say it's
the highest quality content out there well
maybe you like it but that's at least my
take okay so we've now done the first three of
these seven principles so today we're to go
over this understanding market slide and we're
going to dig into the time value of money
and start a bit on on thinking on the margin
so there's two sides to every market
transaction in these goods markets you've got a
buyer and a seller and there are other markets
as well like the labor market we have a
where you have a firm that's hiring labor and
you have people that supply their labor and
in these good markets with a buyer and a
seller the bargaining position of consumers
and producers is limited by three rivalries in
economic transactions. So how much power do
you have to sell or buy at the price you
want? So in the consumer producer rivalry,
buyers want to buy for the lowest amount possible.
If you can get the same product for cheaper,
you're objectively better off. And as
a seller, if you can sell the same product at
a higher price, you're obviously better off
as well. So the way the textbook puts it,
and it's kind of grim in this language, is
everyone's trying to rip each other off and this
is part of the reason why I still haven't
bought a car I'm terrified of the stereotype
of the second-hand car salesman in America
who either sells you a lemon or up charges
you by like three four thousand dollars
compared to the sticker price so we're all kind
of bargaining to get the best price possible
and you can think of it as everyone pursuing
their own self-interest then we have consumer
consumer rivalry so this is when there
are I guess a limited amount of goods that
consumers compete over. Is anyone a Swifty
in this class? Has anyone been to any
Taylor Swift concerts? You went to the Arrows
tour? Yeah. Did you see it like here?
Where are you from? You from Indiana? I'm from
New York. New York. Did you see it in New York?
Yeah. Okay. Was it hard to get a ticket?
It was. It was very hard. What was the
process for getting a ticket? It was just like
all the tickets sold out. Everything was
lagging and everyone's reselling them for super
expensive. Yeah. And a lot of tears for
people who missed out. Yeah. So for tickets
to the Arrows tour especially I think
because it was the biggest store of all time you
had many more consumers wanting tickets and
tickets that existed this resulted in a lot
of crazy things from people like spending all
night up like refreshing having multiple
people including their friends who aren't
swifties opening and refreshing as well so a
lot of people going to other states and even
countries to go see it so the competition
for the tickets were intense finally we've
got producer producer rivalry and this is just
as simple as the more firms there are the
more competition there is so buyers can you
know choose between different companies to
buy the product this puts a downward pressure
on prices and means that it's harder for
you to set your own price and on this final
one the government kind of plays a role in
the in the market as well so for producer
-producer rivalry firms may try and lobby the
government to intervene to avoid these rivalries
so they can set the prices that they
want to increase their profits so I can't
remember was there someone in this class from
Texas was it the next class you're from Texas
so I think I briefly mentioned this but
the electricity market in Texas are you familiar
with how it operates it's just it's at the
Wild West isn't it anyone can be an
electricity provider you don't have to make the
electricity you can just be a subsidiary
and be a medium between like getting the
electricity and providing to houses there are
hundreds of electricity companies on the market
but a lot of other states there's been one
company that's lobbied the government to be
the sole provider so they have essentially
like full control over what the prices are of
energy in that state. So by you know
lobbying the government there's a lot of rent
seeking that goes on with this sort of thing
to get the government to limit competition
so you're able to increase your prices make
more of a profit etc. And sometimes
they intervene in consumer consumer
markets as well. I mean rent is
probably one of these as well where the
government can intervene and
make things either better or worse
so this is a video um trying to to show
you about the absurdity in a way of the the
rip each other off phenomena phenomena
consumer producer rivalry so this is a scene
from the movie um uh monty python and the
life of brian and the basic setup is that
there's someone who's trying to run away
from the roman guards and he's trying to
buy this beard as a disguise and try and get
out as quick as possible so let's see if
this works it didn't work in the other class
so we've got to go to our good old friend
YouTube which means we're gonna get ourselves
a lovely ad poor idea bland is
that everybody was sold a broken promise
when phone tree That's not worth 20
shekels. No. Look at it. Fear of quality. That's
not in your goat. All right, I'll give
you 19, then. No, no, no. Come on, do
it properly. What? Haggle properly.
