index numbers are very useful for making
comparisons especially overtime
sociologists are interested in looking
at index numbers to see what's happening
with population changes businesses look
at index numbers to look at share prices
psychologists use index numbers to
consider intelligence levels of
populations the measure usually works by
establishing a base which is given the
number one hundred variations are then
measured from that so the average
intelligence is supposed to give a
number of a hundred if you have an IQ of
130 you're supposed to be thirty percent
more intelligent than the average
perhaps the most common use of index
numbers is in measuring the extent of
price increases in the goods and
services that we buy one measure of that
is the gross domestic product
now GDP tends to rise for two reasons
one we produce more goods and services
to the prices of these things is going
up now index numbers are very useful in
separating out these two effects but to
do that we first need to be clear on
what we mean by GDP and we could do that
by looking at a particular European
economy
how much output does a society produce
in the course of a year it sounds a
remarkably simple question all you do is
take the output that everybody produces
multiply it by the price it sells for
and you've got the output it's a simple
way of doing it and it's wrong and the
reason that it's wrong is that you are
double counting you're counting some
outputs more than once you see some of
the output which is made isn't sold to
consumers at all it's made and sold to
other producers so the farmer grows his
wheat and he doesn't sell it to
consumers he sells it to Millers who
take this wheat and turn it into flour
and then the flower is sold on to the
bread manufacturer who turns it into
bread so if we took the output of the
farmers wheat the Millers flour and the
bread producers bread
we'd be hopelessly overstating the total
amount of output that's produced we'd be
double counting some of the output so
the way over the problem is this way one
we just count the output that is sold to
consumers so for this particular
industry ignore the contribution of the
farmer producing the wheat ignore the
contribution of the flour producer and
simply say how many loaves of bread were
produced and what's the price we only
count the final output possibility
number two is to say let's look at the
contribution made by each producer by
asking what's its value added what's the
difference between the value of the
output they produce and the value of the
inputs bought from some other industry
so we take the farmers wheat he sells
the wheat for a hundred euros to this
Miller the Miller takes a hundred euros
worth of grain turns it into 200 euros
worth of flour
what's the Miller done he's added a
hundred euros worth of value to the
wheat that is his value-added if we do
the same thing now with a bread producer
value the output of bread
- inputs from the Miller we've got the
value-added at that stage in the
production process if we add up the
values added of each stage in the
process we've got the total value of
output to society which is exactly the
same as the value of the output that we
found when we ignored intermediate
output and went straight to the final
producer the bread manufacturer so got
these two ways of doing it all the
national income accounts that you'll see
use that second way and the reason for
using the second way is that if you
looked at national income accounts in
the first way you'd never know that
there were any farmers you'd never know
that there were any Millers but doing it
via value-added and you see the
contributions made of all producers in
all industries within the country
but GDP increases is it because we're
producing there or because the price
levels rising we need to be able to
separate out these two effects so we
need to be able to measure inflation and
a good way to measure inflation is to
use index numbers since an economy is so
complex and has so many prices and all
these prices are changing at different
rates let's come back to my island
economy and see what's happening with
our very simple economy in an earlier
film we saw how our island economy
suffered from inflation now what we want
to do is to try to measure that
inflation using index numbers
our island produces a number of
different commodities and their prices
have tended to rise but not all by the
same extent so how can we measure the
rate of inflation on our island economy
it's too simple an economy to have
specialization
there's no intermediate output we just
have four of us each producing and
exchanging our products but last year
our prices were different from this year
furthermore although prices have
generally risen they haven't all changed
by the same amount so how much inflation
is there can we take a simple mean
average of all the price changes we
could but it wouldn't be very good
because some items are more important to
us than others and we know that because
we spend more on some items than we
spend on others the table shows that
prices of each commodity sold on our
island in three different years and also
the quantities sold the changes in
quantities will reflect partly changes
in preference and partly changes in the
price of the goods themselves with year
two as the base year will construct a
price index measuring the change in the
price level on our island between years
two and three
remember we can't work out the
percentage change for each price and
then take a mean average of the changes
because this would ignore the fact that
some prices are more important than
others we get an idea of the relative
importance of the prices to our economy
by looking at the quantities of the
goods purchased so we can weight the
changes using the formula below the
index r equals Sigma P n Q naught over
Sigma P naught Q naught times a hundred
where I is our price index Sigma means
the sum of P n represents each of the
given year prices in our case year three
and P naught represents each of the base
year prices in our case year two Q
naught represents each of the base year
quantities that we'll use as weights so
substituting now into our formula we
have the following we're using the year
three prices of each commodity in turn
multiplying each one by the appropriate
base year weights the year two
quantities that's the top line
so I equals 3 times 3 plus 2 times 6
plus 2 times 3 plus 4 times 3
and now we divide by Sigma P naught Q
naught we take the year to price of each
commodity and multiply each in turn by
the base year weights the year two
quantities and add these to give us the
bottom line so the bottom line is two
times three plus one times six plus two
times three plus four times three
now we multiply the results by 100 and
this gives us that I equals 9 plus 12
