okay so um today we're want to start
talking about the long run I've been
talking about the business cycles and
today we're going to start talking about
things that happen over decades H but
before I do that before we finish with
the the short run medium run I just
don't want you to I want I don't want to
give you the impression that that you
know once you understand the ISL MPC
sort of you you can start managing
monetary
policy immediately I
I there's a lot of noise of all sort of
kind of complexity in the real world of
course that can make um policies
uh uh very hard to manage in practice
macroeconomic policies and one
fundamental principle I would say is
that policy makers understand that speed
can kill okay and uh that's very obvious
during financial crisis there we all
understand that ER the response needs to
be large it has to be a response with
overwhelming Force essentially because
things are happening so fast that very
few corporations even healthy
corporations that that can adjust
quickly enough uh to the PACE at which
things are changing prices become
noninformative uh fire cells take place
and and and obviously it's very
difficult to make economic decisions in
that context and so that's the reason
they are the speed in the on the on the
policy Direction goes very clearly in
One Direction do it quickly and very
large
now on the other hand ER when you're
going through a period in which you're
are hiking interest rates for example
ER like we're going through now um the
the Tendencies towards gradualism to do
it very slowly because something can
break along the path and it's often the
case that with for sufficiently large
adjustments something breaks okay and so
here you have an example of sort of
major episodes of hiking in the US and
things that have happened about those
those H major episodes
this one actually I I have a personal
attachment to that one because you know
I was studying in Chile around then
everything was going wonderfully massive
Capital flows to Chile emerging markets
were very popular we all felt very
wealthy rich and so on and right after I
finished College ER I was not planning
to come to the usy things were going
very well in Chile H but the US decided
to hike interest rate very aggressively
all of the sudden Capital flows to
emergy markets disappear we went into an
enormous financial crisis I lost I had
no opportunity cost and I had to come to
study to the US that that's my so I know
that hikes aggressive hikes can matter
can make differences to people but and
that
was there's a decade that followed that
episode that is called the L decade of
Latin America essentially so things did
break and and one of the main reasons
they did break is because at the time
most of the capital close that's not
what happens today we really being
managed by global Banks and the banks
can get very distressed when interest
rate rise H very very quickly and so
that that was essentially a problem with
us the US Banks major Global Banks but
the US Banks in particular that trigger
an Emerging Market
crisis this one also had huge
consequences actually and it's
interesting because this episode is is
similar to to to to what we're going on
what is going on right now or what may
happen in soon so this is episode of
hikes that ended what is called The
Savings and Loan crisis and those so the
best parallel to today are the small
Regional Banks if you will and they they
weren't able to withstand this sort of
sharp rise in interest rate which is
very much what is going on right now in
the US this one actually end up with
also another problem which is the the
the bubble burst in Japan episode of
hiking in the US and there we had a
major crisis in in Japan the price of
real estate
collapsed ER and and essentially they
since then they have never been able to
grow as they used to before that that
episode that's called sometimes the
tequila crisis it's a Mexican
Bond crisis and it was again the result
of a hiking episode in the US conditions
tighten to Emerging Market ER their bone
Market essentially
exploded um well this is the global
financial crisis the Great Recession it
was again preceded by episode of sort of
aggressive hikes which eventually er um
led to a turn around as house prices
were Rising steadily throughout the
episode and a lot of financial assets
were created around that housing wealth
that was been created that hike and
interest rate eventually put a stop an
end to that that appreciation of house
prices in fact they turn around and it
led to a very significant financial
crisis and this is where we're at right
now okay and so we already seen sort of
some Tremors and so on so the point is
when when sometimes you say well why is
isn't the FED more aggressive if we have
high inflation and go very quickly at it
well it's because things can go wrong
okay and it it typically happens that
things do go wrong you don't know
exactly what will blow up but something
may blow up and typically is associated
to some Financial Market that is very
hot and the market and the banks are
always involved in that because the
banks are very
lever you know they have little Capital
relative to the assets they have and
that means small variation in the price
of assets can lead to very large H
changes in the value of their
capital anyway so just a warning so if
you get a job at the FED please be
careful okay now let me switch gears and
and we're going to talk about um um
something a little different from what
we have been discussing up to now so
this is some this is growth projections
