many students come to the Social
Sciences really looking forward to
engaging with ideas then they discover
that they need to understand some
statistics and they get nervous and
worried there's really no need for that
firstly you need to appreciate that some
ideas can only be understood if you
understand some statistics secondly
you'll discover that if you take the
statistics slowly one step at a time
it's much less difficult than you might
imagine to understand this we're going
to look at one particular business and
use a formula to arrive at a conclusion
which is counterintuitive something that
you really wouldn't have expected and
will break the formula down take it
slowly and I'm sure you'll find that it
really won't be as difficult as you
thought it might be I reckon he's gonna
win this thesis he reckons he's gonna
win this you'll see lots of adverts
where the business claims that you can
get the best value by dealing with them
because you can deal directly with them
and cut out the middleman he said you
cut out the middleman yeah when you come
to us direct we can give you savings
it's a really honest wise to avoid a
middleman it'll cost you
I'd say Faro you save on state minimum
coverage because we cut out the
middleman when you buy a big brand
mattress you pay for a lot of stuff you
don't really need and by dealing with
the manufacturer you avoid all the costs
of going through the middleman who is
simply a parasite he does nothing useful
he contributes nothing was all you play
for there's a great mattress no
middlemen mumbo-jumbo one example of
this you often see is with kitchens go
direct to the kitchen manufacturer don't
go to the middleman what we're going to
do is to use a simple formula to show
you that this idea is complete nonsense
the middleman is not a parasite on
society but a man or a woman who
performs a valuable function in keeping
costs down before we come to the formula
you need to understand the idea of what
we call transactions costs any business
as some costs which are directly related
to the manufacturing process but there
are other costs to transactions costs
are the costs associated with the
exchange process you have to have
somebody advertising somebody producing
price lists somebody going around
negotiating deals and so on these are
the cost new directly associated with
the production of the good that we call
transactions costs the guy who started
this business a decade or so ago
actually produced the kitchen units
himself originally now he spends his
time going around discussing with
customers drawing up what they need
discussing a price and so on
we are producing all kind of furniture
kitchens bedrooms office furniture I
don't I don't work any longer here in
the workshop I do a lot of the design
work speaking in with people and
contacts with the customers when this
work is done it's usually about a week
we can begin the work to produce these
are the transactions costs which always
have to be met when you buy any good or
service what we're going to see is that
the middleman is actually somebody who
plays a valuable rock for society in
minimizing such transactions costs
whenever people buy and sell they engage
in an exchange in an advanced economy
they do it through the medium of money
but to illustrate the process of
exchange come to my Island economy where
we only barter that is exchange goods
without money
at the moment there are only two of us
on the island I grow olives
Theodore grows apples I want some of his
apples he wants some of my olives so we
exchange best olives I've got are there
a bit of sand on them but but these are
quality olives kilo of my olives for
fibre you're honest they can give you
only three apples three yeah well it
took me a long time there are four
yeah but take a look at this able to
you're a hard man but there are some
transactions costs associated with the
exchange we have to arrange to meet
agree a rate of exchange and someone but
a third person has joined our community
now Mariela who specializes in catching
fish and wants to exchange her fish with
our goods
how many exchanges on our island now
Theodore exchanges with Mariela
I exchanged with Theodore Marielle
exchanges with me so there are three
exchanges each one with The Associated
transactions costs
how many exchanges if a fourth person
Damion joins us who specializes in
tomatoes suppose we go to a hundred of
us each specializing in some different
product
how many exchanges then assuming we each
want some of the product of all the
others working out the answer for large
numbers is virtually impossible unless
we do it by using a formula to work it
out we'll let the number of people on
our island be represented by a letter n
will write it as a capital n because it
could be a very large number so given we
don't know the number of people on the
island can we use in to establish a
formula that will tell us the number of
exchanges that will take place on the
island each of the N people however many
that is will be exchanging with all the
others everyone except himself or
herself that is n minus one people
so we must multiply the end people with
all the others the n minus-1 people to
give n times n minus one
but that would mean we count my exchange
with Theodore as one exchange and his
exchange with me as another now in
reality it's only one exchange and that
will be true for all exchanges there's
only half the number implied by our term
n times n minus one so now we divide n
times n minus one by two to correct for
that
now that we have our formula we can set
n to any number we choose to see how
many exchanges there are for any
particular economy so for my four-person
economy on our island we have N equals 4
so n minus 1 will be 3 and we have 4
times 3 divided by 2 is equal to 6
exchanges so with 5 people 5 times 4
which we then divide by 2 gives us 10
exchanges suppose there is a hundred of
us then we have a hundred times 99 which
we then divide by two gives us four
thousand nine hundred and fifty
exchanges our formula helps us to see
how quickly the number of exchanges and
hence the amount of transactions cost
rises as the numbers in our society
increase but now before we develop the
idea just let me remind you of the
importance of putting the brackets
around that term n minus 1 without it
we'd have something completely different
our formula without brackets would now
be written as n times n minus 1 over 2
as you probably know there's a
mathematical convention that says when
there's a series of operations to be
performed we stick with a particular
order what's in the brackets comes first
but we multiply before we subtract so
the top line would become n times n or n
squared and then after that we would
subtract one so this gives us N squared
minus one over two
so in our society with a hundred people
if we use this incorrect formula we
would get a hundred times a hundred
equals ten thousand then minus one to
give us 9999 then we would divide that
by two to give us four thousand nine
hundred and ninety nine point five
exchanges this is different from our
formula with the brackets and wrong and
it's wrong
because we left the brackets out of the
formula here
as our island economy grows someone
arrives and produces nothing he simply
sets up as a trader exchanging other
people's Goods is he a useless parasite
because he doesn't produce anything he's
actually very productive and you
understand that if you understand the
nature of transactions costs we're now
in a position to see just how productive
for the community the middle man or the
middle woman can be let's assume we have
a community of a hundred if each of the
members of our society can go and trade
their produce for all other products
how many exchanges will there be each
one of the 99 custom ate just one trade
with the Trading Post so there are 99
exchanges let's generalize that with a
second even simpler formula with a
Trading Post each of the N people trades
with all the others had except himself
so in an in-person economy there'll be n
minus-1 exchanges the formula is simply
n minus 1 so if there are four people
one of whom hacks us a Trading Post each
of the other three will exchange with
her since n is four four minus one
equals three it's now easy to see that
with five people there are four
exchanges five minus one equals four and
with a hundred people 99 exchanges a
hundred minus one equals 99 and so on
so we can now compare the number of
exchanges with and without a trading
post for a hundred person economy with
no trading post four thousand nine
hundred and fifty exchanges with a
trading post ninety nine exchanges
so the result of having a trading post
is that we reduce the number of
transactions costs from those associated
with 495 owe to those associated with 99
exchanges a saving of 4851 lots of
transactions costs
the middleman produces a highly valuable
function in reducing transactions costs
this transaction cost saving is why for
example many supermarkets are successful
in our modern society people use money
instead of barter but the principle is
the same you get all the things you want
and pay just once you do it rather than
go to a lot of different places because
you save time and effort in other words
it reduces transactions costs as the
size of the local population grows so
does the benefit of the supermarket in
savings on transactions costs so we
started off thinking about whether we
could use formula to give us an insight
into the way in which some aspects of
the economy functioned and we've seen in
this case that you really can do that by
using a couple of very frightening
formula we were able to see what is the
value of the middleman and how he's able
to use his services to reduce
transactions costs so we've come to a
conclusion by using these formulae thus
perhaps counterintuitive the next time
you want to buy a kitchen get the best
value for money and that might mean
going direct to the manufacturer buddy