Demand Curves

1
Demand Curves

• Graphical Derivation

2
We start with the following diagram
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.
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.
3
Next we draw in the indifference curves showing
the consumers tastes for x and y.
Then we draw in the budget constraint and find
the initial equilibrium
4
Recall the slope of the budget constraint is
y0
x0
5
From the initial equilibrium we can find the
first point on the demand curve
Projecting x0 into the diagram below, we map the
demand for x at px0
px0
x0
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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
To find the demand for x at the new price we
locate the new equilibrium quantity of x
demanded.
y0
x
x1
px
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
x
x1
x0
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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
x
x0
x1
px
And then connect them with a line.
px1
This is the Marshallian demand curve for x
px0
Dx
x
x0
x1
8

• 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

9
Leontief Indifference Curves- Perfect Complements
y
y0
x
px
x0
Again projecting x0 into the diagram below, we
map the demand for x at p0x
px0
x0
10
Again considering a rise in the price of x, to
px1 the budget constraint swings in.
We locate the new equilibrium quantity of x
demanded and then drop a line down from this
point to the lower diagram.
y0
x0
x1
px1
px0
This shows us the new level of demand at p1x
x0
x1
11
Again we highlight the the px and x combinations
we have found in the lower diagram and derive the
demand curve.
y0
x0
x1
px1
px0
x0
x1
12
Perfect Substitutes
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Putting in the Budget constraint we get
Where is the utility maximising point here?
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Suppose now that the price of x were to fall
y0
Q What is the best point now?
x0
px0
x0
15
At price below px1 what will happen?
y0
x0
px0
px1
x0
16
y
As price decreases further, what will happen?
y0
x
x0
px
px0
px1
x0
x
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• 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?