for different regions in the world ER
this is something that is in publishing
by the IMF it's called the world
economic Outlook I think I mentioned it
before and here you have some forecast
you know well this is actually what
happened so growth in the global economy
was about 3.4% 2022 advanced economies
grew at 2.7% emerging markets and
developing economies at
3.9% and then you see forast and the
further out you go er um the okay the
further out you go sort of it's less
related to the current cycle is more
related to what is structural the
structural
growth of the different parts of the
world and you see that for
2024 the global economy is projected
expected to grow at around 3.1% this
forecast were made before the mess
Financial mess that we're going on right
now so probably the next World economic
Outlook will have at least for 2023 will
will downgrade the growth probably not
for 2024 but yes for 2023 anyways
advanced economies expected to grow
1.4% emerging markets at
4.2% so
these forecasts are based on on a
combination of cyclical factors
fluctuations of the short run medium run
the kind of things we have been
discussing up to now some economies will
have to go through recession some
economies are going through Booms that
probably dominates 20 the forus on 2023
but as I said before the further out you
go the more the less relevant is the
current business cycle and the more
relevant is the structural trend of the
different regions of the world okay so I
would that in this when they formulated
this forecast this is very much based on
more longer run growth model the kind of
models we're going to discuss now okay
while this is probably totally dominated
by the kind of things we discuss up to
now okay
um there are several things that that
that are interesting here aside from
sort of the the the
fluctuations year to year one thing you
can see for example is that regardless
of year
on average Emerging Markets tend to grow
faster than develop economies advanced
economies okay so one of the things we
want to understand is why is that the
case okay but that's is very clear here
that's the first model we're going to
look at which probably will happen on
Wednesday we'll try to explain
essentially that why is it that these
guys tend to grow faster than the
advanced economies
okay so growth is important I mean the
standing economic growth is hugely
important for the weal for understanding
sort of the health of an economy here
you see this comes from the textbook er
er the the US GDP in 20 20
uh2 from
1890 to to 2017 I think is this one the
the end year the important thing to
notice here is how large is the change
in GDP in during the period I mean GDP
here measuring the same prices so 20
2012 prices is 50 times that in 1890
that's a big thing I mean when we talk
about business cycle fluctuations we're
talking about in an economy like the US
two two and a half% up 3% up and down
this is 50 times so over longer period
of time you can almost ignore the
business cycle and it's all about that
long run H trend
here what is this episode so so you here
if you if you look at this picture know
especially the F out you are on the on
the on the room what dominates here is
clearly the
trend the only action you see really
significant action different from the
trend is around here what happened
there it's the Great Depression so even
the Great Depression you know doesn't
look that big relative to what the trend
can do so
of course it's very difficult to affect
the trend of a country but the trend
makes a huge difference for the welfare
for
the economic well-being of a
country
good now a lot of that is because also
the US population grew up grew up grew
up and grew a lot during this episode
so often when you look at sort of long
run Trends rather than looking at the
level of GDP you tend to look at the
level of GDP per person per capita or
something like that and that picture is
exactly the same pictures as the
previous one but divided by population
at each point in time okay and and and
and that's an important over long
periods of you at the business cycle
frequency you can almost ignore changes
in popul no Chang ination you can ignore
completely unless you are in a war you
can you worry about other things labor
force participation and stuff like that
but population is irrelevant that the
business cycle growth is irrelevant at
the business cycle frequency but not
over long periods of time in this period
here population in the US increased from
63 million to 320 million so that's a
lot more workers in principle that you
have you know for that economy so a lot
of that trend is explained by population
growth and that's one of the reason
sorry a lot of the trend in this picture
here is explained by population growth
that's one of the reasons we're in a
tricky time in the global economy
because there are many important regions
of the world where population is no
longer growing so we got used to a
period in which population growth was
very steady and high and now you know
many parts of the world important parts
of of the world have negative population
growth Japan Korea China most of
Continental Europe H even places in
Latin America and so on so so this is a
big change for the world
but anyways during that period there was
a lot of population growth and in the US
in particular when again as I said
before from 63 to 320 million so if you
really want to measure sort of welfare
of the economy how well how the
well-being of
individuals in in in in the US the
previous picture is misleading because