This isn't worth 19. You just said
it was worth 20. Oh, dear. Oh, dear. Come on, haggle. All right, I'll give you 10. That's more like it. 10? Are you trying
to insult me? Me with a poor
dying grandmother? 10? All right, I'll give you 11. Now you're
getting it. 11? Did I hear you right? 11? This cost me 12. You want to ruin me? 17? No, no, no, no, 17. 18? No, no, you're
going to 14 now. All right, I'll give you
14. 14? Are you joking? That's what you're
telling me to say. Oh, dear. Oh, tell me
what to say, please. Offer me 14.
I'll give you 14. He's offering
me 14 for this. 15. 17. My last word. I
won't take a penny less or strike me
dead. 15. Done. Ask to do
business with him. Tell you what,
I'll throw you in this as well.
I don't want it, but thanks.
All right. Yeah. All right. 16 oh yeah that's right
that's four all right all right so yeah that
shows kind of in an absurd way the idea
is that buyers want to buy the lowest price
sellers want to sell the highest but this
this guy obviously cared a lot more about the
process of haggling so i don't know if
anyone's traveled to the Middle East at all or
gone to any Arabic markets but you see a lot of
this haggle process take place in those
markets and it's a lot of fun if you like
that sort of thing so I highly recommend it and
go into this consumer rivalry we had our
Taylor Swift example but to drive the point
home this is a tweet from yesterday as you
can tell I'm terminally online and saw this
was relevant Florian who's an economist up in
Massachusetts somewhere said there have been
500 million ticket requests for the random
selection draw of FIFA tickets for the World
Cup, but there are only 6 million tickets
available across all games. So this is
almost 100 times excess demand. So the consumer
-consumer competition here is insane, to the
point where he argues that it's all going to
go to this secondary market, which will
feature some truly insane prices. The current
price structures we'll talk about in supply
and demand next week is too low and as a
result there is incredibly an incredible amount
of excess demand so tickets are a product
especially that's limited which results in this
consumer consumer rivalry okay so we're
now going to talk about the time value of money
but before jumping into their formula of
net present value in comparison I think it's
nice to take a step back and just think
about these intertemporal choices so time is
important in most decisions because the
choices we make will have future consequences so
it doesn't just result in something happening
today a lot of the time there'll be
something down the track that changes as a
result of our choice so these what we call
intertemporal so in between time choices relate
to decisions involving trade-offs between costs
and benefits occurring in different time
periods and how should we value things that
occur between different time periods so there
are two types of ways to think about
this things that have immediate costs and
delayed benefits so think about you know questions
or topics where we can force ourselves to
do it now so studying like kind of sucks in
the moment you'd much rather be doing other
things but you get benefits by doing better
on the exam by studying so can you force
yourself to do it now rather than procrastinate
and put it off other things like exercising
and dieting there's an upfront cost to it
now i know a lot of people do enjoy exercise
but it still falls under this but the delayed
health benefits are the reason we do it on
the other hand there are also some things
that have immediate benefits but delayed costs
is anyone a psychology major in this room
by any chance or a minor have you heard of
the walter michelle's marshmallow test
before does that seem familiar no so walter
michelle was a developmental psychologist and
he ran this famous experiment called the
marshmallow test where he'd get usually like
primary school kids so you know between four
and seven he'd place them down on a table in
a room and he'd put a marshmallow in front of
them and he told them you can eat this
marshmallow but if you wait 15 minutes I'll
put another marshmallow in front of you and
you have two and it's essentially you know
testing whether they can you know fight temptation
or they succumb to temptation and he used
that data to correlate it with people's later
life decisions to see if this like ability
to avoid temptation had any other correlations
with other skills that are in life. I
don't fully recall what his results were
from that, but it's this idea of fighting
immediate gratification. So something like, you
know, getting drunk as well falls under
this category. So maybe you all in your early
20s don't experience this, but after a night
out heavy drinking for me in my 30s,
I have the worst hangover ever the next
day. So drinking is essentially borrowing
happiness from tomorrow. So can I fight
temptation in the moment so I'm better off in
the future? things like high sugar food
and gambling fall under this and from a finance
point of view if you have money now you
can spend it on you know immediate
gratification or you can invest it and save
it and grow it in the future so this is
fighting temptation to pursue immediate
gratification to make your future self better
off so what is better would you rather a
thousand dollars today or a thousand dollars in
one year hands up if you'd prefer one
thousand dollars today? Pretty much everyone?
