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Derivation of Demand Curve of a good from Indifference curve | DU SOL | YouTubeToText
YouTube Transcript: Derivation of Demand Curve of a good from Indifference curve
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This content explains how to derive a good's demand curve using the indifference curve technique, illustrating the relationship between a good's price and the quantity demanded by a consumer.
Chapter theory of consumer behavior
topic derivation of demand curve of a
good using indifference curve. Welcome
students. Now we will derive the demand
curve for a good by using indifference
curve technique.
The starting point of this problem is
use the consumer's equilibrium diagram
and after that
derivation of the demand curve will take place.
place.
We take good Y here,
good X here.
The budget line
is given like this.
When price of good X falls, the budget
line will move to the right keeping this
point constant.
So we will
Let us say price of good X falls because
we are going to derive the demand curve
for good X.
Once the price of good X falls, the
budget line moves like this on the
horizontal axis where good X is
On the budget line A B let us say the
price of good X is P1.
You know budget line is written like
this. Initial budget line is P1X
+ P2 Y gives you the income.
This is AB budget line.
When the budget line has moved to AB
dash due to falling price of X,
income is same but price of X has
fallen. Let us say P1 dash is the new
price of X.
and this is A B dash. Now
Now
find out the equilibrium point. The
equilibrium point on the first budget
line lies somewhere here.
That is the point of tangency between
the indifference curve and the budget line.
line.
Call it I1. The first indifference curve
and equilibrium point is point E where
the consumer is purchasing X one amount
of good X.
As a result of fall in price on the new
budget line AB dash the new equilibrium
point of the consumer will be somewhere
here where the point of tangency
lies. So the new point of tangency is E
dash and this indifference curve is
labeled as I2.
The new quantity demanded is X2.
Clearly due to falling price of X.
The budget line moves from AB to AB dash.
dash.
The equilibrium point moves from point E
to E dash. The consumer purchases more
of X from X1 to X2.
The equilibrium points when they move
we get a locus of all equilibrium points
where X is purchased as a result of fall
in its price. This locus is called price
consumption curve of good X.
This is the upper part of the diagram.
Now draw the demand for good X on the
Take price of X on the vertical axis
and quantity of X on the horizontal axis.
axis.
The lower panel is drawn symmetrically
and in the same alignment as the upper panel.
panel.
Quantity of X say X1
can be directly extended this way with
the same measurement. So X1 is here. X2
is here. Level it this way.
Now x1 is associated with
price p1
which corresponds to the point e which
is the initial equilibrium on budget
line a b. P1 can be labeled somewhere
here on the vertical axis on the lower panel.
panel.
Quantity X2
is associated with price P1 dash
which corresponds to point E dash on the
upper panel of the diagram
on budget line AB dash and you know that
P1 dash is below P1 that is P1 dash is
less than P1 so level it below P1 on the
Find the combination of X1 and P1
at point E1.
The combination of P1 dash with X2
Join both E1 and E2 to get demand curve
DX which is downward sloping. Now you
can find that the demand for X is
derived from the price consumption
curve. Thank you.
Look at the derivation of the demand
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