The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those available to it The available choices constitute the choice set How is the most preferred bundle in the choice set located ID: 648440
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Slide1
Chapter Five
ChoiceSlide2
Economic Rationality
The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those available to it.
The available choices constitute the choice set.
How is the most preferred bundle in the choice set located?Slide3
Rational Constrained Choice
x
1
x
2Slide4
Rational Constrained Choice
x
1
x
2
UtilitySlide5
Rational Constrained Choice
Utility
x
2
x
1Slide6
Rational Constrained Choice
x
1
x
2
UtilitySlide7
Rational Constrained Choice
Utility
x
1
x
2Slide8
Rational Constrained Choice
Utility
x
1
x
2Slide9
Rational Constrained Choice
Utility
x
1
x
2Slide10
Rational Constrained Choice
Utility
x
1
x
2Slide11
Rational Constrained Choice
Utility
x
1
x
2
Affordable, but not the most preferred affordable bundle.Slide12
Rational Constrained Choice
x
1
x
2
Utility
Affordable, but not the most preferred affordable bundle.
The most preferred
of the affordable
bundles.Slide13
Rational Constrained Choice
x
1
x
2
UtilitySlide14
Rational Constrained Choice
Utility
x
1
x
2Slide15
Rational Constrained Choice
Utility
x
1
x
2Slide16
Rational Constrained Choice
Utility
x
1
x
2Slide17
Rational Constrained Choice
x
1
x
2Slide18
Rational Constrained Choice
x
1
x
2
Affordable
bundlesSlide19
Rational Constrained Choice
x
1
x
2
Affordable
bundlesSlide20
Rational Constrained Choice
x
1
x
2
Affordable
bundles
More preferred
bundlesSlide21
Rational Constrained Choice
Affordable
bundles
x
1
x
2
More preferred
bundlesSlide22
Rational Constrained Choice
x
1
x
2
x
1
*
x
2
*Slide23
Rational Constrained Choice
x
1
x
2
x
1
*
x
2
*
(x
1
*,x
2
*) is the most
preferred affordable
bundle.Slide24
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*(p1,p2,m) and x
2
*(p
1
,p
2,m).Slide25
Rational Constrained Choice
When x
1
* > 0 and x
2
* > 0 the demanded bundle is
INTERIOR.If buying (x1*,x2*) costs $m then the budget is exhausted. Slide26
Rational Constrained Choice
x
1
x
2
x
1
*
x
2
*
(x
1
*,x
2
*) is interior.
(x
1
*,x
2
*) exhausts the
budget.Slide27
Rational Constrained Choice
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.Slide28
Rational Constrained Choice
x
1
x
2
x
1
*
x
2
*
(x
1
*,x
2
*) is interior .
(b) The slope of the indiff.
curve at (x
1
*,x
2
*) equals
the slope of the budget
constraint.Slide29
Rational Constrained Choice
(x
1
*,x
2
*) satisfies two conditions:
(a) the budget is exhausted; p1x1* + p2
x
2
* = m
(b) the slope of the budget constraint, -p
1/p2, and the slope of the indifference curve containing (x1*,x
2
*) are equal at (x
1
*,x2*).Slide30
Computing Ordinary Demands
How can this information be used to locate (x
1
*,x
2
*) for given p
1, p2 and m?Slide31
Computing Ordinary Demands - a Cobb-Douglas Example.
Suppose that the consumer has Cobb-Douglas preferences.Slide32
Computing Ordinary Demands - a Cobb-Douglas Example.
Suppose that the consumer has Cobb-Douglas preferences.
ThenSlide33
Computing Ordinary Demands - a Cobb-Douglas Example.
So the MRS isSlide34
Computing Ordinary Demands - a Cobb-Douglas Example.
So the MRS is
At (x
1
*,x
2
*), MRS = -p1/p2
soSlide35
Computing Ordinary Demands - a Cobb-Douglas Example.
So the MRS is
At (x
1
*,x
2
*), MRS = -p1/p2
so
(A)Slide36
Computing Ordinary Demands - a Cobb-Douglas Example.
(x
1
*,x
2
*) also exhausts the budget so
(B)Slide37
Computing Ordinary Demands - a Cobb-Douglas Example.
So now we know that
(A)
(B)Slide38
Computing Ordinary Demands - a Cobb-Douglas Example.
So now we know that
(A)
(B)
SubstituteSlide39
Computing Ordinary Demands - a Cobb-Douglas Example.
So now we know that
(A)
(B)
Substitute
and get
This simplifies to ….Slide40
Computing Ordinary Demands - a Cobb-Douglas Example.Slide41
Computing Ordinary Demands - a Cobb-Douglas Example.
Substituting for x
1
* in
then givesSlide42
Computing Ordinary Demands - a Cobb-Douglas Example.
