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Lecture-66 Substitution Effect and Income Effect - YouTube
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now we are going to study the effect of
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change in price on optimal bundle from a
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different angle okay let's look at it
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what happens here we have let's say this
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is our this is what we have this is
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let's say again this is X 2 this is X 1
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and this is the bundle
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let's pay attention to the budget line
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what is budget line P 1 X 1 plus P 2 X 2
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is equal to I this is the budget line or
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what we can write X 2 is equal to minus
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P 1 by P 2 X 1 plus I by P 2 I by P 2 P
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2 so if P 1 changes P 1 changes what
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happens if P 1 changes amount of extreme
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amount of at optimal level of course
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both will change but the point here is
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that the effect of change in P 1 we can
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decompose it into two part effect of
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change in P 1 because two roles that P 1
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is playing change in P 1 would bring to
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the optimal consumption bundle one
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effect would be like let's say that
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relative attractiveness of these two
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goods now let's say everything else is
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same okay and the relative price forget
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about the actual price that everything
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is same just the relative price of good
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1 and good 2 good 1 with respect to good
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2 has changed ok so in other word if
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everything else is same it means this
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person should is getting the same
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utility ok
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and of course how we are able to manage
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it that we will see it later how we do
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it but let's say this person is getting
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the same utility but now the prices of
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these two goods are different in the
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economy and let's say that P 1 has gone
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up so what will happen if we are on the
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same utility level then the new budget
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line should be tangent to this utility
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function due to this utility level this
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indifference curve and how would it look
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like because P 1 has gone up so then
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this line would become steeper so it
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will be something like
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and what will be the optimal level there
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will be decrease in amount of it's good
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one consumed and there will be increase
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in amount of good to consumed
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that's one effect because of change in
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price but artificially because if price
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is changing let's see what happens to
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the budget line income remains the same
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so we will not this is not the new
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budget line not the new budget line what
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will be the new budget line of course
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the maximum amount of quantity to that
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can be bought in the market would not
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change because of change in price of
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good one so and what I am saying that P
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one has increased so then budget line
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will rotate we voted at this particular
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point and it would rotate in clockwise
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direction so the new budget line is
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going to be like this so how did we get
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this budget line what did we say here if
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budget line will rotate then this
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utility level it becomes unachievable
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unless unless the optimal optimal point
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is a corner point so I'm not talking
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about those scenarios okay unless it is
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the optimal point the corner point is
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the optimal point the earlier utility
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level cannot be achieved in this new
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scenario fine so let me say again it
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would be something like and of course I
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am drawing
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I'm sorry
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this is the new new bun new optimal
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bundle fine and of course this is
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approximation this is not exact graph
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okay so now how did we move from here to
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here what's the difference so what we
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are basically doing now because the
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budget line is changing but we want to H
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we want to reach to the same utility
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level so artificially we are giving
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enough income to this consumer so that
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he is able to achieve the same level of
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utility in this new chased world and why
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this world is different because the
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prices of the price of good one is
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different
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so basically in that case this line and
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this line these two lines should be
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parallel because the slope of this line
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is new price p1 divided by p2 and this
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line also has the slope new p1 new if I
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want to say p1 new divided by p2 what is
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the difference that here this person has
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little more income and we did it
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artificially we did it in a way so that
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this person is able to achieve his
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earlier utility label and why did we do
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it because we want to untangle the
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effect of change in price into two
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different component that price is doing
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two things one it is changing the
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relative attractiveness of
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of two goods and second what it is doing
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it is also decreasing the purchasing
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power of the consumer how it is
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decreasing let's say rather than
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expressing this person and person's
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income in rupees let's say the good one
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is food and good to his cloth let's say
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food is 10 rupees per kg and the income
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of this person is 100 so we can express
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this person income in terms of food that
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would be 10 units of food but now the
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price of food let's say it goes up from
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10 to 20 it goes up from 10 to 20 now
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his income is just 5 units of food so
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there is decrease in his purchasing
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power ok so change in price is bringing
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doing two different things one it is
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changing the relative attractiveness of
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good and it is also changing the
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purchasing fine okay
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so when we talk about this first one
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when we talk about the first one that
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it's changing the relative struck
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attractiveness of the wood that's what
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we did here that what we did we kept the
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utility level fixed and we change the
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budget line so that the new budget line
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remains tangent to the
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same utility level and so that's why we
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are keeping everything fixed here we
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there is only one change income is not
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changing in the real terms only the
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relative attractiveness of these two
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goods are changing because of change in
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price of good one sir income is changing
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here in again income is changing but in
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other in the purchasing power term it's
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not changing what is the role that
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income is playing here that income is
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used to achieve certain utility level so
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the monetary value of income may be
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different but in terms of utility
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achieved it hasn't changed the person is
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achieving same level of utility okay so
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in the real sense income doesn't change
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okay in nominal since it has changed
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so in that sense I am talking about that
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income oriole income remains the same
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because same level of utility is being
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achieved in this case so this this here
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gives us substitution effect let me give
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you the definition the change in the
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amount of quantity demanded because of
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the change in the price of that good
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while all other prices and level of
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utility achieved cubed are kept constant
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fine so again let us look at it here
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this is the utility indifference curve
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achieved the maximum the maximum level
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being achieved in this case here we have
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x1 and x2 and earlier this is the x1
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star that is the quantity demanded for
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good one and now the new one is x1 start
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- fine clearly whenever we have convex
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indifference curve or convex preferences
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that would be more appropriate convex
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preferences fine then what will happen
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if p1 goes up x1 star goes down and this
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I am NOT talking about overall effect I
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am just talking about because of
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substitution effect because this is the
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substitution effect we are changing only
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the relative attractiveness of the good
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but this is something artificial because
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we have this is the original budget line
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and the new budget line that we are
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using is this one we are artificially
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jacking up the income of this person so
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that he is able to achieve his earlier
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utility level in the new scenario but
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this is done artificially what's really
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happening that because of change in
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income
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this will budget line will become
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something like this and then we can have
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let's say optimal here
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something like this this is the new
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optimal level fine
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and so we can trace to changes from here
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to here and then from here to this is
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the final so this change is the total
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change total change and how about change
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from here to here this is changed
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because of substitution effect and then
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what is remaining from this artificial
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point to the final point in what is that
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change that is the change in quantity
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demanded because of income effect okay
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so let me write what is income effect
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the change in quantity change in the
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change in the amount of quantity
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demanded
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manded because of changing purchasing
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power of a consumer while all the prices
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are kept constant fine
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so remember these two lines this budget
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line and this budget this artificial
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budget line and the new budget line they
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are parallel to each other so it means
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the relative price of these two goods
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are so insane what is the difference
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that income label the real income level
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are different purchasing power is
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different so this change is because of
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only purchasing power fine okay now
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let's look at it
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substitution effect whenever P 1 goes up
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let me write it here P 1 goes up X 1
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star decreases just pure substitution
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effect can we say something similar for
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the income effect no we cannot say there
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are two scenarios here that we you have
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studied already that either it can go up
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or it can go down here let me introduce
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P 1 is going up so what's happening
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income is income real is decreasing and
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the 1 when real income is decreasing and
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X 1 star is going up it means this is
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inferior good and this is normal good so
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in case of normal good the substitution
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effect and
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income effect they work in the same
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direction
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but in the case of inferior good
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substitution effect and income effect
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they are in the opposite direction
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