proxies for their values then allocative or economic efficiency might be
represented as:
value of output
P Q +P Q
X
X
Y
Y
Allocative efficiency =
=
value of input
P L +P K
L
K
90
5.3.2 Production Possibilities Function
Q
Given the original PPF as line RA. An
Y
improvement in technology that impacts
H
H
only the production of xebecs can be seen
as a shift from RA to RB. An improvement
ls
in technology that influences only the
aw
R
R
production of Yawls would be a shift from
RA to HA. Technology that impacts the
production of both goods would be a shift
uantity of YQ
from RA to HB. These outward shifts are
sometimes cal ed “economic growth.”
A change in inputs could also be shown as shifts in
the PPF, a decrease in inputs would shift the PPF
inward toward the origin. An increase in inputs
would shift the PPF outward.
A
B QX A
B
Quantity of Xebecs
Figure 5.2
Allocative efficiency is not only influenced by the quantities of the goods
produced and quantities of the inputs used, but the relative values of the
inputs and outputs are also important. The benefits or value of an alternative
can be expressed as PXQX +PYQY. The costs of the alternative could be
expresses as PLL + PKK. Given a set of inputs and technology the solution that
achieves allocative efficiency is the highest valued output possible given the
inputs and prices.
A
Given inputs and a state of technology, the alternative sets of outputs are
53
B
shown by the production possibilities function. If all inputs are used to
50
produce Yawls (good Y, or QY), a maximum of 53 units can be
)
C
Y
produced. If the inputs are reallocated to produce 5 Xebecs (good X, or
Q 40
QX), it will be possible to only produce 50 yawls. At the output shown
ls (
D
by point C, 16 units of xebecs and 40 units of yawls are produced. If all
aw 30
inputs are used to produce Xebecs (QX= 32 at point G), a maximum of
32 units of X can be produced.
E
20
H
Given technology and inputs, all possible output combinations are shown
uantity of YQ
F
by all points that lie along and inside the line ABCDEFG. A change in
10
inputs or technology will shift the production possibilities frontier.
G
5
16
24 29 32
Quantity of Xebecs (QX)
Figure 5.1
91
5.3.2 Production Possibilities Function
Using the same production possibilities function as in Figure 5.1, allocative
efficiency can be described in Figure 5.3. In this example, the optimal output
alternative is that with the highest value. Since value cannot be measured
directly, neoclassical economists use market price as an approximation of
value. In order for market price to be a reasonable approximation, exchanges
must be voluntary exchanges of goods with exclusive property rights. If the
price of xebecs were $4 and the price of yawls were $2 the “value” of each
alternative identified in Figure 5.2 can be calculated. Alternative A is worth
$106, alternative B is worth $120, C is worth $144, D is worth $156, E is also
“valued” at $156. The output at alternative F is worth $144 and at G is worth
$128. These calculations can be seen in Table 5.3. The highest valued output,
based on market prices will lie on the PPF between alternatives C (valued at
$156) and D (also $156).
If the prices of the goods are accepted as the value of the goods, the
calculation of each alternative are shown in Table 5.1
If the price of good Y should rise to $3.50 (and the price of X stay at $4)
the alternative with the “highest value” is at point C as shown in Table 5.2.
The alternative that is allocatively or economically efficient is dependent on
a set of prices that measures value. We will explore the ability of the market
to accurately reflect values of outputs. It is also important to note that there
are many things that humans value that cannot be expressed as a market
price.
92
5.3.2 Production Possibilities Function
($106)
A
($120)
The PPF is determined by the finite quantity of inputs and technology. If
53
B
the price of xebecs is $4 (PX=$4) and the price of yawls is $2 (PY=$2),
50
($144)
at point A the “value” of good X is 0 and the “value” of good Y is
)
C
$106, the “value” of the output (given prices) is $106.
Y
Q 40
At point B the value of the output of good X is $20 ($4x5
($156)
ls (
units X), the value of good Y is $100 ($2x50 units Y).
D
aw 30
The value of output of good X and Y is $120.
