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Lecture-52 DMRS and Convexity: Example - YouTube
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let's take some example where what we
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have is on x-axis we have good one and
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on X Y axis let us say just share put
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good 1 and good you not necessarily the
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item 2 item 1 and item 2 let's say there
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is an individual who doesn't care for
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the item 2 let's for example let's say
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that good 1 is milk and good 2 is Ola
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and an individual doesn't like Cola he
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doesn't drink his he is indifferent then
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how would his indifference curve look
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like he doesn't care about good - so
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then it is vertical line nothing else so
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what would be the marginal rate of
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substitution here marginal rate of
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substitution of good one with respect to
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go to is infinity by the way here in
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this case we call good two as neuter
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neuter for this particular person what
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we can have his and let's say if I
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change let's say now I talk about
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marginal rate of substitution that's a
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good one is milk and good two is Cola
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now I say milk is on x-axis y-axis and
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cola is on y-axis can you draw the
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indifference curve horizontal line and
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what would be the marginal rate of
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substitution see just be careful when we
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are talking about marginal rate of
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substitution of milk with respect to
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Cola it would it still is infinity but
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marginal rate of substitution of Cola
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with respect to milk is zero so when we
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do not say when we say just mrs
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we are not using any particular term you
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can use both way either you can say of
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good one with respect respect - good -
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or of good - with respect to good one
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but by convention we will follow that
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whenever we say mrs what we mean is mrs
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of good one with respect to good is it
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clear we will always use this this here
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is zero and mrs here is infinity but in
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both the examples america what is
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affinity taxes marginal rate of
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substitution would not change okay fine
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so just be careful what you are talking
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about this is you know a point of
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confusion many people just change the
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axis when they talk about it and you get
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completely different result instead of
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getting X you get one by x + y let's see
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what do we mean by marginal rate of
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substitution mathematically so let's say
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this is good - and hey this is good one
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what we have here is an indifference
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curve of course I have taken an
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indifference curve of a person who
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exhibit whose preference exhibits
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convexity what we are talking about is
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let's say two points let's say this is 2
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and this is 4 doesn't matter this is and
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then what we have here is 3 and this is
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3 doesn't matter and what is marginal
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rate of substitution in this case minus
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1 we will let's change it little bit
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let's put it here three point two five
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just for example because what is the
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marginal rate of substitution here
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Mrs by the definition that we have used
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is minus 0.75 why - just wait I will
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come to that why what's happening
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increase in X is why we are getting
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minus sign because of course when we
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have convexity what we will get I think
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the better explanation for this why why
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do we get this what is the reason why do
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we see this that you get one good you
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will have to give up the other good both
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what we are assuming that both these
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items are good means they give certain
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satisfaction or certain you know utility
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to the person and what we want we want
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this person to have the same level of
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utility same level of satisfaction by
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consuming these one of these two bundles
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so of course when we are increasing the
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amount of one good to bring what will
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happen using if we use the monotonicity
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what will happen more of one good and
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theme of the other good what will happen
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if more of one good what's happening let
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us see from here you are moving here in
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this direction here look at the screen
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it will it's increasing from two it's
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going to three and while the amount of
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second good is four of course your
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satisfaction would be higher
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using monotonicity so to bring this
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person back to the original satisfaction
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level what you need to do is this is
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Delta x1 and this is Delta x2 you will
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have to decrease the amount of good to
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so increase should always be accompanied
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by decrease in the other code if both
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are the goods okay if one is bad
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remember the definition right from the
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beginning if one is bad then marginal
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rate of substitution would be positive
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because to increase the amount of bad
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you will have to compensate that person
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by giving more
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the other good when that case marginal
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rate of substitution would be positive
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but here in this case it is negative and
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what is this point seven five to give up
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basically what we are talking about that
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to get one more unit of good one so here
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we have in denominator we have good one
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and changes one unit how much change do
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we need in the second need good four
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minus three point seven five three point
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two five and of course I should put a
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minus sign there okay and this is you
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get 0.75 so what is this what is
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marginal rate of substitution marginal
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rate of substitution is nothing but the
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slope of this indifference curve okay so
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what would be mathematically more sound
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rather than talking about one more unit
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of good one we should talk about very
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very small unit of good one okay and
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with respect to get to get very little
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amount of good one how much the other
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person is willing to give up the another
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good but we have to measure in terms of
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per unit of good one so that's why in
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that case mrs is going to be let's say
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in other word let's see if we just do it
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mathematically the original bundle is XY
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and let's say what's happening from XY
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what we are having change is x plus
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delta x and y plus delta y and what
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would be the slope what we are certain
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about that let us say this is x y and
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this is X plus Delta X from a y plus
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Delta Y
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what would be the slope the slope is
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going to be y plus Delta Y minus y
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divided by X plus Delta X minus X
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although I am not using it here see what
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I have done I have increased the amount
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of good one and I also have increased
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the amount of good 2 typically if Delta
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X is positive Delta Y has to be negative
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so we will get here negative value but
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in some time in some books you would see
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that mrs is given as a positive number
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that only means that the author has
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introduced a negative sign here to
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convert the mrs into a positive number
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okay
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so it doesn't matter is it clear ok
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