Indifference Curves and Individual
and Social Production Possibilities
International Economics
Professor Dalton
ECON 317 – Fall 2014
1
Indifference Curves
Y/time
Characteristics
U3
U2
U1
1. Fixed preferences
2. Negatively-sloped
3. Higher indifference curve
represents greater utility
4. Convex
5. Non-intersecting
6. Slope = Marginal Rate of
Substitution (MRSxy)
X/time
2
Indifference Curves
Y/time
11
9
The Marginal Rate of Substitution
represents a trade-off ratio;
the marginal benefit from a
unit of one good in terms of
another.
A
If the individual is at point A, an
additional unit of X is worth 2Y.
B
3.2
U2
3
34
11 12
If the individual is at B, an
additional X is worth 0.2 Y.
X/time
3
Budget Constraint
 A budget constraint is negatively-sloped,
reflecting the notion of opportunity cost one must give up one good to get more of
another.
 The slope of a budget constraint
measures the opportunity cost of one
additional unit of a good in terms of the
foregone units of the other good.
4
Budget Constraint
 In consumer choice, the budget constraint
usually consists of an income constraint
reflecting relative prices of the two goods.
 The budget constraint can also consist of a PPF.
• In either case, the slope of a budget constraint
measures the opportunity cost of one additional unit
of a good in terms of the foregone units of the other
good.
5
Budget Constraint
What is the slope of the budget constraint?
Slope equals rise over
run.
For an income
constraint, slope
equals I/Py divided by
I/Px. (where I is
income and Pj is the
price of good j)
I/Py/I/Px =
Px/Py
Y/time
I
Py
0
C
The slope of the budget
constraint equals the
price ratio
Px/Py
I
Px
A
X/time
6
Budget Constraint
What is the slope of the individual production possibility frontier?
Slope equals rise over
run.
For an PPF, slope
equals Y divided by X,
and is the Marginal
Rate of
Transformation,
MRTx,y.
Y/time
Y
C
The slope of the budget
constraint equals MRTx,y
A
0
X
X/time
7
Individual Production
Possibilities
Y/time
An individual’s production
possibilities frontier shows the
quantities of goods, X and Y, that
can be produced within a given
time period while efficiently using
the resources at hand.
30
15
X/time
8
Individual Production
Possibilities
Y/time
30
Begin with simple case of
constant productivity. Suppose
that L = 10, and MPLY = 3 and
MPLX = 1.5.
At maximum, individual can
produce Y = (10)(3) = 30
units of Y and X = (10)(1.5)
= 15 units of X.
15
The slope equals
ΔY/ΔX.
Y = MPLY (L) and X
=MPLX (L),
so ΔY/ΔX = MPLY
(L)/MPLX (L),
or simply MPLY/MPLX.
X/time
9
Individual to Social
Production Possibilities
Y/time
Slope is called the marginal rate
of transformation between X
and Y, abbreviated MRTx,y, and
30
it representahow much it costs
in Y to produce an X
Slope is 30/15 = 2
The marginal cost of X = 2Y
The marginal cost of Y = 1/2 X
15
X/time
10
Three Individual PPFs
Y
Y
Joe
100
30
30
X
Y
Sam
150
180
Bill
X
120
X
Which individual is the best producer of X?
Which individual is the best producer of Y?
It depends upon what is meant by “best”!
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Comparative and Absolute
Advantage
 A person is said to
have an absolute
advantage in
producing a good if
he can produce more
of the good than can
another.
 A person is said to
have a comparative
advantage in
producing a good if
he can produce the
good at a lower cost
than another.
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Three Individual PPFs
Absolute Advantage
Y
Y
Joe
100
30
30
X
Y
Sam
150
180
Bill
X
120
X
Absolute Advantage: Good X
Absolute Advantage: Good Y
Sam (150)
Bill (180)
Bill (120)
Sam (100)
Joe (30)
Joe (30)
13
Three Individual PPFs
Comparative Advantage
Y
Y
Joe
100
30
30
X
Y
180
Sam
Bill
150
X
120
X
Comparative Advantage:
Good X
Comparative Advantage:
Good Y
Sam: 2/3 Y
Bill: 2/3 X
Joe: 1 Y
Joe: 1 X
Bill: 3/2 Y
Sam: 3/2 X
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Building the Social PPF
Y
Y
Y
Comparative Advantage:
Good X
Joe
310
30
180
Sam: 2/3 Y
Bill
Joe: 1 Y
Bill: 3/2 Y
30
X
120
Y
Sam
100
150
X
300
X
15
X
Building the Social PPF
 The Social PPF is the “summation” of all
the individual agents’ PPFs in the
economy, constructed by applying the
principle of comparative advantage.
16
Many Person Social PPF
Slope is flat at A. Low
opportunity cost of X.
A
Slope is steep at B. High
opportunity cost of X.
B
X/time
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Choice: Combining Indifference
Curves with Production Possibilities
Y/time
Here, MRSx,y > Px/Py (or MRTx,y).
The individual can buy an
additional X for less than the
additional unit is valued.
MB
MC
U3
U2
Here, MRSx,y < Px/Py (or MRTx,y).
The individual would have to
pay more than the additional
unit of X is valued.
U1
1 2
X/time
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Choice
Y/time
1Y
U3
U2
When the MRSx,y > Px/Py
(or MRSx,y > MRTx,y) , the
individual can make himself
better off by selling a unit of Y
to purchase additional units of
X, since a unit of X is valued
more highly than a unit of Y at
the going prices.
So long as this remains true, the
individual continues to move
“down” his budget constraint.