Does anyone prefer $1 ,000 one year from now?
Anyone in the class? Yeah? Great. Can you tell
me the reason why you prefer $1,000
in one year? Um, maybe because I
would forget about it and I'd be happy
for like $1,000. That's such a good
reason. And one person gave that answer
in the last class. Yes, there's actually
something to that. So there's like other
ways to get happiness besides money. And one
thing people get happiness over is like the
psychological aspects of utilities, so bullies.
So forgetting that you're about to get a
windfall of $1,000 and fighting out in a
year, that's actually a really good thing and
you might feel happier. So that's completely
legitimate. Also, we just talked about it.
You might succumb to temptation and spend it
all on, you know, food and drinks today,
whereas you want to, you know, put it down for
a payment in a year's time. So by delaying
receiving it, you're committing to like not
spending it on anything today. so there are
actually some reasons to prefer a thousand
dollars in one year to today but in general we
like to say a thousand dollars today is
preferred to a thousand dollars tomorrow in
the future in general people are impatient
they prefer immediate rewards to delayed rewards
that's a descriptive fact about the world
but there are other I think more logical
reasons to prefer the money now the first is
is relatively you know dismal but it's this
idea that there's uncertainty about the
future so we don't know like the world could
end in six months and if you decided to wait
for a thousand dollars in a year compared to
today you don't get to harness it at all so
that's one reason why we prefer things today
compared to the future uncertainty about the
future will the world and will life continue
there's also option value so if you have
a thousand dollars today there could be
20 different investment opportunities over the
next year that you only have if you've got
the money now so you have a larger set of
things you can do with the money if you get it
today compared to the future finally there
is a lot of things that you can do with a
thousand dollars such as put it into a an account
with a safe you know um investment with
an interest rate of let's say six percent
and what that means is if you put the thousand
dollars in that in one year's time it's worth
more than a thousand dollars it's worth a
thousand dollars in 60 and this is the
key reason here at the bottom that a thousand
dollars today is not worth a thousand dollars
in the future because you can always invest
it and grow that money in a safe way i should
say as well so in the book they really
like to talk about the time value of money so
for example if i put a hundred dollars in
the bank and there's ten percent interest paid
on a lump sum annually which is an insane
amount after one year you would get paid ten
dollars in interest ten percent of the
hundred is ten and you now have a hundred and ten
dollars in the bank so that additional
ten dollars is now effectively part of your
principle so now you have 110 instead of 100
and in the future if you keep in the bank
for another year you're earning 10% on $110
not 100 so if you leave it in for another
year you'll get 10% on $110 which is $11 in
interest now you have got $121 in the bank
and let's just tangent a little bit there's
something really important in that simple
example I mean for your finance majors
there you probably know all this already but
I think for a lot of people who don't study
business or aren't doing a major in business
this this is i think really interesting
and important so let's say you're a consultant
for an employee and a company offers
this employee a bonus and gives them a choice
so they can get paid one billion dollars
today or option b the there's a chessboard
and the employer says i'll put one cent on
the first square i will double and put
two cents on the second square four cents on
the third so on and so forth for all 64
squares and you can keep all the money on the
chessboard so as the consultant what do
you think the employee should do so hands up
if you think they should take 1 billion dollars
today hands up if you think option B
we've got quite a few hands up so you are
you confident in this answer yes why why do
you think option B yeah so this is this is the
whole thing that option B is exponential growth
is doubling every square and if we
calculate it out is 2 to the power of 64 minus
1 the reason why it's minus 1 is because the
first number is one not two and if we calculate
this in cents we have a number which i
can't even say but this is 184 quadrillion
dollars which is far more than one billion and
this is the power of exponential growth
compounding interest essentially leaving that
hundred dollars in the bank at 10 interest
over time will grow to an astronomical amount