($156)
($104)
At D and E the value of the output is $156. Some where between
E
20
H
alternatives D and E on the PPF the value of the output will reach a
($144)
P
uantity of Y
maximum. It is where the slope of the PPF is equal to X
Q
F
10
P .
Y
($128)
Any alternative inside the PPF will be valued at less than the maximum
G
value.
5
16
24 29 32
Quantity of Xebecs (QX)
Figure 5.3
93
5.3.2 Production Possibilities Function
Table 5.1 Allocative Efficiency and Value of Output
Value of
Value of output
Value of
output
Q
of X
output of Y
X
PX
QY
PY
(P
(P
XQX +
X QX)
(PY QY)
P
Alternative
YQY)
A
0 $4.00
$0.00
53 $2.00
$106.00
$106.00
B
5 $4.00
$20.00
50 $2.00
$100.00
$120.00
C
16 $4.00
$64.00
40 $2.00
$80.00
$144.00
D
24 $4.00
$96.00
30 $2.00
$60.00
$156.00
E
29 $4.00
$116.00
20 $2.00
$40.00
$156.00
F
31 $4.00
$124.00
10 $2.00
$20.00
$144.00
G
32 $4.00
$128.00
0 $2.00
$0.00
$128.00
H
16 $4.00
$64.00
20 $2.00
$40.00
$104.00
94
5.3.2 Production Possibilities Function
Table 5.2 Allocative Efficiency and Value of Output
Value of
Value of output
Value of output
of X
Q
output of Y
X
PX
QY
PY
(P
(P
XQX +
XQX)
(PYQY)
P
Alternative
YQY)
A
0 $4.00
$0.00
53 $3.50
$185.50
$185.50
B
5 $4.00
$20.00
50 $3.50
$175.00
$195.00
C
16 $4.00
$64.00
40 $3.50
$140.00
$204.00
D
24 $4.00
$96.00
30 $3.50
$105.00
$201.00
E
29 $4.00
$116.00
20 $3.50
$70.00
$186.00
F
31 $4.00
$124.00
10 $3.50
$35.00
$159.00
G
32 $4.00
$128.00
0 $3.50
$0.00
$128.00
H
16 $4.00
$64.00
20 $3.50
$70.00
$134.00
95
5.3.3 Pareto Efficiency
5.3.3 PARETO EFFICIENCY
At a technical level, economics provides a set of tools to aid in choosing
among competing alternatives. In 1906 an Italian, French, Swiss, engineer,
sociologist, economist Vilfredo Pareto (1848-1923) introduced the concept of
Pareto optimality as a means to undermine the role of utilitarianism in
economics. Instead, it became the foundation for what is now called benefit
cost analysis and its derivative measures of allocative performance such as
rate of return on investment and cost effectiveness.
Consider a community of individuals. Your task is to choose an alternative
to maximize the welfare or utility of the group. If there were an alternative
that would improve the welfare (or increase the utility) of at least one person
in the group without making any one worse off (decrease their welfare or
utility), you should choose to that alternative. However, if all the alternatives
that would make at least one person better off would also make at least one
other person worse off, you cannot know if that alternative would improve the
wellbeing (utility) of the group.
Pareto efficiency is the condition where all alternatives that would
increase the welfare of at least one person without decreasing the welfare of
others have been exhausted. There is nothing that can be done to improve the
welfare of anyone without making someone else worse off. In the PPF model
(Figure 5.4), Pareto efficiency exists at any point on the PPF once you have
attained that point.
96
5.3.3 Pareto Efficiency
A
Given the PPF, point H is not Pareto efficient: more X (Y) can be
53
B
produced with no sacrifice of good Y (X). A move to any output
50
combination identified in the triangle HEC is a Pareto improvement;
)
C
some one (or everyone) is better off and no one is any worse off; this area
Y
is Pareto Safe. A move to any point in the Pareto Safe area is a Pareto
Q 40
improvement or is Pareto superior.
ls (
D
aw 30
Once on the PPF (point D for example) any change to improve the
E
welfare of an individual (or group) who prefers good Y, would make
20
H
those who prefer good X “worse off.” To increase the quantity of Y, from
point D to point C, would require that less X would be produced.
