Topic #3
General Equilibrium
Our consumer theory will have a framing premise and three assumptions.
A framing
premise is something that can’t be proven – it’s either accepted or rejected.
Our framing
premise is that individuals are selfinterested.
That is, they act to be made as well off as
possible under the circumstances.
Further, our consumers are rational and goaldirected.
We assume that they act in a purposeful manner.
This does not mean that our consumers
are
selfish
.
Being selfinterested does not mean you benefit from depriving others.
For example, let Carol’s ordinal utility be represented by the following equation,
U
=
F
+
B,
where F is footballs and B is books. An
indifference curve
connects all the consumption
bundles that generate the same level of utility.
Thus, a consumer is indifferent among the
consumption bundles on a particular indifference curve.
For example, the following
indifference curves represents X units of utility.
Higher indifference curves yield more
utility.
Thus, consumption bundles to the northeast are superior bundles and
consumption bundles to the southwest are inferior bundles.
Footballs
Figure 1
SUPERIOR BUNDLES
36
a
d
b
16
INFERIOR
c
BUNDLES
1
4
16
49
Books
In addition, our theory has three assumptions:
1.
Completeness 
the consumer has and can rank in order of preference all
consumption items.
No flipping of coins or enemeneminemo.
2.
Transitivity 
preferences are rational and consistent.
No rock, paper, scissors.
The following indifference map violates the assumption of transitivity.
For example, try
to rank consumption bundles a, b, and c.
Consumption Good Y
a
c
b
Consumption Good X
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentIt appears that a>b, a=c, and b=c, which does not make sense.
So, we conclude that
indifference curves can't intersect.
3.
Nonsatiation 
more is preferred to less.
This means that indifference curves
can’t be positively sloped and that indifference curves can’t be fat.
The
Marginal Rate of Substitution (MRS
YX
)
is the amount of the consumption good
measured on the Y axis that an individual would be willing to give up in order to obtain
another unit of the consumption good measured on the X axis.
We assume that the
marginal rate of substitution is diminishing as we move from left to right along an
indifference curve.
This makes indifference curves convex.
For example MRS
FB
is the maximum amount of footballs the consumer is willing to give
up to obtain another book.
Find the MRS between bundles “a” and “b” and “b” and “c”.
Does the MRS increase or decreases as we move from left to right?
Suppose consumption bundle “e” has 49 footballs and 1 book.
Calculate the MRS
between “e” and “a”.
Footballs
Figure 1
36
a
b
16
c
1
16
49
Books
Formally, ∆U = MU
F
(∆F) +
MU
B
(∆B).
Since utility is constant along an indifference
curve, 0 = MU
F
(∆F) +
MU
B
(∆B) when calculating MRS.
Thus, MU
B
/MU
F
= ∆F/∆B.
To see why the MRS is diminishing, suppose I give you 10 large pizzas (each with 10
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Stengos
 Econometrics, Consumer, edgeworth box, walrasian equilibrium, Pareto optimal allocations

Click to edit the document details