is anyone here a fan of futurama by any
chance yeah so there's an episode where where fry
like um who the premise of the show is he gets
frozen in the year 2000 wakes up a
thousand years later and he goes to the bank
to see if his old bank accounts open and he's
like oh i only had three dollars in there and
with the interest rate compounding over a
thousand years it grew to like a billion dollars
essentially so the power of exponential
growth is wild so with compounding interest
that is what is going on and when we talk
about some of the costs as well there is
exponential cost growth as well so this is what
the chess board looks like when it doubles
every square you can see it gets up to these
like ridiculous levels and there's a really
famous i think riddle that uses this with
grains of rice on the chessboard so this comes
from wikipedia so if you like write out
chessboard um exponential growth you can find this
article in the original example as well so
they they talk about the time value of money
in terms of present value so what money is
worth today and future value or one is what
money is worth in the future so let's say
you've got a hundred dollars there's an interest
rate of four percent if i put this money
in the bank for two years what will it be
worth then and this is the future value so we
have a formula to go between the future
value and the present value so the future
value is just a present value multiplied by one
plus the interest rate multi sorry to the
power of the number of time periods in the
future so sometimes this is also denoted as
t in the book at the moment they have n usually
we say t t for time but it can also be n
as well so look at what the definitions are
and using this same formula we can calculate
the present value in terms of future values
so we just take the one plus i to the power
of n take it to the other side and we
get this formula here and what this means
is as n increases this term because it's going
to be greater than one also increases which
is because it's the denominator will make
the whole number smaller so as n increases
the present value decreases and it's the
same thing if the interest rate increases then
the denominator will increase and the number
will decrease the smaller the present value
and essentially what this means is if the
interest rate increases you can leave less
money today in the same account to get the
same future value you don't have to leave
the same amount because the interest rates
were higher so on and so forth so going back
to our example before you've got a hundred
dollars today interest rate is four percent
what is the future value and we can calculate
it using the same formula one plus the
interest rate which is four percent to the
power of two because we're leaving it in for
two time periods two years and we get the
future value of 108.16 dollars and what present
value reflects is the difference between
the future value, whatever the future
streams of income are, and the opportunity cost of
weighting. So because there's always some
interest rate, you can leave what you have
today in the bank and it will grow that
interest rate. So if someone's saying, hey,
if you lend me $100 today and I pay you back
$150 in the future, is it worth it compared
to just putting that $100 in the bank and
letting it grow at the interest rate? So that's
what we're actually trying to measure
here in present value. And then what we can
do is we can look at the present value of a
stream of future values so as you can see
here it's possible to have some income or
investment or income stream where you get a
hundred dollars tomorrow three hundred dollars
a day after two hundred dollars in you
know three days so on and so forth and we
can calculate what the present value of that
income stream of future values is using this
simple formula so in the first time period
you've got the value that you get in that
time period divided by one plus the interest
rate to the power of that time period
and so on and so forth for each one so you
get the future value in the second period one
plus the interest rate to the power of two
all the way up to n which is however many
time periods you'll get an income and what
we can do is we can simplify this this is
sigma it just means the sum of and what we're
summing is every time period from one until
the end of whatever our time definition
is n and we're adding it all up together to
get our present value And what this does, and
what the book really wants, and why it's
teaching this so early on, is as someone who
you know might invest in projects, you want
to figure out how to compare these different
income streams to make the best decision
possible. so consider two projects project
a you get 150 000 today from this project
that is what the present value is 150 000
today and project b generates the following