uantity of YQ
F
10
G
5
16
24 29 32
Quantity of Xebecs (QX)
Figure 5.4
Pareto efficiency can be used as a criterion to decide whether to chose
an alternative. If a choice makes some one better off and no one any worse
off, it is a choice that will increase the achievement of the goal or end of
maximizing the utility or welfare of the group. This can be
“Pareto Safe,” i.e. the output can be altered so someone is “better off”
and no one is worse off. Any change that increases the welfare of one person
or persons that does not reduce the welfare of another is a “Pareto
improvement” or Pareto Safe and will clearly increase the welfare or utility of
the community. Any alternative that results in a greater utility of at least one
person and no decrease in the utility of anyone can be referred to as “Pareto
superior.”
The problem is that this criterion tends to support the status quo. Almost
all choices that increase the utility of an individual or group will make others
worse off. Since a Pareto efficiency criterion is very restrictive, Pareto
Potential is may be used. This is the same as the benefit/cost criterion.
Pareto potential holds that if a choice or alternative makes one person or
97
5.3.3 Pareto Efficiency
group better off but others are worse off, if the “winners” or those who gain
can hypothetically reimburse those who are “losers” (or are worse off) and still
be better off, the alternative will increase the utility of the group. In a more
simplistic way, the benefits associated with the choice exceed the costs.
PARETO POTENTIAL, BENEFIT/COST AND MARGINAL ANALYSIS
The Pareto potential criterion for decision making is the foundation of
analysis that use benefit/cost, cost effectiveness and rate of return for
decision making.
Marginal Analysis
The process of making decisions is like the proverb “The longest journey
begins with the first step.” Or like the question posed by Albert Camus (1913-
1960) about the individual deciding each day about suicide or continuing life.
The individual taking a journey must make the decision about taking the first
step before they decide on the second. In Camus’ case, one must decide not
to committee suicide before you tackle the rest of the day.
Decisions in economics are always made at the “margin.” A decision to
change one variable will cause a change in some other related variable. An act
or choice will have benefits and costs associated with that act. An increase in
the production of xebecs may require a reduction in the production of Yawls:
the benefit is more xebecs, the cost is fewer yawls.
A change in the price of a good will change the quantity sold, a change in
the quantity sold will change the total revenue collected. The change in total
revenue caused by a change in units sold is called marginal revenue. The
marginal concept is applied to a wide variety of relationships. In principles of
economics, these are usually described as a “one unit” change in the
variables. The Greek letter delta, ∆ is used to identify a change calculated by
98
5.3.3 Pareto Efficiency
subtraction. In other cases, a derivative (d) or partial derivative (∂) will be
used to denote a change that approaches 0.
The use of marginal is applied to many economic relationships. In fact, the
early period of the development of microeconomics (mid to late 19th century)
was called the “marginalist revolution.” Below are some definitions of several
useful marginal relationships.
Marginal Cost (MC)
MC is defined as the change in Total Cost (TC) or variable cost (VC) caused by
a one unit change in the quantity produced, output (Q). MC represents
opportunity cost.
ΔTC
ΔVC
MC =
=
Equation 5.3
ΔQ
ΔQ
Marginal Benefit (MB)
MB is defined as the change in total benefit (TB) caused by a one unit change
in quantity consumed (Q).
ΔTB
MB = ΔQ
Equation 5.4
Marginal Utility (MU)
ΔTU
MU =
Equation 5.5
ΔQ
MU is the change in utility caused by a change in quantity consumed (Q)
CHOICE AND MARGINAL ANALYSIS
99
5.3.3 Pareto Efficiency
If Pareto Potential or the Benefit/Cost criteria are to be used for decision-
making, the rule is quite simple: if the benefits associated with a choice (or
alternative) exceed the costs associated with that choice, then the choice will
increase net benefits. If the costs of an alternative exceed the benefits of that
alternative, then that alternative is not a good choice.
EXAMPLE BENEFIT/COST USING MARGINAL ANALYSIS
Using the example PPF presented in Figure 5.5 (Same PPF as in 5.1, 5.3,
5.4 )
Consider the PPF in Figure 5.5: Xebecs are priced at $4 (PX= $4) and
yawls are $3.50 (PY = $3.50). If the initial output were where QX= 16 and QY
= 20, which is represented at point H. At these prices, the output of xebecs is
“worth” $64 and yawls are worth $70. The “value” of the output alternative
identified at point H is $134.