U1
1 3
X/time
19
Choice
Y/time
Y*
U3
U2
U1
X*
When MRSx,y = Px/Py (or
MRSx,y = MRTx,y), the
individual will have
reached a point where
he can make himself no
better off by a
rearrangement of
resources in X and Y
consumption.
He will have maximized his utility!
X/time
20
Changes in
the Budget Constraint
Y/time
Starting from an original
budget constraint …
Suppose that the
price of X falls…
The consumer can now
buy more X if all income is
spent on X…
But can buy no more Y if
all income is spent on Y…
X/time
The budget constraint rotates outward
“around” the original Y-intercept
21
Changes in
the Budget Constraint
Y/time
Starting from an original
budget constraint …
Suppose that the
price of X increases…
The consumer can now
buy less X if all income is
spent on X…
But can buy no more Y if
all income is spent on Y…
X/time
The budget constraint rotates inward
“around” the original Y-intercept
22
Changes in
the Budget Constraint
Y/time
Starting from an original
budget constraint …
Suppose that the
price of Y falls…
The consumer can now
buy more Y if all income is
spent on Y…
But can buy no more X if
all income is spent on X…
X/time
The budget constraint rotates outward
“around” the original X-intercept
23
Changes in
the Budget Constraint
Y/time
Starting from an original
budget constraint …
Suppose that the
price of Y increases…
The consumer can now
buy less Y if all income is
spent on Y…
But can buy no more X if
all income is spent on X…
X/time
The budget constraint rotates inward
“around” the original X-intercept
24
Changes in
the Budget Constraint
Y/time
Starting from an original
budget constraint …
Suppose that money
income I increases…
The consumer can now
buy more Y if all income is
spent on Y…
and can buy more X if all
income is spent on X…
X/time
The budget constraint shifts outward.
Does the slope change?
NO.
25
Changes in
the Budget Constraint
Y/time
Starting from an original
budget constraint …
Suppose that money
income I decreases…
The consumer can now
buy less Y if all income is
spent on Y…
and can buy less X if all
income is spent on X…
X/time
The budget constraint shifts inward.
Does the slope change?
NO.
26
Changes in
Indifference Curves
Y/time
11
9
Start from an original set of
Indifference Curves (only one of
which is shown).
If the individual is at point A, an
additional unit of X is worth 2Y.
A
6
U2
34
X/time
Suppose that the individual’s
preferences change so that X is
now valued more highly (he
prefers X relatively more)…
Now the individual will value an
additional unit of X at more than
2Y, say 5Y…
The set of indifference curves will become steeper…
27
Changes in
Indifference Curves
Y/time
11
10
Start from an original set of
Indifference Curves (only one of
which is shown).
If the individual is at point A, an
additional unit of X is worth 2Y.
A
U2
34
11 12
X/time
Suppose that the individual’s
preferences change so that Y is
now valued more highly (he
prefers X relatively less)…
Now the individual will value an
additional unit of X at less than
2Y, say 1Y…
The set of indifference curves will become flatter…
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Changes in Behavior: Price
Y/time
Beginning from
equilibrium,
Y**
Y*
suppose that Px falls.
The budget constraint
rotates outward around
the Y-intercept…
U3
U2
U1
X* X**
X/time
The consumer chooses a
new X, Y combination:
X**, Y**
29
Changes in Behavior: Price
Y/time
Beginning from
equilibrium,
Y’
Y*
suppose that Px rises.
The budget constraint
rotates outward around
the Y-intercept…
U3
U2
U1
X’
X*
X/time
The consumer chooses a
new X, Y combination: X’,
Y’
30
Changes in Behavior: Income
Y/time
Beginning from
equilibrium, suppose that
Income rises.
Y**
Y*
U3
U2
U1
X* X**
X/time
The budget constraint
shifts outward and the
slope doesn’t change
(why?)
The consumer chooses a
new X, Y combination:
X**, Y**
31
Changes in Behavior: Income
Y/time
As this graph what kind of
goods are X and Y?
Both are normal goods.
Y**
Y*
U3
U2
U1
X* X**
X/time
32
Changes in Behavior: Income
Y/time
Suppose, that instead,
money income had fallen.
Again that means a new
equilibrium, and a new
equilibrium combination of
X’ and Y’.
U3
Y*
Y’
U2
U1
X’ X*
X/time
33
Changes in Behavior:
Preferences
Y/time
Y*
Start from an original
equilibrium, A.
Suppose preferences become
more favorable to X…the IC
steepen.
A
B
Y**
X*
X**
The individual now moves to a
bundle favoring more X and
Less Y, at B.
X/time
34
Social Indifference Curves?
 Can we sum up the preferences of individuals
into a social indifference curve?
• We could if we could measure the intensity of preferences
independent of income levels, or measure utility directly.
• But we can’t.
 Further, Arrow’s Impossibility Theorem shows
that there exists no rule that allows us to
combine preferences without giving some one
person in society totalitarian power over the
resulting choice.
35
TANSTAASIC
There ain’t no such thing as a Social
Indifference Curve…(sometimes called a
Social Welfare Function).
But BEWARE, textbooks and journal articles
often present graphs that pretend that we
can aggregate individual preferences into
a Social Preference Ordering – a Social
Indifference Curve.
36
TANSTAASIC
For a two good world, we can employ the
fiction that the indifference curve
represents the preferences of the
marginal or representative individual in
society.
When we move to more than two goods,
however, this fiction becomes untenable.
37
TANSTAASIC
 Why use graphs that show Country PPFs
and Country ICs? (that violate
TANSTAASIC!)
 As a short-hand for the more complicated
process of actual price formation…that’s
all.
 Don’t commit the fallacy of misplaced
concreteness.
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