income nothing today 10 000 one year from now
50 000 two years from now and 100 000 three
years from now now without any like
consideration of the interest rate if we just add
up all the numbers here it's 160 000 10
plus 50 plus 100 160,000 so without any
conversion to the time to the present value
without any interest rate project B would
generate more money but because we can put this
hundred and fifty thousand dollars in an interest
account for three years we need to
consider that when evaluating these two
projects and decisions so with the annual rate at
three percent what we can do is calculate
the present value for project B so as you can
see here we're using the same formula as
before at the end of the first year you get
an income of 10,000 so that's divided by 1
plus the interest rate 3% to the power of
1 then in the second year it's 50,000 divided
by 1 plus 0.03 3% to the power of 2 this
is two years in the future so you've got to
compound that interest and it's the same
thing for the income in the third year as well
so the formula itself once you set it up is
pretty easy to negotiate and as you can see
this comes out to $148,352. And that means
project A has a higher present value than
project B, so you will choose project A. If
you so desire, you can calculate the future
value of project A by using the reverse
formula, just $150,000 times 1 plus 0.03 to
the power of 3, and it'll spit out a number
higher than $160,000. Fairly
straightforward stuff. Now, this is where
the net aspect comes into it. So far,
we've only looked at income streams, but
you can also have costs as well. So
the net present value is just taking into
account the present value of these benefits
minus the cost. So, for example, let's
say my uncle borrows $100 from me now and
promises to pay me back $150 in five years.
Is this a good deal if I know I can earn
10% interest on my investments today? so we
have a cost which is we're giving a hundred dollars
today and we have a benefit which is
a hundred and fifty dollars in five years
so the future value of a hundred dollars in
five years is one plus zero point one that's
the interest rate to the power of five because
you're waiting five years to get the the
benefit yeah so the future value of that
is a hundred and sixty one dollars and that's
more than what your uncle has given you in
five years and we can also calculate it
from the present value perspective what's the
present value of this 150 dollars in five
years the present value is 150 divided by one
plus the interest rate 10 percent to the power
of five which equals 93.18 so we can
calculate the net present value which is the
present value of the benefits minus the present
value of the cost the present value of the
benefits as we just calculator is 93 you're
given 100 today that's your cost so it's minus
6.86 so it's fairly trivial but essentially
if your net present value is less than
zero the cost of investment outweigh the
benefits so it's a bad deal unless you kind of
really like your uncle and you want to help
them out but like financially speaking
it's a bad deal and vice versa if it's above
zero and if it equals zero you should be
indifferent between lending and not lending so it
gets slightly trickier to calculate, not that
much trickier, but slightly trickier to
calculate when the costs and benefits accrue
at different times. So rather than lending
your uncle $100 today, imagine you lend them
under this policy $50 today and $50 in
one year from now. So the costs occur at
different times. And he agrees to pay you back
$35 a year, starting from three years after
the first money he got from me. And the
interest rate is 3%. Is this a good deal? What
is the net present value of this deal.
So the key thing when answering a question
like this on the exam is just write down
when these costs and benefits accrue. So you
can see the two costs occur one today at t
equals zero and one one year from now with t
equals one. So this $50 won't need to be
transformed into a present value calculation
but you will have to transform this into
present value. And all the benefits accrue in
the future so you will have to transform them
into present value so as you can see here
we're looking at the present value of the
cost the first 50 dollars which we give
today that's already in present value terms
and in one year's time we have to convert it
into present value so it's 50 divided by
one plus the interest rate to the power of
one one time period in the future which gives
us total cost of 98 .54 in terms of present
value and the benefits like what we've done
in the past it's just when you get the
income divided by one plus the interest rate
to the power of what time period you get
it. So three years from now, four years from
now and five years from now is when you receive
the three payments from your uncle.
