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Theological Thinking Grading Rubric
Criteria Levels of Achievement
Below Expectations Basic Proficient Outstanding
Summary of Exegetical
Work
25%
0 to 69 %
The discussion does not cover the features of
the exegetical analysis, or is incomplete, or
does not properly contribute to an
understanding of the passage.
70 to 79 %
The discussion covers features of
the exegetical analysis but is not
sufficiently clear and
comprehensive.
80 to 89 %
The discussion adequately covers
the features of the exegetical
analysis.
90 to 100 %
The discussion displays depth of
understanding and clearly articulates
all of the features of the exegetical
analysis.
Summary of Schools of
Thought
20%
0 to 69 %
Consensus or opposing schools of
thought about the theological meaning of
this passage are not adequately
explained or contrasted. Sources are
poor and not well used in the
explanation.
70 to 79 %
Consensus or opposing schools
of thought about the theological
meaning of this passage are
adequately explained or
contrasted. Sources are adequate
to poor and are used adequately
in the explanation.
80 to 89 %
Consensus or opposing schools
of thought about the theological
meaning of this passage are well
explained or contrasted. Sources
are good and used adequately to
well in the explanation.
90 to 100 %
Consensus or opposing schools
of thought about the theological
meaning of this passage are
insightfully explained or
contrasted. Sources are excellent
and used well in the explanation.
Personal Analysis
25%
0 to 69 %
The theological meaning of the passage
is not adequately developed. The
reasoning used is poor, and sources are
not adequately used or not used at all.
70 to 79 %
The theological meaning of the
passage is adequately developed.
Adequate reasoning is
employed, and sources
adequately used in support.
80 to 89 %
The theological meaning of the
passage is clearly developed.
Good reasoning is employed,
and sources are used well in
support.
90 to 100 %
The theological meaning of the
passage is clearly and
persuasively developed.
Excellent reasoning is employed,
and sources are used very well in
support.
Contemporary
Application
20%
0 to 69 %
The application is not directly related to the
analysis of the text and/or is not applied to a
contemporary situation which clearly
correlates to the text, and/or is poorly
explained.
70 to 79 %
The application relates to the
analysis of the text and is applied in
to a contemporary situation.
However, the correlation between
the text and its application is not
clear and/or not clearly explained.
80 to 89 %
The application is true to the
analysis of the text and is
appropriately applied in a
contemporary situation.
90 to 100 %
The application is consistent with
the analysis of the intended meaning
of the text and is thoughtfully and
appropriately applied in a
meaningful contemporary situation.
Writing Style
10%
0 to 69 %
Obvious grammatical stylistic errors that
make understanding difficult are present.
70 to 79 %
There are obvious
grammatical/stylistic errors; and/or
there are numerous typos, and/or
sources are not cited.
80 to 89 %
Errors are limited to a “typo” or two,
Turabian style is followed
adequately, and sources are cited.
90 to 100 %
There are no obvious grammatical
or stylistic errors, and content is
well constructed and easy to follow
and Turabian style is carefully
followed.
Exchange Economies 91
The length of an Edgeworth box shows the total supply of good
1, while
the height shows the total supply of good 2. Given the
Edgeworth box and
the initial endowment, any exchange of goods between the
consumers en-
tails a movement to another allocation inside the box. Starting
from any
allocation inside the Edgeworth box — say, the center, C = ((6,
5), (6, 5))
— to an allocation to its northeast makes consumer a better off
and b worse
off because both consumers’ preferences are strictly monotonic.
Conversely,
any allocation to the southwest of the box makes b better off
and a worse off.
6.2 Properties of Allocations
Given the preferences of the individuals and the initial
endowment, we can
now discuss properties of allocations. Some allocations may be
more desir-
able than others. We explore two different notions of
desirability.
6.2.1 Individually rational allocations
Individual rationality embodies the idea that if two people trade
voluntar-
ily, that trade must leave each person at least as well off as
before they trade;
if trade hurts either consumer, they will have no incentive to
engage in such
an exchange of goods.