you have to yeah it's the final Pi is 50
times larger than the first one than the
beginning Pi but you have 320 million
people to split it among as opposed to
63 million so this picture captures that
statistic that is often described when
you talk about long run
growth ER is GDP per person and you
still see that what dominates this
picture is a trend ER but the difference
between this out out GDP per person in
the US at the end of the sample versus
the beginning of the sample is 10 to1
not 50 to1 so it makes a difference
population it's still big it's still
what dominates this picture is that of
course the Great Recession looks bigger
now because you know you comparing it
with with a number that grows by a
factor of 10 not by a factor of 50
that's so it looks bigger naturally know
the same 30% decline output is a lot
bigger when you're comparing it with
the a factor of 10 than when you're
comparing it with a factor of 50 but
still it looks bigger but the picture is
dominated by the
so all this to say that we're going to
study now is very important it's not
what dominates the day-to-day news
because it happens slowly and over time
but it is very
important so how do we measure these
things well when you're looking within a
country you do reasonably well not
perfect but reasonably well and perhaps
not over periods as long as I want I
show you by looking at GDP per capita
that's that's fine is you measure it
real GDP per capita that's about fine
but when you compare across different
regions of the world and so on those
comparisons is very misleading so to say
that the US has um I don't know
ER what is the US GDP per capita today
in the US somebody should check it but
but about maybe $70,000 something like
that I don't know ER and then then then
you see a another country that has say
Italy $50,000 per
capita that comparison is not that
meaningful it's indicative of something
but it's not completely meaningful and
I'm going to show you an example which
is much more extreme than that but the
reason is not very meaningful is
essentially because the prices are not
the same across different parts of the
world so we have a method to to to to do
that to to be able to compare across
countries and again even for a one a
given country over long long period of
time we make a correction to the GDP
numbers we have and we make we call them
we correct them by what is called the
PPP purchasing power parity and I'll
explain what that is okay so whenever
almost whenever you see comparisons of a
GDP per capita across countries when
somebody's doing a growth analysis is
going to be PPP adjusted okay now let me
explain the logic of
PB
um and and and again I said within the
same country over periods perhaps not
300 years but over periods of 40 years
it's reasonable H to use just real GDP
but when you start comparing sort of you
know bana versus the US it gets a lot
tricky trickier because there's a lot of
goods that are a lot cheaper in poorer
countries in particular food okay and
and so so you have to be careful with
those comparisons so I'm going to give
you this example which is somewhat
hypothetical but the numbers are not
crazy so suppose you have a a two
economies the US and Russia
and
um anyways
ER and suppose that that in both
economies ER households consume houses
and firms consume cars and
food okay and suppose that the average
consumer in the US buys one car a year
for $10,000 and a bundle of food for
$10,000 as well okay so the total
expenditure in consumption for this
household on average is about $20,000 a
year that's what a US household consumes
these numbers are fantasy numbers but
the big picture is not that fantasy
ER
Russia the average consumer buys
0.07 cars a year for 40,000 rubles and
the same bundle of food that in the US
okay same assume that same bundle of
food goes for 880,000
rubles so the total expenditure of this
H average household in Russia is
120,000 rubles suppose that exchange is
60 rubles per dollar this thing has
moved a lot recent times but suppose
that's the the number of rubles per
dollar so you divide $120,000 and you
want to convert them into Dollars you
divide the 120,000 rubles by 60,000
rubles per dollar and then you get how
much the Russians spend a Russian
household on average spends on on on
consumption in a year and and it's
$2,000 a year okay so here you have
120,000 divided by 60 is 2,000 that's
the number of dollar
that an average household in Russia
consumes so the question
is you have a US household spends
$20,000 a year a Russian household
spends $22,000 a year and the question
is then is Russia 10 times poorer than
the
US
okay that if you were to compare real
GDP that would be answer so yeah they
and it's true if you look at a again in
this
example if you look at the at the real
GDP numbers of on the same year
converted all into dollars that answer
is
correct but it doesn't represent the
point is that it doesn't represent
really The Well beinging of the average
household in Russia for this reason at
least why not well
let's what you ultimately matter is how
much real Goods the house
consumes that's what really matters I
mean if you live in a country where the
price of everything is zero your
consumption expenditure consumption will
be
zero but that doesn't mean that you are
as unhappy as somebody that consumes
zero you're consuming whatever it is it
happens the prices tend to be very low
and that's essentially the story here as
I said before it tends to be the case
that in poorer countries a lot of things
are cheaper there is certain very high
