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The aggregate production function and growth | APⓇ Macroeconomics | Khan Academy - YouTube
Channel: Khan Academy
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in a previous video we have introduced
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the idea of an aggregate production
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function which is a fancy way for a
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mathematical model that an economist
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might use to tie the factors of
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production in an economy to the actual
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aggregate output of an economy the
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aggregate output is why and then the
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factors of production we've talked about
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this before it's human capital it's
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technology and it is regular capital or
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non-human capital and so a is really
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representing the technology factor here
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and this term is often known as total
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factor productivity
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k is referring to the non-human capital
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and of course capital starts with a c
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but they use k for capital and then l
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stands for the human capital you could
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view it as standing for labor but
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standing for a little bit more than that
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and we'll talk about that in a second
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and just to make this tangible because
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it's written in function notation here
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which might seem a little bit abstract
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it's just saying hey some function of k
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and l you could imagine an aggregate
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production function that looks like this
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where our aggregate output is equal to
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our total factor productivity which is
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once again a measure of our technology
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times our capital to some power times
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our human capital to some other power
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and
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in an introductory economics course you
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wouldn't actually have to do this type
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of computation taking things to
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fractional exponents if although we have
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many videos on khan academy explaining
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how to take fractional exponents if you
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are curious but this gives you a sense
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that look if any one of these inputs
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goes up well then you would expect
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aggregate output to go up and if for
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whatever reason these were to go down
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then you would any one of these to go
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down that that would have a negative
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impact on aggregate output
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but the focus of this video is really
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thinking about if you were an economist
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how would you actually come up with the
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values for a k and l pause this video
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and think about that so let's start with
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l
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which sometimes we imagine
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represents labor but you really should
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think of it as human capital how would
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you measure human capital
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well the most obvious thing is you could
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measure labor
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and how would you measure labor
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well you could go and see well how many
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people are in the labor force so measure
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measure
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the labor
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force
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and you might say well isn't that all
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that there is to human capital but
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remember not all labor is equivalent if
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people are unhealthy they're not going
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to be able to be
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output as much if people aren't trained
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they're not going to be able to output
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as much so it's not just the quantity of
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people in the labor force it's also
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measures of education
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that would factor into l so the more
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educated a labor force the more trained
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l would go up so higher people in labor
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force l goes up more educated labor
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force l goes up and a healthier labor
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force
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l would go up they're going to be able
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to do more
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now what about k
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what about the capital stock of a
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country
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well you might be tempted to say well
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maybe i could count the amount of
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capital or something like that but that
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wouldn't really make sense because there
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could be some types of capital that
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might be you know some just tools while
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you might have another capital that's a
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big building or a rail car or whatever
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else and so the k
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is actually measured by economists as
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the value of the capital stock in a
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country so let me write it this way
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so the value
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of capital
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capital
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in
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your country or in the economy that we
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care about
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now a really interesting one is how do
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you measure a
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there isn't an obvious index for hey i
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can just observe that and say that has
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more technology than that other thing
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and the way that economists often figure
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out an a for an economy is by backing
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into it
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they can figure out an l and they can
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figure out a k
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and they know what the output they know
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what the gdp of that country is the real
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gdp
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and then if different countries have the
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same k and the same l but then their
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gdps are different then that means that
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they have a different a so the a you
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could almost view as an adjustment to
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fill in the gap to connect the dots
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between the kl and the y but it would be
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a measure of how technologically
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advanced something is if my economy has
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an a of 1 in order to make the numbers
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work and your economy has an a of two
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that means for some reason you're
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getting twice the productivity given the
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same capital and human capital as i am
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which implies that you have twice the
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technology
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