We define an allocation (xa, xb) to be individually rational if
ua(xa) ≥ ua(ωa) and ub(xb) ≥ ub(ωb), (6.3)
i.e., each person’s utility at her consumption bundle xi is at
least as great as
her utility from her endowment ωi, where i = a, b. Thus, the
movement from
the endowment bundle ωa to the bundle xa leaves consumer a no
worse off
than initially, and similarly for consumer b.
In Figure 6.3, the individually rational allocations lie in the
blue lens-
shaped area (labeled IR) between the indifference curves of
each consumer
that pass through the initial endowment. For example, in
moving from ω
to A, both consumers are better off than initially because A lies
on a higher
indifference curve for each consumer. At an allocation such as
B, consumer
a remains on her initial indifference curve and so remains as
well off, but
consumer b is on a higher indifference curve. You can verify
this by drawing ¶b
b’s indifference curve through point B. At C, consumer b is as
well off as
initially but a is better off.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
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0
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B
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92 Chapter 6
x1
a
x2
b
x2
a
x1
b
Oa
Ob
IR
A
B
C
E
F
D
ω
Figure 6.3 Individually rational allocations
Note that any allocation inside the Edgeworth box but outside
of the IR
area places at least one consumer behind her indifference curve,
signifying
that she is worse off than at ω. For example, at D, consumer a is
worse off;
at E, b is worse off, and at F, both consumers are worse off. If
we expect
the consumers to barter and trade with each other starting at ω,
the only
allocations that they would agree to move to voluntarily must
lie within the
IR area since neither is made worse off by such a move; indeed,
it is quite
possible for one or even both of them to be better off.
Individually rational allocations inside the Edgeworth box can
be found
by following the three steps summarized below.
1. Identify the initial endowment, ω, in the Edgeworth box.
2. Draw an indifference curve for consumer a that passes
through ω, us-
ing arrows to show the direction in which her utility is
increasing. Do
the same for consumer b.
3. The area between the indifference curve for consumer a and
that for
consumer b (including the indifference curves themselves) is
the set of
individually rational allocations.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
0 :M = ? =
0
IP
B
AM
Q
7
ME
=
.
EE
B
AM
=
Exchange Economies 93
6.2.2 Pareto efficient allocations
Pareto efficiency (or more traditionally, Pareto optimality)
embodies the
idea of non-wastefulness in allocating the total supply of goods
at our dis-
posal among consumers.3 Given an allocation, if it is possible
to reallocate
the goods so as to make at least one person happier and no one
worse off,
then the original allocation is wasteful in the sense that there is
scope for im-
proving on it. At a Pareto efficient allocation, it is not possible
to reallocate
the goods so as to make one consumer better off without hurting
someone
else, so it is non-wasteful.
To illustrate this idea simply, suppose we have an apple and a
banana to
allocate between two persons. Consumer a is indifferent
between an apple
and a banana, but consumer b has an aversion to bananas and
strictly prefers
apples over bananas. Then the allocation that gives a the apple
and b the
banana is wasteful because it is possible to make at least one
person better
off without hurting the other. Simply give the banana to
consumer a and the
apple to b; then a is as well off, but b is better off. Giving the
banana to a
and the apple to b is a Pareto efficient allocation because it is
not possible to
reallocate the goods and make at least one person happier
without hurting
the other.
Before we can define what a Pareto efficient allocation is
formally, we
need another definition. Starting from an allocation (xa, xb), the
allocation
(x̄ a, x̄ b) is said to be Pareto superior to (or a Pareto
improvement over)
(xa, xb) if nobody is worse off at (x̄ a, x̄ b) and at least one
person is better off.
In other words, if we started with the initial allocation (xa, xb)
and moved
to (x̄ a, x̄ b), then that would constitute an improvement because
nobody is
hurt and someone is happier. An allocation (x̂ a, x̂ b) is Pareto
efficient if there
is no other allocation that is Pareto superior to (x̂ a, x̂ b). In
other words, at a
Pareto efficient allocation, it is not possible to make at least one
person hap-
pier without hurting anyone else — any reallocation of goods
either hurts
somebody, or leaves everyone as well off.
