PAM 200 – Microeconomics  Week 4 Lecture Notes
In the next section we will review some of the results that were introduced during the discussion of
budget constraints.
Now that utility has been included, we can verify some previous conclusions.
I.
EFFECTS OF CHANGES IN INCOME
In the following diagram there is an initial equilibrium at point A., which results in utility of U
1
.
Y
1
X
1
M
2
/P
Y
P
X
/P
Y
M
1
/P
Y
D
C
B
A
P
X
/P
Y
Y
U
1
X
M
2
/P
X
M
1
/P
X
Now assume that income increases from M
1
to M
2
, and that prices are held constant.
The budget
constraint shifts out in a parallel manner.
The question is where is the new equilibrium?
I have
dissected the possibilities into three sections: B, C or D.
Notice that it is possible for me to draw
rational indifference curves (i.e. downward sloping, convex, tangent to the budget constraint, don’t
intersect the existing indifference curve U
1
) in each of the three sections.
This indicates that our
theory of utility does not preclude a final equilibrium in any of the three areas.
Of course only one
of the three blue, red or green indifference curves is actually the right one, it is just that without
further information we can’t rule out which one is correct.
If an increase in income from M
1
to M
2
moves the equilibrium from A to a region of B, then X is
inferior and Y is normal.
If the move results in equilibrium in C, then both X and Y are normal.
If
the move results in equilibrium in D, then X is normal and Y is inferior.
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II.
EFFECTS OF A ROTATION AROUND THE INITIAL EQUILIBRIUM POINT
In the following diagram there is an initial equilibrium at point A., which results in utility of U
1
.
The
initial utility maximizing quantity of X is X
1
.
Y
1
X
1
U
1
M
1
/P
Y
A
P
X
/P
Y
Y
Now I rotate the budget constraint clockwise around the point A, indicating that X has become
more expensive relative to Y ( the slope of the blue budget constraint is steeper indicating that the
price of X has increased relative to Y).
Notice that now it is impossible to draw a conventional indifference curve on the section of the new
budget constraint below point A that does not violate one of the conditions for drawing indifference
curves.
In the diagram it is clear that the red indifference curve crosses the black indifference curve,
which is not rational.
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 Spring '07
 EVANS,T.

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