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Lecture-74 Isoquants - YouTube
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let's move little further coming back to
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the production function again we will go
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back and forth rather than finished one
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and go to another I'm describing it in
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this particular way so that you can
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relate the bees to representation so now
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we have we had drawn a graph where we
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have one input and we have one output
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now let's say what if because I said
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that production function we will do when
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we have only one output I didn't put any
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restriction on number of inputs what
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will we do when we have let's say two
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inputs and one output we will have a
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three-dimensional graph okay we can have
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here input 1 input 2 and on the third
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axis we can have output that's one way
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to do it but this is quite if this three
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dimensional graph is little less
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tractable than a two dimensional graph
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so a better way to represent this
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production function is to use something
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called ISO quant and what do we mean by
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a by n I so quant
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what is an ISO point
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not bad so what we have is basically a
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set of input combination or factors why
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I am saying vectors because vectors is
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well suited to represent the input
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combination that after transformation
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give out the same amount of
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seem amount of output let's say for
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example say Q naught or a particular
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level okay further further the same
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combination
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further the same combination cannot be
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used cannot provide
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more than
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q not output that's very important this
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is very important for example let's take
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is it clear let's take this here we have
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one dimensional world where we have one
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input and one output so two dimension
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input is one dimensional fine
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now we have the example that we took
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root X can you tell me the iscope wants
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a single point at any level let's say we
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talk about y is equal to 5 so we draw a
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line y is equal to 5 so it's only 25
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units of X would give us 5 units of Y so
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I took 1 2 y is equal to 5 has only one
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point has only one point we are talking
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about and that is X is equal to 25 so
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similarly what did we do here we try to
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obtain basically ISO quant is nothing
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but a level curve of the production
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process
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ISO font let me say an ISO want
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I so quant is a level curve of the
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production function
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and how do we obtain the level curve we
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draw like here in this case we draw Y is
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equal to a if we are interested in level
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curve a then we draw y is equal to a and
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here in this case it is a line and of
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course it will intersect the curve
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wherever it intersects the curve all
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those combination would be on the I so
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Kwan so it is in one dimensional so we
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get only one point but what we have
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typically here in the two demands three
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dimension where input are on two
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dimension and output on the third
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dimension what we do when we draw y is
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equal to a what do we get a plane a
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plane and then we may get more than one
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point Y is equal to a will be a plane
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here okay so what we this plane may
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intersect the production function at
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more than one point and all those points
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will be on isoquant
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Y is equal to a what it means that you
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take the combination of those inputs you
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will be able to produce a amount of
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output and you cannot produce more than
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amount of output okay fine so for
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example let's take two dimensional world
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that you have already looked at earlier
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let's say the bread let's continue with
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the bread example the production of
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sandwich what we have here is y is
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minimum of X 2 X divided X 1/2 and X 2 X
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1 is amount of bread and this is butter
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how would the graph look like here in
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this try to draw a three-dimensional
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here is set of plane it won't be a set
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of plane and you think about it that's
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what I said
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the easier way is to use the concept of
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also Kwan to describe this production
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function how can we describe it we can
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take a particular value of y starting
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with y is equal to let's say 1 so to get
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1 units of one unit of sandwich how many
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units of bread I need to and what we
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need one unit of butter that will give
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so here we have two and here we have one
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but also notice in this particular case
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even we if we have three bread for bread
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five bread or just one unit of butter we
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are still able to produce only one
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sandwich
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so all these mines here that represents
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that butter remains fixed at 1 but
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amount of bread keeps on increasing
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doesn't matter we get the same amount of
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sandwich and similarly in the other
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direction also so this is the ISO quant
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and similarly we can draw for y is equal
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to 2 y is equal to 3 and so on if you
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remember sorry
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is it clear these are the ISO Quan one
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two three we had drawn very similar
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curves when we talked about indifference
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curve okay in case of perfect
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complementarity between two goods can
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you say what is the big difference from
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there and here any difference that you
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can think of any difference that comes
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to your mind from the earlier case or
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it's exactly the same of course this is
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we are talking I'm not talking about the
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process I am talking about
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mathematically what is the big
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difference of course here we are talking
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about production and there we talked
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about consumption now of course that is
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the difference but here the bigger
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difference is that 1 2 & 3
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these are cardinal in nature they were
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ordinal they were the 1 2 3 they're
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represented only the levels here these
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are cardinal two is twice as much as one
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so if you think in this way this topic
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is much easier than the consumer theory
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isn't it that's here everything is
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Cardinal you don't have to you know here
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that's what we deal with all the time
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numbers and immediately it cardinality
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pops in in our mind so this is what we
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are more familiar with ok and so we will
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use the very similar concept fine is it
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clear
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ok let's look at one more production one
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more ISO Quan and this time for
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cobb-douglas function and how can we
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represent the cobb-douglas function here
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be particular about it when we say
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cobb-douglas function we write here X 1
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a X 2 B where a and B are greater than 0
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and typically I am NOT saying always
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that a plus B is equal to 1 but this is
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not true always that we will learn
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shortly ok here be careful you cannot do
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the monotonic transformation it you can
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do if you are putting log on both side
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then of course log X 1 plus B log X 2
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remember earlier we did the monotonic
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transformation and we took this out we
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said that level would be
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zurk so we don't need to put here law
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but here we have to put log because the
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numbers have meaning okay so we cannot
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take blindly monotony transformation on
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only one side is it clear to you and I
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so quant in the case of cobb-douglas
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function would look like something like
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this downward sloping
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