So we have discovered that the most
preferred affordable bundle for a consumer
with Cobb-Douglas preferences
isSlide43
Computing Ordinary Demands - a Cobb-Douglas Example.
x
1
x
2Slide44
Rational Constrained Choice
When x
1
* > 0 and x
2
* > 0
and (x1*,x2*) exhausts the budget,and indifference curves have no
‘kinks’, the ordinary demands are obtained by solving:
(a) p
1
x
1* + p2x2* = y
(b) the slopes of the budget constraint, -p
1
/p
2, and of the indifference curve containing (x
1*,x2*) are equal at (x1*,x2*).Slide45
Rational Constrained Choice
But what if x
1
* = 0?
Or if x
2
* = 0?If either x1* = 0 or x2* = 0 then the ordinary demand (x1*,x
2
*) is at a
corner solution
to the problem of maximizing utility subject to a budget constraint.Slide46
Examples of Corner Solutions -- the Perfect Substitutes Case
x
1
x
2
MRS = -1Slide47
Examples of Corner Solutions -- the Perfect Substitutes Case
x
1
x
2
MRS = -1
Slope = -p
1
/p
2
with p
1
> p
2
.Slide48
Examples of Corner Solutions -- the Perfect Substitutes Case
x
1
x
2
MRS = -1
Slope = -p
1
/p
2
with p
1
> p
2
.Slide49
Examples of Corner Solutions -- the Perfect Substitutes Case
x
1
x
2
MRS = -1
Slope = -p
1
/p
2
with p
1
> p
2
.Slide50
Examples of Corner Solutions -- the Perfect Substitutes Case
x
1
x
2
MRS = -1
Slope = -p
1
/p
2
with p
1
< p
2
.Slide51
Examples of Corner Solutions -- the Perfect Substitutes Case
So when U(x
1
,x
2
) = x
1 + x2, the mostpreferred affordable bundle is (x1*,x
2
*)
where
and
if p
1
< p
2
if p
1
> p
2
.Slide52
Examples of Corner Solutions -- the Perfect Substitutes Case
x
1
x
2
MRS = -1
Slope = -p
1
/p
2
with p
1
= p
2
.Slide53
Examples of Corner Solutions -- the Perfect Substitutes Case
x
1
x
2
All the bundles in the
constraint are equally the
most preferred affordable
when p
1
= p
2
.Slide54
Examples of Corner Solutions -- the Non-Convex Preferences Case
x
1
x
2
BetterSlide55
Examples of Corner Solutions -- the Non-Convex Preferences Case
x
1
x
2Slide56
Examples of Corner Solutions -- the Non-Convex Preferences Case
x
1
x
2
Which is the most preferred
affordable bundle?Slide57
Examples of Corner Solutions -- the Non-Convex Preferences Case
x
1
x
2
The most preferred
affordable bundleSlide58
Examples of Corner Solutions -- the Non-Convex Preferences Case
x
1
x
2
The most preferred
affordable bundle
Notice that the “tangency solution”
is not the most preferred affordable
bundle.Slide59
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1Slide60
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
MRS = 0
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1Slide61
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
MRS = -
¥
MRS = 0
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1Slide62
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
MRS = -
¥
MRS = 0
MRS is undefined
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1Slide63
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1Slide64
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1
Which is the most
preferred affordable bundle?Slide65
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1
The most preferred
affordable bundleSlide66
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1
x
1
*
x
2
*Slide67
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1
x
1
*
x
2
*
(a) p
1
x
1
* + p
2
x
2
* = mSlide68
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1
x
1
*
x
2
*
(a) p
1
x
1
* + p
2
x
2
* = m
(b) x
2
* = ax
1
*Slide69
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
(a) p
1
x
1
* + p
2x2* = m; (b) x2* = ax1*.Slide70
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
(a) p
1
x
1
* + p
2x2* = m; (b) x2* = ax1*.
Substitution from (b) for x
2
* in (a) gives p
1
x
1
* + p
2
ax1* = mSlide71
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
(a) p
1
x
1
* + p
2x2* = m; (b) x2* = ax1*.
Substitution from (b) for x
2
* in (a) gives p
1
x
1
* + p
2
ax1* = mwhich givesSlide72
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
(a) p
1
x
1
* + p
2x2* = m; (b) x2* = ax1*.
Substitution from (b) for x
2
* in (a) gives p
1
x
1
* + p
2
ax1* = mwhich givesSlide73
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
(a) p
1
x
1
* + p
2x2* = m; (b) x2* = ax1*.
Substitution from (b) for x
2
* in (a) gives p
1
x
1
* + p
2
ax1* = mwhich gives
A bundle of 1 commodity 1 unit and
a commodity 2 units costs p1 + ap2;m/(p1 + ap
2
) such bundles are affordable.Slide74
Examples of ‘Kinky’ Solutions -- the Perfect Complements Case
x
1
x
2
U(x
1
,x
2
) = min{ax
1
,x
2
}
x
2
= ax
1