tech things that that are not even
consumed in poorer countries so you have
to adjust for that as well but a lot of
the regular things the bulk of the
purchases tend to be a lot cheaper in
poorer countries and that's exactly what
is behind the reason why in this example
the answer is
no it's not true that the Russians are
10 time that Russian household in this
example is 10 times poorer than the US
let's check it so that's our
example and I said no so fast
let's use so assume that the goods are
the same so the cars that the Russians
buy is the same as the as the cars that
the US households buy that was
truer a few months ago than now but but
assume that's the case it's just that
the Russians by you know change their
cars less frequently in this example the
US household is changing the car once a
year while while while the Russians are
changing the car you know less than once
every 10 year one every 15 years or
so let's assume also that the the bundle
of the of food is exactly the same in
both Place places so since the car is
the same and the and the and the and the
bundle of food is the same I can use us
prices to
measure Uh Russian consumption and
that's is comparable to what us
consumption is because I'm taking I'm
trying to convert the goods they're
consuming into something is comparable
to what the US consumes since the goods
themselves are the same if I value them
at the same price either of the two
prices but at the same prices then I'm
going to be able to make the comparison
I really want that's what purchase power
PVP adjustment means okay so look at our
particular example here the Russian
would household would be consuming 0.07
cars times 10,000 dollar which is the
price of a car plus one unit of of the
bundle of of of of food and the price us
price is 10,000 for that so the total
consumption of the household PPP
adjusted the Russian household is
10,700 okay that's not one10 it's
53% of us consumption so true Russian
household is poorer than than than than
an average US household but it's not 10
poor no it has it's
a is
53% uh as rich as the US household okay
and so this is big and all the numbers
I'm going to show you next especially
when we compare across sort of countries
that are very different in terms of
level of development and so on have
these kind of Corrections built in okay
if you need the data for these kind of
things for whatever reason you find them
in what is called the pen tables the pen
tables essentially collects all the
national accounts of all places and
makes these
Corrections the problem is they don't
have update them very frequently but but
if you look in Fred for example which
you use in one of the p sets there will
be numbers for a few countries that have
this um PPP
adjustment okay so that that's that's
going to remain in the background now
but I just wanted to tell you how how
you construct numbers when you want to
talk about long run and comparison
across
countries first set of numbers here look
at these are obviously all today at
least develop economies look at the
growth between 1950 2017 obviously the
war created a big mess there but before
that so let's start from
1950 and what you see here is you know
France on average during this period
France grew 2017 I think is the last yes
it's the last
year I think they were recently updated
but at least when the book was published
that was the last year they had pen
tables for but
um er France grew on average 2.6% per
year on average they also had a business
cycle and so on but on average 2.6% per
year Japan during this period grew by
four four
4.1% the UK 2.1% the US 2% so the
developed World essentially grew around
2.7% on average during this
period look at the effect that that this
has on on the level of GDP per per per
per person and all this PPP
adjusted ER for the case of
France 5.6 times so they started with
$7,000 and they were close to $40,000 in
2017 so the r is RA
5.6 look at the US the US is 2% and that
ratio is is still richer than France per
per person in
2017 but but the ratio of that to that
is smaller than that so over a long
period of time that's what a trend in
the picture capture a small difference
in the rate of growth if they are
sustained for a long period of time can
make quite a bit of difference for the
change in in GDP okay and so what do you
what is the first what is the p is I
mean let's find the pattern here here
there's a very clear pattern in that
picture in that table what is it do you
can you spot
it I hadn't
actually realized it when I was looking
at my notes and then I realized is very
clear in this table that's the reason I
added this line I updated the slide this
morning do you see a pattern
yes the higher growth rate have a higher
multiple yeah well that's yes that but
that's
math okay which is so it's a true
statement but that's just
math there's an economic thing that that
that I want
to so so you're right but but I want
they should have clarified there's an
economic pattern there
let let me simplify just look at these
two columns because a higher number here
simply sorry a higher number here simply
means that you had a higher rate of
growth that's your math fact so ignore
this column what I suggest is that you
just look at these two
columns do you see a
pattern just look at these two columns
this one in a sense just repeats
information that is here for the reason
you describe but just look at these two
columns is there a pattern
there exactly very important Richard
countri sent to grow slower the richest
country here is the US had the lowest