Adding that all up you get 93.31 as the present
value of benefits. Net present value is
just the the benefits minus the cost in
present value terms and this is negative.
So no this is not a good deal for you in
terms of the loan. So present value decisions
can grow indefinitely. A lot of you know
firms calculating this way where cash
flow is constant over time and it is divided
by one plus the interest rate. Remember that's
the the opportunity cost of the of the
project and what we can do is have the present
value of like this perpetual income forever
which is the cash flow divided by the
interest rate. I'm going to show you in a second
how we can come up with a denominator
in this geometrically infinite series. I know
most people here aren't you know math isn't
probably your strength so I'll go through it
with you but at the end of the day you can
just memorize it that's completely fine as
well so I loan my uncle $100 and he says I'll
give you a dollar every year for the
rest of my life then my children will give you
a dollar every year for the rest of their life
so on and so forth forever so you'll get
a dollar every year for the rest of your
life assume the interest rate is 10% is this
a good deal or a bad deal so we can calculate
this using that formula the present value
in perpetuity forever equals this you know
constant future payment per year divided by
the interest rate so the present value of
getting a dollar every year forever is one
divided by 10 percent or 0.1 which equals
ten dollars so the the benefits is ten dollars
the cost what you're giving today in present
value terms is a hundred so this is a bad
deal and the intuition behind this is if you
put $100 in the bank today at 10% per
year that exponential growth would take off
quite quickly so the higher the interest rate
the higher this yearly payment needs to be
so we can answer this question what would
the minimum amount that your uncle and his heirs
need to pay to make you indifferent between
putting the $100 in the bank and giving
him the loan and we have all the information
we need to calculate this so we know that
the net present value needs to equal zero
and that the present value of the cost is
a hundred dollars what we're lending so this
is our equation here we replace the net present
value with zero and the present value of
cost with minus 100 so the present value
of benefits equals 100 and that means we know
what the equation for the present value of
benefits is it's a future payment per
year over i the present value of benefits based
on the equation we did up here is equal to
100 and then we know the interest rate is 10
percent we solve this and that means the
future payment per year for you to be indifferent
between them is ten dollars and we can
do the same thing as well for the interest
rate so if we said they're still going to
pay one dollar a year what would the interest
rate need to be to make them indifferent
and the interest rate will turn out i believe
to be one percent which is a low interest
rate so you need to think about the lower
the interest rate the less incentive you
have to put in the bank and the more incentive
you have to invest. So yeah out of nowhere
they're throwing this relatively complex
equation in the textbook and this is the value
of a firm with current profits pi zero with
no dividends paid out and expected constant
profit growth rate of g. So this profit's
going to grow over time assuming i is greater
than g and this infinite series you can
translate because this is a common factor in
everything but pi zero here is one plus g
divided by one plus i and they somehow end up
with this formula here now i'm going to show
you how to get this using the infinite
geometric series just to show you how it's done
because i don't show you in the textbook so
that means you'll just have it on the slides
but don't fret over it i don't think this is
that important but i wanted to take you
through it in case this was something you were
worried about so this 1 plus g divided by
1 plus i is a common factor in all the terms
except the first term pi zero so if we collect
all these like terms and we can define r
equals this common factor of 1 plus g divided
by 1 plus i and then for r we have this
geometric series of 1 plus r plus r squared
plus r cubed for eternity what this comes out
to is 1 divided by 1 minus r now what we can
do is we can substitute our 1 plus g divided
by 1 plus i into r so we have 1 divided
by 1 minus r and we've put back in this term
here it's all multiplied by pi zero because
that is the common factor here and we can
simplify the denominator so don't look at the
numerator here we're just going to look at
the denominator 1 minus 1 plus g divided by 1
plus i if we all wanted over the same denominator
we got it times 1 by 1 plus i so we