plus 6 plus 12 divided by 6 plus 6 plus
6 plus 12 and we multiply by a hundred
which equals 130 so the index of prices
in year 3 is 130 and we've had an
inflation rate in our island economy of
30 percent between years 2 & 3 according
to this inflation measure
we've just produced a laspeyres index
after the name of the guy who thought of
it but we've got a problem the problem
is this that when prices are rising and
some are rising faster than others
consumers respond to that by changing
their expenditure patterns buying more
of the goods which are falling
relatively in price and less of the
goods which are rising in price
relatively so there's a case for saying
that we ought to change on a weighting
system to allow for the fact that
consumers expenditure patterns have
changed let's do that for our island
economy referring back to our table of
prices we can now calculate the
inflation rate in an alternative way
again with year two as the base year
will construct a price index measuring
the change in the price level on our
island between years 2 & 3 this time we
use the Posche index as before we can
get an idea of the relative importance
of the prices to our economy by looking
at the quantities of the goods purchased
but this time we use the current weights
the weights that pick up the changes in
quantities consumed over the period we
can weight the changes differently this
time using the formula I is Sigma P n Q
n over Sigma P naught Q n times 100
where I is our price index Sigma again
of course means the summer
P n represents each of the given year
prices P naught represents each of the
base year prices and Q n represents the
current year quantities that we'll use
as weights so substituting into our
formula this time we perform the same
operation as before except that each of
our year three prices is multiplied by
its current year weight the year three
quantity the top line so I is 3 times 6
plus 2 times 4 plus 2 times 7 plus 4
times 3 and on the lower line we
multiply each year to price by the
appropriate year 3 quantity wait 2 times
6 plus 1 times 4 plus 2 times 7 plus 4
times 3 and then again we multiply by
100 so that I is 18 plus 8 plus 14 plus
12 which we add up and divide by 12 plus
4 plus 14 plus 12 multiplying the result
by a hundred gives us a hundred and
twenty three point eight one so the
index of prices in year three is
according to this measure a hundred and
twenty three point eight one and we've
had an inflation rate in our island
economy of 23 point eight one this
measure tends to show a lower inflation
rate because it allows for consumers
adjusting their purchases to relative
price changes
there are various sets of index numbers
that measure inflation for the UK
they're all constructed in the way we've
described for our island economy but the
weights used to calculate price changes
will vary according to the use to which
we put them we'll mention just a few
here the best-known measures are the
retail price index the RPI sometimes
called the headline rate and the CPI the
Consumer Price Index which is the one
which is used throughout the European
Union over a hundred thousand price
quotations are analyzed for price
changes each carrying its own weight to
reflect our expenditure patterns so in
recent years some items have been added
these include lip gloss hair
straighteners and small bottles of
mineral water others have been removed
these include squash court hire and
eyesight tests which have become free in
some areas for many people others have
stayed the same but the size of the
weights is altered so now for example
people tend to spend a higher proportion
of their income on travel a lower
proportion of their income on food so
what's the difference between the RPI
and the CPI there are things left out of
CPI that RPI includes RPI for example
covers council tax and monkeys interest
payments
the CPI measure does not and that's true
of some other housing costs also we also
have a wholesale prices index any store
will buy its goods for less than it
sells in order to cover its costs and
make a profit so we can measure prices
not only at the point of sale to the
customer but we can also measure prices
at the point of sale to the store one of
the advantages of doing this is that it
gives us an indication of price rises
yet to come
one worried about inflation is how
easily it can become hyperinflation
that's where prices are rising so fast
that people lose confidence in money as
a medium of exchange as a way of
settling debts as a way of selling and
buying goods and services the fastest
ever known rate of inflation took place
here in Hungary during the 1920s 30s and
40s the unit of account of that time was
called the Penghu and hyperinflation was
such that by the time we get to the
1940s there were notes being printed by
the government for a hundred million
billion peng goes
one of the effects of rapid inflation
means that the value of the currency
internationally Falls so if we come back
to this example of Hungary in 1927 a
u.s. dollar exchanged for five pen goes
by 1946 one US dollar bought four point
six times ten to the twenty-nine pen
goose that is to say it bought forty six
plus twenty eight zeros with pengus that
is a serious rate of inflation in
Western Europe we've been accustomed to
seeing price indexes rising by only a
few percentage points a year but there
have been exceptions to this rule
not only in Hungary but some countries
have experienced hyperinflation in their
history while such country was Germany
now a prosperous relatively low
inflation economy
let's look at the index numbers of
German inflation for the period from
1914 to 23
note how the base doesn't have to be a
year long period or indeed be equal to
100 here it's a particular month and the
base period is given a value of 1 let's
get a sense of how fast prices were
rising using the index above if the
German 1923 rate were to be repeated
this year we can work out what a typical
good that cost 1 pound in July would
cost by November current index is P n
over P naught times 100 which is 7 - 6 0
0 0 0 0 0 0 0 0 the November price over
a hundred and ninety four zero zero zero
the July Price Index which we then
multiplied by a hundred which gives us
three seven four two two six eight oh
four
so the good whose price was a pound in
July would if the German 1923 rate of
inflation were to take place in our
economy have a price now in November of
three hundred and seventy four million
two hundred and twenty six thousand
eight hundred and four pounds
we focused in this film on the
measurement of inflation a subject of
great importance in the social sciences
yet it hasn't been our main purpose to
help you understand inflation our chief
purpose hasn't been to enable you to
understand everything about prices but
to help you feel confident in the
handling of index numbers
you