Choice
Ch 5: Choice
Ch 6: Demand
(sec. 2,5,6,8 & appendix)
Ch 15: Market Demand
(sec. 1& 2)
2
Rational Choice
The principal behavioral postulate is
that a decisionmaker chooses its
most preferred alternative from those
available to it.
In terms of our model, this means
choosing a bundle from the highest
indifference curve that can be
reached without exceeding the
budget set.
3
Rational Constrained Choice
x
1
x
2
Affordable
bundles
4
Rational Constrained Choice
Affordable
bundles
x
1
x
2
More preferred
bundles
5
Rational Constrained Choice
x
1
x
2
x
1
*
x
2
*
(x
1
*,x
2
*) is the most
preferred affordable
bundle.
6
Rational Constrained Choice
The most preferred affordable bundle
is called the consumer‟s ORDINARY
DEMAND at the given prices and
budget.
Ordinary demands will be denoted by
x
1
*(p
1
,p
2
,m) and x
2
*(p
1
,p
2
,m).

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7
Choice with monotonic preferences
Supposed preferences are monotonic,
i.e. more is better;
Then the consumer will always
choose a bundle that exhausts the
budget.
The chosen bundle is “interior” if it
contains strictly positive quantities of
both goods.
8
Rational Constrained Choice
When preferences are monotonic,
indifference curves are smoothly
convex and the chosen bundle is
interior, (x
1
*,x
2
*) satisfies two
conditions:
(a) the budget is exhausted;
p
1
x
1
* + p
2
x
2
* = m
(b) the slope of the budget constraint, -
p
1
/p
2
, and the slope of the indifference
curve containing (x
1
*,x
2
*) are equal at
(x
1
*,x
2
*).
9
Choice: The canonical case
x
1
x
2
x
1
*
x
2
*
(x
1
*,x
2
*) is interior .
(a) (x
1
*,x
2
*) exhausts the
budget; p
1
x
1
* + p
2
x
2
* = m.
(b) The slope of the indiff.
curve at (x
1
*,x
2
*) equals
the slope of the budget
constraint.
10
Solving for the optimum bundle
If the budget is exhausted, then the
optimum bundle must satisfy the
budget constraint with equality:
p
1
x
1
* + p
2
x
2
* = m
If the optimum bundle is interior,
then it must be a point at which the
slope of the budget line equals the
slope of the indifference curve, i.e.:
- p
1
/p
2
=
MRS
We can use these two equations to
solve for the two variables
x
1
*and x
2
*
.
11
Computing Ordinary Demands -
a Cobb-Douglas Example.
Suppose that the consumer has
Cobb-Douglas preferences.
Then
U x
x
x x
a b
(
,
)
1
2
1
2
MU
U
x
ax
x
a
b
1
1
1
1
2
MU
U
x
bx x
a b
2
2
1
2
1
12
Computing Ordinary Demands -
a Cobb-Douglas Example.
So the MRS is
At (x
1
*,x
2
*), MRS = -p
1
/p
2
so
MRS
dx
dx
U
x
U
x
ax
x
bx x
ax
bx
a
b
a b
2
1
1
2
1
1
2
1
2
1
2
1
/
/
.
ax
bx
p
p
x
bp
ap
x
2
1
1
2
2
1
2
1
*
*
*
*
.
(A)