get 1 plus i minus 1 plus g 1 minus 1 that
disappears so we end up with i minus g over 1
plus i that's our new denominator so we have
pi zero which is one divided by i minus g
divided by one plus i and when you have a
divided over another divided you take the
very bottom term here and move it to the top so you
get pi zero multiplied by one plus i divided
by i minus g which is what we have here
so i know that's a lot there this isn't
meant to be a math class but the fact that they
don't show you how to do it i just wanted to
take you through the math briefly these
slides are online so you can go through it again
yourself that's how they get there and
I'm actually kind of upset they don't take
you through that in the subject materials itself
okay so we're going to start a little bit
on marginal analysis so any questions on
the time value of money that's probably the
more formulaic stuff we're going to do in
the first week and I apologize for like not
putting in anything video wise or
interactive there I just want to make sure you
all know how this formula works when they ask
you questions or usually be in the
form of calculate the present value because
you're making investment decisions today, which
one's worth more. So given a control
variable such as quantity, and it's
called a control variable because
you can control how many units of a
good you'll produce, the managerial
objective is to maximise profit. So you want to
think about the total benefits of producing
that many goods and the cost of producing that
many goods. So your object is to maximise
the net benefits, which is the total benefit
and the total cost, of producing that
number of goods. It can also be written
as maximizing profit rather than maximizing
the net benefit. So how do you maximize
the net benefits? We use something called
marginal analysis. So the marginal benefit
of the quantity you produce is essentially
saying, if you currently produce 150
units, what's the benefit of producing one more
unit? So it's the change in benefits
arising from a change in this quantity or
whatever control variable there is. And it's
the same with costs. if you increase your
output by one unit it will cost more as a
result you got to take into account both the
marginal benefit and the marginal cost
and the marginal net benefit is just a
marginal benefit of the change minus the marginal
cost of the change yeah so when you are
able to get the marginal benefit equaling the
marginal cost that's when you've maximized
your profit if the marginal benefit is
greater than the marginal cost you're essentially
leaving on the money money on the
table by not producing more and if the
marginal cost is greater than the marginal
benefit you're obviously losing money on that
extra unit of production so you should dial
it back all the way until marginal benefit
equals marginal cost so going back to our
example with Lamar let's say he makes one more
glass of lemonade and the additional costs
the economic costs of producing that extra
glass of one dollar and he's able to sell
that extra glass for three dollars his marginal
benefit of producing one more glass is
three cost is one as a result his profit of
producing one more unit is two dollars should
he make one more yes fairly straightforward
what if the next glass costs a little bit
more a dollar fifty and he can sell it for
slightly less two dollars this is still in the in
the positive marginal benefit is greater
than marginal cost so we should produce that
extra grass of lemonade all the way up until
the marginal benefit equals the marginal
cost so when we make decisions in life not
just as managers as people we compare the
costs and benefits of an action so when we decide
how much is something we compare the cost
of each unit with the benefit of each
unit and are engaging in marginal analysis so
a floor is like let's say um let's go to this
piece for example let's say I said your average
happiness of eating seven slices of pizza
is 20 utils should you have seven slices
I mean that number should be meaningless to
you meaningless to you what matters to you
is how much happiness you get from that sixth
to seventh slice so with food you can assume
the first slice of pizza you eat will be
the best like you're hungry that first taste
is amazing the second one might still bring
you happiness and joy but less than the first
so on and so forth until you're so full
the next one isn't going to produce as much
happiness to you as the cost of you know that
that yuck feeling from overeating so
even though the average benefit overall of eating
seven slices of pizza may be positive the six
to seven slice might actually have a higher
marginal cost and the marginal benefit
so this is why thinking on the margin is really
important when making decisions about when