rate of growth on
average the poorest was Japan there and
they had the highest rate of growth okay
so that's a very important correlation
and again the first model we're going to
see of economic growth is going to
explain that correlation why is that we
see
that those were for five economy you
could say it's an accident but look at
this this this is just a this is rich
countries in general since 1950s and you
look at here in this axis you have the
annual rate of growth the average rate
of growth and here the GDP per person in
1950 so at the beginning of the sample
1950 these countries had have this level
of GDP per capita and then here is the
rate of growth on average from 1950 to
1987 and it's very clear there that
there's a downward sloping pattern no so
that's the same fact now for many more
countries there's a downward sloping
relationship really the richest
countries tend to grow much slower than
the countries were poorer at the
beginning of the
sample
okay there are some interesting
liers like Mexico and and is an
interesting in itself I'm not going to
say a lot about why that's the case
but but but let me for now stick to the
to the pattern the dominant pattern
which is is a downward sloping
relationship that's another way of
seeing it and this is for just a bigger
variety of countries I have Botana China
Thailand and so on and and you see here
GDP at the beginning of the 1950 and GDP
rate
2018 and the pattern here which is
essentially a repetition of the pattern
that I showed you before is that there
is much more compression here than
here how can you have more compression
here than here well because there is
some sort of convergence no there's a
sense of convergence is that those that
were poorer tend to grow a little faster
than those that were richer and
therefore they tend to converge to each
other so that's the the point I'm
highlighting here a lot of this persion
1950 much less isers in 2018 that means
that on average the poorer countries are
growing faster than the Richer
countries and again all this is per
capita PPP adjust and all that okay
this
picture again sort of makes the the
point but now it takes a much many more
countries and you can what the point of
this picture is in the book is is is to
highlight that it's a little messy the
picture but to highlight that if you
look in different regions oecd a major
the major economies H tend to the
pattern I show you holds if you look at
only isolate only the blue the blue
squares you tend to see that negative
relationship if you look at within
Asia it's also it's a little bit noisier
but you also tend to see a negative
relationship
okay if you look at
Africa that relationship is lost
completely
okay so so when you look at the world as
a whole
the picture is not as neat as the one I
show you because there are certain
pockets of the world that are not
behaving according to the kind of mods I
want I discuss in the next few lectures
and the reason they're not behaving is
entirely it's almost outside economics
it has it's political conflicts Wars and
things of that nature which continuously
disrupt sort of the economic forces that
I'm going to highlight in the next few
lectures
okay so that's a different different
different issue where going to be about
the all the moles I'll show you next are
about the blue and the and the
green squares and and and triangles
there not about the red
ones what about so I look I show you
what happens across countries over over
certain period of time which is long but
not that long here you see what happens
in longer here history there are two
patterns that I like to highlight here
is that H first for a while sort of you
you didn't see much but but you tend to
see a sort of a big acceleration in the
Western World especially around the the
1950s or so okay so so clearly the
Western world was growing faster than
the rest of the world H the Western
Hemisphere this is a um um world Bank
IFI type type
um
grouping and and you see that there's a
very fast acceleration in growth in this
episode here Western Europe H was also
flattish and then picked up very
strongly there and you see the different
regions of the world and again you see
the sub Sahara Africa region that sort
of has hasn't really picked up okay
much longer history well that's the way
it looks for the world as a whole
okay you know exponential pictures tend
to look like that but but this is more
dramatic than exponential and again what
happens is
that what happen here is is going to be
very different from from the kind of
mods I'll describe
next this period here is mostly
dominated by what's called sort of the
malthusian era which is essentially
people live population grew and so on
depending on how good was the the
harvest that year and so on no so so you
had this mod in which you know his
population grew faster that was a main
driver of of of growth well but you know
there wasn't enough food to sustain a a
higher population and then you stay
soort of there was a fight between food
and and and people and and and no much
space for most people were in
agriculture and and the and and and
there wasn't sort of
much to build on nowadays there are
pocket in the world and we had the
severe situations during covid but food
is not really a constraint for growth
for the world as a whole
okay and but you see
so in other words had you taken this
course in 20 in year 1000 or in the
Renaissance nobody would have talked
about growth it's not something that
happened really it's it's a very modern
thing to think about these pictures with