A
Original allocation is at H (QX=16, QY=20);
53
B
PX = $4 and PY = $3.50
50
Alternative E (C, D or any choice in triangle HEC) has no MC, the output of X or
)
C
Y
Y or both X and Y increases so the MB is positive. The B/C ratio of any
Q 40
alternative is grater than one, the MB>MC.
ls (
D
If production were at point D (QX=24, QY=30), a choice of alternative C would
aw 30
result in QX=16, QY=40, 8 units of X are traded for 10 units of Y. Six fewer units
of X at $4 each is a MC of $24. The MB is 10 additional units of Y at $3.50 each
E
H
or $$35. The MB>MC, The B/C ratio >1, the net benefits will increase by $11 by
20
selecting alternative C over D. Alternative C is worth
uantity of YQ
F
10
G
5
16
24 29 32
Quantity of Xebecs (QX)
Figure 5.5
100
5.3.3 Pareto Efficiency
Ranking of Alternative H with Alternative E
If alternative E were chosen over alternative H, 13 additional units of
xebecs would be produced (29-16=13). This is the marginal benefit (MB) of
the choice of reallocating resources from alternative H to E. If xebecs were
valued at $4 each, that would be a MB of $52 in monetary terms. This can be
viewed as a move from row H to row E in Table 5.3
Table 5.3
Allocative Efficiency and Value of Output
Value of
Value of
Value of
Alte QX
PX
output of X QY
PY
output of Y
output
rnat
(PXQX)
(PYQY)
(PXQX + PYQY)
ive
A 0
$4.00
$0.00
53 $3.50
$185.50
$185.50
B 5
$4.00
$20.00
50 $3.50
$175.00
$195.00
C 16 $4.00
$64.00
40 $3.50
$140.00
$204.00
D 24 $4.00
$96.00
30 $3.50
$105.00
$201.00
E 29 $4.00
$116.00
20 $3.50
$70.00
$186.00
F 31 $4.00
$124.00
10 $3.50
$35.00
$159.00
This reallocation of resources would not reduce the output of yawls, so the
marginal cost of the reallocation is 0. Since the MB > MC, the reallocation or
inputs to move the output alternative from H to E would be an improvement in
the achievement of the objective (producing the highest valued output). The
output of xebecs and yawls at point E is $186 (134 + 52: the value of the
output at H added to the MB of reallocation of inputs)
The relative prices of xebecs and yawls are irrelevant since the marginal
cost (MC) is zero. Any increased production of xebecs at any positive price
would be a Pareto improvement. A reallocation to point D, C or any output
combination that lies in the triangle HEC would be a Pareto improvement (or
Pareto superior to the allocation at point H).
101
5.3.3 Pareto Efficiency
Ranking of Alternative E with Alternative F
If the current output were at point E (QX= 29 and QY = 20), and alternative
F (QX= 31 and QY = 10) is considered. The marginal benefit (the benefit
associated with reallocating resources to point F) would be an additional 3
units of xebecs (31-29=3). At $4 each this is a MB of $12 in monetary terms.
However, the reallocation of resources from H to F requires a sacrifice or MC
of 10 units of yawls (20-10=10). At a price of $3.50 the MC is $35 in
monetary value. The MC = 35: MB = 12. A reallocation of inputs to move from
point E to point F would be trading $12 for $35: not a good idea.
Ranking of Alternative E and Alternative D
A reallocation of resources from alternative E to alternative D would result
in an increased output of 10 yawls. At a price of $3.50, the MB is $35. This
reallocation reduces the output of xebecs from 29 to 24, a marginal cost of 5
units of xebecs. At $4 each this is a MC of $20. Since the MB > MC (35 > 20),
the reallocation of inputs from the production of the output at point E to point
B is justified by our benefit/cost criterion. Notice that the net gain to society is
$15, so point D is “worth” $15 more than the output at point E. D is “valued”
at