Graphical representation
Typically an Edgeworth box will have many Pareto efficient
allocations. These
Pareto efficient allocations can be found by following this
algorithm.
3Pareto efficiency is named after Vilfredo Pareto, an influential
economist and sociologist.
The phrase “non-wastefulness” was coined by Leonid Hurwicz.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
0 :M = ? =
0
IP
B
AM
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94 Chapter 6
1. Fix the utility of one consumer, say individual b, at some
arbitrary level
ūb inside the Edgeworth box.
2. Maximize the utility of consumer a while keeping b on the
indifference
curve ūb. Then the allocation reached is a Pareto efficient
allocation.
3. To find other Pareto efficient allocations, repeat the process
by picking
a different utility level for b in step 1.
To find one Pareto efficient allocation and understand how this
algorithm
works, arbitrarily fix b’s utility at ūb shown by the green ūb
indifference curve
in Figure 6.4. Maximize a’s preferences while keeping b on her
green indiffer-
ence curve, yielding the allocation A. Then A is a Pareto
efficient allocation.
To check this, consider the different regions of the Edgeworth
box where an
x1
a
x2
b
x2
a
x1
b
Oa
Ob
A
I
II
III
IV
ub
ua
Figure 6.4 A Pareto efficient allocation
alternative allocation could be picked. Any allocation in region
I (which lies
to the southwest of the green indifference curve) makes
consumer a worse
off. In regions II and III, both a and b are worse off as they are
behind their
indifference curves ūa and ūb. In region IV (which lies to the
northeast of the
orange indifference curve ūa), b is worse off. Therefore,
beginning with A,
there is no Pareto superior allocation in the Edgeworth box, and
hence A is
Pareto efficient.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
0 :M = ? =
0
IP
B
AM
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Exchange Economies 95
Two remarks are in order. First, the fact that we fix the utility
of b in step 1
is totally arbitrary. In other words, the same set of Pareto
efficient allocations
can be found by reversing the roles of a and b, namely, fixing
the utility of a
instead in step 1, and maximizing b’s utility while keeping a at
this utility in
step 2.
Second, unlike individually rational allocations, Pareto efficient
alloca-
tions do not depend on the initial endowment as a reference
point. They
only depend on the consumers’ preference and the aggregate
supplies of the
goods, Ω. In other words, given the consumers’ preferences and
the dimen-
sions of the Edgeworth box, the set of Pareto efficient
allocations would re-
main unchanged if the initial endowment were to be some other
point inside
the Edgeworth box.
Algebraic derivation
The algorithm to find the Pareto efficient allocations
graphically is tedious
since there are infinitely many utility levels that could be
picked in the first
step. The alternative algebraic method presented here holds the
promise of
finding many, if not all, the Pareto efficient allocations in the
interior of the
Edgeworth box at once.
The algebraic derivation is motivated by Figure 6.4 which
suggests that
at an interior Pareto efficient allocation, the tangency of the
consumers’ in-
difference curves is a necessary condition, i.e., if (x̄ a, x̄ b) is
Pareto efficient,
then MRSa(x̄ a) = MRSb(x̄ b). When preferences are strictly
monotonic and
convex, the tangency of the indifference curves is also
sufficient to guaran-
tee Pareto efficiency, i.e., if MRSa(x̄ a) = MRSb(x̄ b), then (x̄ a,
x̄ b) is Pareto
efficient. Therefore, the tangency of the indifference curves is
often a way to
find (interior) Pareto efficient allocations algebraically, or to
verify whether
a given allocation in the interior of the Edgeworth box is Pareto
efficient.
To find the interior Pareto efficient allocations algebraically for
the econ-
omy in section 6.1, set the marginal rate of substitution for a
equal to that for
b to obtain
MRSa = xa2/x
a
1 = MRS
b = 2.
Then xa2 = 2x
a
1, which means that when the two consumers’ indifference
curves are tangent, person a consumes twice as much of good 2
as good 1.
