Transcript The Demand Curves - The Economics Network

Demand Curves
Graphical Derivation
We start with the following diagram
y
In this part of the diagram we have drawn
the choice between x on the horizontal
axis and y on the vertical axis. Soon we
will draw an indifference curve in here.
x
px
Down below we have drawn the
relationship between x and its price
Px. This is effectively the space in
which we draw the demand curve.
x
Next we draw in the
indifference curves
showing the consumers
tastes for x and y.
y
y0
x0
x
px
x
Then we draw
in the budget
constraint and
find the initial
equilibrium
y
Recall the slope
of the budget
constraint is:
y0
px
dy

dx
py
x0
x
px
x
y
From the initial equilibrium we
can find the first point on the
demand curve
y0
x
px
Projecting x0 into the
diagram below, we
map the demand for
x at px0
px0
x0
x
Next consider a rise in the price of
x, to px1. This causes the budget
constraint to swing in as –px1/py0
is greater
y
y0
x1
x
px
To find the demand for
x at the new price we
locate the new
equilibrium quantity of
x demanded.
Then we drop a line
down from this point to
the lower diagram.
px1
px0
This shows us the new
level of demand at p1x
x1
x0
x
y
We are now in a position to draw
the ordinary Demand Curve
First we highlight
the the px and x
combinations we
have found in the
lower diagram.
y0
px
x1
x
x0
And then connect
them with a line.
px1
px0
This is the
Marshallian demand
curve for x
Dx
x1
x0
x
• In the diagrams above we have drawn our demand
curve as a nice downward sloping curve.
• Will this always be the case?
• Consider the case of perfect Complements (Leontief Indifference Curve) e.g. Left and Right
Shoes
Leontief Indifference CurvesPerfect Complements
y
y0
px
x0
x
Again projecting x0
into the diagram
below, we map the
demand for x at p0x
px0
x0
Again considering a rise in the
price of x, to px1 the budget
constraint swings in.
y
y0
px
x1
x0
x
We locate the new
equilibrium quantity of
x demanded and then
drop a line down from
this point to the lower
diagram.
px1
px0
This shows us the new
level of demand at p1x
x1
x0
x
y
y0
px
x1
x0
x
px1
px0
x1
x0
x
Again we highlight
the the px and x
combinations we
have found in the
lower diagram and
derive the demand
curve.
y
Perfect Substitutes
x
px
x
y
Putting in the Budget
constraint we get:
Where is the utility
maximising point
here?
x
px
px0
And hence the
demand for x = 0
x
y
Suppose now that the
price of x were to fall
The budget
constraint would
swing out
y0
px
x0
x
Q: What is the
best point now?
A: Anywhere on
the whole line
px0
px1
The demand
curve is just a
straight line
x0
x
y
At price below px1
what will happen?
Now budget
constraint pivots
out from y axis
y0
px
x0
x
px0
And the best
consumption point
is x max
So at all prices less
than px1 demand is
x max
px1
x0
x
y
As price decreases
further, what will
happen?
y0
px
x0
x
x max (the best
consumption
point) moves out
as price falls
px0
px1
x0
x
• So here the demand curve does not take the usual
nice smooth downward sloping shape.
• Q: What determines the shape of the demand
curve?
• A: The shape of the indifference curves.
• Q: What properties must indifference curve have to
give us sensible looking demand curves?