to stop and it can be anything how many
times should you see the same movie that first
time you see it you see the plot for the
first time really great i don't know about you
i've re-watched like the matrix like probably
20 times in my life and after a long delay
i'm happy to watch it again i know the
plot but i enjoy the movie but if i watched
it again a day later the marginal cost would
be greater than the marginal benefit of
watching the movie for me so it's not just about
how many quantity of units to produce marginal
analysis falls out to anything in our
everyday life how long do you need okay okay
so I want to show one more slide so I know
there's no calculus in this course or not
meant to be even though this slide from the
like in the textbook is calculus I want to take
you through it quickly because what marginal
analysis is is essentially the slope
of any curve which is calculus so let's say
your benefit curve is the benefit of producing
some quantity q equals 250 times q minus 4q
squared we can take the first derivative the
benefit according to q and we get 250 here
q to the power of 1 so we take 1 here 250
times 1 is 250 and we reduce the power by 1
so 1 minus 1 is 0 the q disappears we get 250
minus we do the same thing taking the first
derivative take the 2 to the front 2 times
4 equals 8 reduces by 1 from 2 to 1 and we get
8q and we do the same thing for our cost
curve as well and then to find the profit
maximizing quantity we just set the marginal
benefit function to the marginal cost function
here so the marginal benefit 250 minus 8q
equals 2q and get that gives us 25 so this
is the the final slide before I hand it over
and as you can see here we are producing the
maximum amount when the marginal benefit
which is the tangent of the line the slope of
the line here on our benefit curve is equal
to the slope of the line of the cost curve
so before that as you'll see the slope of the
the benefit line is going to be steeper
and steeper and steeper it will be higher
than the marginal cost curve which is flatter
flatter and flatter and as you go beyond this
point this line is going to get flatter
and flatter and flatter and this one's going to
get steeper and steeper and steeper so
marginal costs will be greater than marginal
benefits. We'll go back over this slide on
Wednesday there's no class on Monday but I just
wanted to give you this introduction to
the graphical version of marginal analysis.
Before you head off we have Celia, I forget
is it? Celia who's the the president of the
Women in Econ Club who wants to talk to you
about her amazing club so please give her your
undivided attention. Hey guys, real quick.
Hi, my name is Celia. I'm actually the
Public Affairs Officer for Women in Economics,
so I do outreach. We have our call-out
next Wednesday in Cranark G005 from 6
to 7 p.m. Anybody's welcome. All genders,
no matter what. If you want to follow
us, we are WBC Purdue. Additionally, kind
of what our goal is and what we do in
Women in Econ, we build a lot of
community. We make sure people are in touch
with others. If you're in Econ 251 or 252,
we will be holding tutoring sessions
with PEA as well. That could be
helpful to you. We also bring
in speakers from outside of
Purdue as well as host some of our
own speakers. Dr. Grodek was actually
one of our speakers the last semester.
We have Dr. Galen coming in from UChicago
in the next couple weeks. I would really
like to see you there. No worries if
you can't make call -out. If you just want
to come to one meeting that you see that
interests you, you're more than welcome
to do that as well. And you can
use the QR code there if you're
interested. Yeah. Thank you so
much, everyone. No class on
Monday. If you've got any questions
for Celia or myself, you can
see us after. I can't open
the text back. Yeah, so if you
click on it, what happens?
Yeah, it shows... Yeah, it shows... ...on battle video. As you do not have
access to the e-book. A lot of people have
had this. I don't know what's going on. I
mean, it's your setting. Do you think
it's my settings? Yeah, for
example... ...for other class... Oh, wait. You can go into my, um, because if you can
help, you know, me fix this now.
No, I don't know. Yeah, but, um. I can
always ask him as well, so don't, don't
worry. For the most part I'd say like 90% are
on the literature. That class is
really really. We're not the
lucky of the . I don't know. Because for
us, you can see that there's like three. So we can access
the textbook. Yeah. So if I go. I don't know
where my settings are, so you
shouldn't be so much. Assignments. I thought it should
be accessible because I started it. Yeah,
but that's strange. I'll have to get
in touch with them. Oh, okay. Yeah,
no, I've apologized for that. It's
really annoying.