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Lecture-83 Decreasing MRTS - YouTube
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now we are going to talk about
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diminishing marginal rate of technical
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substitution or diminishing
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technical rate of substitution technical
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rate of substitution is just another
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name of
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marginal rate of technical substitution
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so again just what is mrts just to
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revise it what is mrts
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what does it measure slope of isopod it
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measures the slope of isoquant but that
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is very
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mathematical answer
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what does it mean in economic sense
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that
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how much
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amount you have to substitute
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if you of capital if you add one more
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unit of labor to get the same out so
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broadly speaking it talks about
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the marginal rate of technical
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substitution is nothing but
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rate at which one input can be
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substituted for the other input while
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keeping the output
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fixed
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we have to be on the same isoquant
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ok and when we are talking about capital
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and labour as we had done in the past
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this is
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the amount of capital that needs to be
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decreased
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to have the same output when we increase
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labor by one unit
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that's how we have defined
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so now the thing is if we keep on
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increasing the labor so whenever we
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increase
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labor what does it mean
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that here on this graph
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this is one isoquant let us say we are
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producing q naught and we are increasing
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l it means we are moving in this
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direction and on this isoquant we are
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moving
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along this curve
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ok so whenever we increase
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labor
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we have to decrease the amount of
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capital
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to obtain the same amount of output and
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if just we keep on increasing labour
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without decreasing the capital what will
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happen
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output will increase if marginal
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productivity of labor is positive
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okay and
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it will decrease its marginal
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productivity of labor is negative
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okay so unless unless
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we have marginal productivity of labor
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equal to zero
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and we want to
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you know we we wont be on the same
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isoquant if we increase the labor
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and when marginal productivity of labor
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is 0 how would this isoquant look like
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at that point it should be horizontal it
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should be horizontal as we get in the
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case of perfect complement when we are
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talking about this horizontal arm
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okay
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so basically we have to decrease the
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amount of capital
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so what do you think what happens to the
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amount of capital that we need to
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decrease whenever we increase labor by
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one unit and we want to be on the same
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isoquant what happens to this amount of
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capital
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that needs to be decreased in order to
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be on same isoquant should it be should
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it increase
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or should it decrease decrease why
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should it decrease
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why should it decrease
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of course this is what diminishing
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marginal rate of technical substitution
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what does it say that
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when we are on the same isoquant and we
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keep on increasing l
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okay we keep on increasing on l so then
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respective decrease in capital
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to maintain the same level of production
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is
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decreasing
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so delta k that is required will
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decrease as we move in
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this direction ok just look at it here
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here we have
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let us say this is
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roughly same
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here we have l naught
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here we have l naught plus one here we
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have l naught plus two
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let us take this
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and let us take one more
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fine
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so earlier this is the
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delta k
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in the next turn
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this is smaller
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so if this is the shape of course it is
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specific to the shape
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it is specific to the shape
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so what we are talking about remember
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let us think about it
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mpl is
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positive typically we take it as
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positive it means if we keep the
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capital fixed and increase the labor
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what will happen
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output will increase
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and mpk is also positive
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what will happen
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q will increase whenever we keep the
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labour fixed and increase the capital
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fine
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ok
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now
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that is why we we get this particular
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shape
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isn't it
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this particular shape of isoquant we
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obtain because what we take mpl is
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greater than 0 and mpk is greater than 0
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it means mrts
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the way we have defined
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is negative
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so we will always get a downward sloping
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isoquant
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that also
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the reason is also because we have
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talked about monotonicity earlier
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so this is the shape we get
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fine
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but what happens as l goes on increasing
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mpk also increases
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what is mpk marginal product of capital
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think about is the scenario is
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that
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of course
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we have
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now again whenever we are talking about
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mpk we are fixing at two particular
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level so let us look at it we have label
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l one and label
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l naught and l one and l one is greater
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than l naught
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we have
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m p marginal productivity of labor
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at l is equal to l naught
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and we have marginal product of capital
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at l is equal to l one
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and what happens that this one is
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greater than typically this one is
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greater than this one why
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can you think of a reason
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so by example it is very easy so tell me
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one example like sir if you have seven
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computers and seven labels now
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if one more label label come like eight
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labels and seven computers now if you
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increase
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the
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one computer more its productivity would
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increase more rather than
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decreasing if you have six products and
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six if you have six computers and
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eight labels
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okay
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is it clear
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what we have here is
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mpl
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delta l
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okay plus
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mpk
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delta k
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this should be equal to
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zero
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on the
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same isoquant
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is it clear
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now what happens as l
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increases
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as l
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increases what happens to mpl
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decreases
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we don't know all the time we don't know
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we don't know what happens all the time
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okay it may increase it may
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decrease as we have talked about earlier
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fine
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ok
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so but how about here
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mpk
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mpk typically
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increases
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so basically what's happening the
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capital is becoming
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more and more productive
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capital as with more
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labor capital is becoming more and more
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productive
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so small amount you take out and you get
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equivalent reduction
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because more productive goes in the both
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direction
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and that is why
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marginal rate of technical substitution
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diminishes as l increases
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or in other word
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it becomes because
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it becomes
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it tends towards it becomes more
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horizontal as l keeps on increasing and
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in the opposite direction it tends to
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become vertical but see one exception is
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here
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one exception is here
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where we have
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both the
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factor of production
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as
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complement
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there it is not applied
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there it is not applied so this is a
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property of convexity
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this is a property of convexity that we
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had talked about earlier
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ok so when production technology is
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convex what do we get that marginal rate
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of technical substitution diminishes as
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the first input
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amount of first input increases is it
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clear
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now let us talk about
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elasticity of substitution
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ok what is elasticity of substitution
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sir can you repeat the last sentence
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once more again
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which one
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about the lp and lpk which right right
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now
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here in this case yes sir
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as l increases mpk increases typically
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so but it goes in the board
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mpk is increasing at that point it's not
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marginal product of labor is not just in
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one particular direction it is in the
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both direction
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so to compensate for the same you know
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to know to
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just because labor has increased so
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output will
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increase so what we do we need we need
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to take out little bit of we need to
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take out some capital so that we come
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back to the
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same level of production so mpk is
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increasing
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so if we take little bit of capital
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what will happen we will come back to
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the same level of production as mpk goes
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on
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increasing we need to take less and less
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amount of
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capital out to come back to the same
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level of production and that is why we
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get diminishing marginal rate of
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technical substitution is it clear
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fine
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okay
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