The Big Mac Index. METAL film 1.04


Uploaded by METALMathProject on 11.12.2008

Transcript:
Wherever you go in the world you can always find a Big Mac. McDonald's have
places in virtually every country in the world
and it's the same good wherever you go, always made to exactly the same recipe.
So we can use that idea
to compare prices of big macs in different countries.
This is called the Big Mac Index
and it was first published in The Economist magazine
as a way of comparing different currencies
to see if they are overvalued or undervalued.
If the Big Mac Index shows that the burger is cheaper in Poland than say in
the USA
this suggests that the Polish currency is undervalued when compared with the
US Dollar. To understand why this is so we need to understand one of the most
basic laws of economics sometimes called Law of One Price
This law
states that we expect an identical good
to be sold everywhere for the same price.
If it were not so,
people would buy the good where it's cheaper
which will increase its price there.
They'll sell where it's dear
and in doing so depress the press there.
This process, sometimes called arbitrage,
leads over time to the same good being sold
everywhere for the same price.
The law of one price
is easy to test in one country:
all we have to do is compare prices of goods.
Is the price of fuel the same in different markets?
Is the price of a Big Mac the same in different towns?
But what if we want to compare prices between say poland and the USA,
where different currencies are used?
We can still do so
by looking at international currency markets where traders exchange currencies
at some rate of exchange depending on the supply and demand for the
currency.
We can find out, for example, the rate that they're exchanging dollars for
Polish zlotys at any one time you seem to go home prices we would expect a
basket of goods including to be the same as the same basket of goods in the
USA
when converted at the going exchange rate.
Suppose the goods are generally cheaper in Poland
we would expect people to be keen
to buy goods from Poland. Cheaper prices in poland should cause people to buy polish
currency in order to buy their goods
the increase in demand facilities will cause the value of the currency to rise
until average prices of goods are the same in each country
when converted
at the new exchange rates.
The Big Mac Index gives us a neat way to see if prices in one country higher or
lower
in another country
whether a country's currency is in equilibrium.
We use the Big Mac as being representative of a whole basket of goods. Of course,
we wouldn't expect people to fly to Poland just because they can get a
Big Mac more cheaply
but assuming the Big Mac is typical of prices generallly in two countries
we would expect currency prices over time to asjust
if the prices of goods are different.
How do we measure the extent to which a currency is undervalued or indeed overvalued
against the US Dollar according to the big mac index?
We can do so
by our understanding of percentages.
Armed with an understanding of percentages
we can work out the implied
under valuation
or over valuation of a currency.
Remember this is for any one moment of time:
over time,
prices and currency values will change.
And if we know the price of the Big Mac
in a country
and the current exchange rate
it's easy to work out the implied
purchasing power parity or p p p
of the dollar
we divide column one in the table
by the US big mac price.
So taking Germany
as an example
if we divide
two point seven one euros
the price of the big mac in germany
by two point seven one dollars (the price of the big mac in the US)
and he implied purchasing power parity
is two point seven one
over two point seven one
one
now we've done the same
for the british pound and the polish zloty
in the table
and show in their respective purchasing power parities.
What is the meaning of purchasing power parity
(this needs care)
PPP says
you would expect
one dollar
to buy the same amount of goods in the US
as one euro buys in germany
and as two point three two
zlotys
buys in Poland.
We can argue that this is the
correct
rate of exchange.
But the actual rate of exchange is different in each case
as you can see from the table.
But we can work out there'll be under or over evaluation of the currency
by comparing the implied rate
but we got from the big mac
with the actual rate.
So let's look at the euro
and asked whether
at this particular moment in time
it was under-
or over-valued according to the big mac index.
We'll take the difference between the implied rate
and the actual rate
but we need to express that as a proportion
of the actual rate
it's not the absolute difference that were interested in
it's the proportional difference
so the under- or over-valuation
is
column three
minus column two
over column two
and then multiplied by one hundred.
So let's see that for Germany
we've got
1.0
minus
1.1
and take that difference
and express it as a proportion of one point one
so we've got 1.0 minus one point one
divided by one point one
now we multiply that by a hundred
and we get
minus nine.
What does that minus nine tell us?
That according to the Big Mac Index at this moment in time
the euro
is nine percent
undervalued
against the US Dollar.
According to our table
all three currencies that we're looking at
were undervalued against the dollar at that time
but to differing extents.
Alternatively expressed,
the US Dollar was
overvalued against these currencies and we might expect therefore that in the
long run
if the big mac index is useful
the US Dollar will tend to fall in value.
So when we want to know the significance of the difference between two numbers
it's helpful to express that difference
as a percentage.
We take the difference between the two values
and express that difference as a proportion
of the original value
and then multiplied by a hundred.
Notice that for the Big Mac Index
we've only work this out for one moment of time
and you might be interested
to look up more recent examples of the big mac index and do these calculations
for yourself.