these long Trends and so on
okay I mean there you would have talked
about a lot more interesting things than
this but but not not about growth that's
for sure and growth the last point I I
think I want to make about this is it
makes a big
difference I don't know if you can read
that I I can't but er um what I have
here is GDP per capita in
1950 versus GDP per capita in 2016
and you have this isoquants here you
move you as you move up so this line
here is what happens to countries that
is a 45 degree line so if you are on the
45 degree line means that you haven't
grown at all during this period no
because that means that your GDP per
capita 1950 is the same as you g GDP per
capita in 2016 that means on average you
grow okay but as I keep moving these
lines up means you grew faster and fter
faster and
faster okay so and if you if you move
along this line here that means you have
negative growth on average during that
period okay so each of these lines
represents multiples so I think this is
for example this top line here is 30
times richer these are guys that grew
very very fast yeah you I cannot read
either but I I sort of know who is in
each
Place
h this is an example here this is
Taiwan okay this is Taiwan and H this is
Singapore they have a name how do we
call those
countries no
well the Asian tigers they grew very
very strong for for a long time since
the 60s or so but there you see you can
compare if you could see you would see
that you know that that Taiwan and the
Democratic Republic of Congo had the
same GDP in
1950 okay now the Republic Democratic
Republic of of of of Congo has less GDP
than it had ER in 1950 it had 1700 here
and 800 today while Taiwan Taiwan has 30
times what it used to
have and so today is one of the richest
economies in the world close to 7
$50,000 per capita while the Republic of
Congo ER has
700 $800 per capita so growth makes a
big big difference okay and these are
not that many years I mean you know this
is just 70 years H and I can assure you
that these people they have other
concerns but
their standard of living is a lot higher
than these people and at some point they
were the same the big difference is some
countries that grew and some
countries got a stuck um where is
Argentina here I don't know somewhere
here
probably it's
Argentina I don't know I cannot
see have the chance here I can say okay
good so growth that's make a difference
and he has made a huge the world we see
today and the countries we think as rich
or poor were not the same countries that
you thought in in those terms in
1950 Asia is one of the most prominent
differences they have massive growth
through the
60s
um starting with Japan but then the rest
and again were the famous the Tigers
Hong Kong Taiwan
Singapore uh
and Korea South
Korea good so let's start building some
moles of what we have just
seen remember when we look at the short
run we really didn't care about the
supply side of the economy remember it
was all about demand they said well you
know demand look what consumers invest
firms and governments do with demand
that determines output and output
happens well it happens we didn't really
care too much about it then when we talk
about the medium term we say okay we're
going to no no we have to care because
you know to produce you need workers and
and you know workers are not going to
work for any wage and so we had to begin
to talk about ER the the supply side of
the economy but we made it very simple
we just look at the problem of wage
bargaining and price setting but the
production function itself wasn't that
interesting it was outputting equal to
labor and I told you it's very
unrealistic but it was convenient for
that part of the course because Capital
doesn't grow that fast so typical
production function we have both capital
and labor but at the business cycle
frequency investment the change in
capital can be large but the stock of
capital doesn't move that much and so
you can ignore it for business cycle
type fluctuations but if we want to look
at the long run Capital plays a huge
role capital accumulation and so we have
to be explicit about the role of capital
in the the production
function so this is going to be our now
and now we're going to forget about
aggregate demand we're going to say look
we're going to focus about AGG supply
and demand will do whatever it needs to
do so so so we get what what the supply
site says so output now will be will be
a an increasing function of both capital
and
labor now this function will have a
bunch of er properties which are many of
which
are no at a broad level they are
empirically validated but they're also
very convenient from the modeling point
of view the first and most
important
property um is constant returns to
scale okay we're going to use a lot of
property so so please get that concept
constant return to scale means simply
that if you scale the factors of
production you also scale the output
okay so say if x is 1.1 that means if
you increase capital and labor by 10%
you get 10% more output okay so that's
Conant return to scale if I scale all
the factors of production by the same
amount the same proportion then output
Grows by the same proportion it's
scalable that's what it mean constant
return to
scale very important property what comes
next decreasing returns to
Capital that
is H as you increase capital for a fixed
amount of Labor so conent scale is a
property of scaling everything
up the property I'm describing here is
what happens if we increase only K what
happens to Output if we increase only K
but fixing
n in other words set this to one and
start moving this
up you're not going to get X here you're
going to get something different from
X and but this tells you is that yes
you're going to get more output but less
and less the more Capital you
have Okay so this says for example
suppose you start with 100 workers and
100 units of capital and it happens that
this produces 100 units of
goods if you add now 10 units of capital
say you're going to
get seven units of output not 10 seven
because you didn't increase labor had I
increased labor also by by 10 I would
have gotten 10 of output but I
increasing only h capital by 10 then and
keeping output fixed then labor fixed
then output will increase by less than
10 but what this decrease in returns to
Capital says is that now if you increase
again from 110 to 120 units of capital
you're going to get get less than seven
units of output more you're going to get
five and if you increase a again from
120 to 130 you're going to get less than
five you're going to get three and so on
so forth that's decreasing returns to
scale and and decreasing returns to
Capital and the reason for that is is
economically is that more and more
capital is working with a fixed number
of workers so labor becomes very scarce
for
capital okay and that's the reason so so
you have very little
the other these are factors of
production which are complementary they
need each other labor and capital if you
fix one and it start increasing only one
then it's harder and harder for each
extra new unit of this one to work with
sort of fewer and fewer of the other
factor of production so the same
principle applies to labor if you fix
capital and you only increase labor then
initially you get a big jumping output
but it's going to be smaller and smaller
and smaller the more you keep adding a
um
labor okay so in pi so let me One X that
we're going to use
throughout is we want to make x one of
our favorite X will be 1 /
n you see what I'm trying to do when we
set x equal to 1 / n so that x equal to
1 / n what I get here is output per
person
no that's what I
get y Over
N so if I set xal to 1/ n i can using
con to scale I know that this is equal
to
y/n k/ n n/ n so that is one so this guy
doesn't move and I have now
that a output per person is increasing
in capital per worker worker and
population this part of the course are
the same for get an EMP employment and
is population is employment if labor
force is everything I'm not this is not
a place to worry about unemployment
okay okay so remember that all the plots
I show you the different Figures were
about this variable how it changed over
time how was different across different
countries how grew at a different rate
in in different countries but from this
very simple model you see that in order
to
explain the change in this or growth in
why over and why one country grows more
than the other you have with the simple
model only two
options so if I tell you country a grew
more over this period than grew more per
per person than this other
country er um over this period of time
there are only two options here the
first one is that in that country there
was more capital accumulation per worker
so K Over N went up no if K Over N goes
up more in one country than the other
one y Over N will go up more in that
country than the other one and the other
option is that the this H function
itself shifted
up so for any given amount of K Over N
now you could produ more y over n and
that's what we call technological
progress that's a second thing so so if
if if the difference in in in in growth
of output per
person is due to an increasing K Over
end well we call that a capill
accumulation mechanism if it is because
the function f shifts up that's
technological progress and what we're
going to do is in the next lecture we're
going to talk about this channel the
capital accumulation Channel and in the
lecture after the spring break we're
going to talk about shift in the
function f so in in in in
figures
so fixing the technology that this is
the function f is fixed and you just
move K Over N this is the picture you
have now that's a produ this I'm
plotting this function here as a
function of k/ n for a fixed function f
and that's what you get so output per I
have here Capital per worker and output
per per
worker and you see that obviously it's
in an increasing function the more
Capital per worker you have the more
output per worker you'll
produce but it's also
concave why is it
concave that's decrease in returns to
Capital is look for any when you have
very little Capital per work
a change in capital per worker gives
gives you a big jumping output per
worker because you know there was sort
of very little Capital that was the
problem of that
economy when the economy has more and
more Capital the same change in capital
leads to a much smaller change in output
here at this level when when Capital per
worker was very low the economy was very
poor then this change LED to this change
in output per capita at this level of
wealth if you get as capital economies
with higher Capital are richer Capital
per worker the same change this change
is of the same size as that leads to a
much smaller change in
output okay and that's a result of
decreasing returns to
Capital and that's the other option
again that's what we're going to talk
about in the next lecture this this one
and two lectures from now we're going to
talk about growth that comes from shift
in the production function this
technological progress
okay very good see you on Wednesday