Plot the equation xa2 = 2x
a
1 in Figure 6.5 beginning from O
a, joining interior
Pareto efficient allocations such as R and S where the
consumers’ indiffer-
ence curves are tangent as shown.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
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0
IP
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96 Chapter 6
x1
a
x2
b
x2
a
x1
b
Oa
Ob
R
T
S
PE
Figure 6.5 The Pareto set or contract curve
However, there are other Pareto efficient allocations in addition
to the
allocations that lie along the line xa2 = 2x
a
1. For instance, verify by inspec-b·
tion that a point like T = ((9, 10), (3, 0)) which is on the edge
(and not
the interior) of the Edgeworth box is also Pareto efficient.
Generally, the
tangency condition will not hold at Pareto efficient allocations
along the
edges of the Edgeworth box. For instance, at T, MRSa(9, 10) =
0.9 while
MRSb(3, 0) = 2.4 The set of all Pareto efficient allocations
(often called the
contract curve) for this economy is labeled PE.
When the contract curve consists of allocations in the interior of
the Edge-
worth box, it is possible to find an equation for it by following
these three
steps.
1. Set MRSa = MRSb.
2. From the supply constraints for the two goods, xa1 + x
b
1 = Ω1 and x
a
2 +
xb2 = Ω2, derive x
b
1 = Ω1 − x
a
1 and x
b
2 = Ω2 − x
a
2. Use these to eliminate
xb1 and x
b
2 in the equation from step 1.
3. Solve the equation from step 2 to write xa2 as a function of x
a
1. Then this
is the equation for the contract curve with Oa as the origin.
4In general, at a Pareto efficient allocation that lies on the left
hand or top edge of the
Edgeworth box, it will be the case that MRSa ≤ MRSb; the
inequality will be reversed for a
Pareto efficient allocation that lies on the right hand or bottom
edge of the Edgeworth box.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
0 :M = ? =
0
IP
B
AM
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ME
=
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B
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Exchange Economies 97
To illustrate, suppose both consumers have Cobb-Douglas
preferences,
where a’s utility function is ua(xa1, x
a
2) = x
a
1 x
a
2 while b’s utility is u
b(xb1, x
b
2) =
(xb1)
2 xb2. Suppose that there are 10 units of each good in this
economy, i.e.,
Ω = (10, 10). Then from step 1, we get
xa2
xa1
=
2xb2
xb1
.
From step 2, xb1 = 10 − x
a
1 and x
b
2 = 10 − x
a
2. Substituting these into the
equation above and solving, we get the contract curve ¶b
xa2 =
20xa1
10 + xa1
,
where 0 ≤ xa1 ≤ 10.
Finally, to end this section on Pareto efficiency, note that in
moving from
one Pareto efficient allocation to another, there will typically be
a change in
the distribution of the goods that makes one person better off at
the expense
of another. In other words, no Pareto efficient allocation can be
Pareto supe-
rior to another Pareto efficient allocation. For example, the
extreme situation
where consumer a gets the aggregate endowment (at the point
Ob) or its
polar opposite where consumer b gets everything (at the point
Oa) are both
Pareto efficient. Thus, the notion of Pareto efficiency is
insensitive to distri-
butional concerns.
6.3 Walras Equilibrium
We will now consider the possibility of the two consumers
trading goods 1
and 2 in markets at a per-unit price of p1 and p2. Even though
there are only
two consumers for now, we will assume that each takes the
market prices
as given and outside of their control.5 Given these prices, each
consumer
decides how much she wishes to buy or sell of each good. The
markets are
said to clear if the quantity demanded of good 1 by both
consumers equals its
supply, and likewise for good 2. Then the question that Léon
Walras asked
in the 1870s in the context of our Edgeworth box economy is:
does there exist
a price pair (p̂ 1, p̂ 2) for which both markets clear? We explore
this question
graphically to uncover the basic insights and then fill in the
more technical
details.
5This assumption would of course be more plausible if there
were a very large number of
consumers.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
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98 Chapter 6
6.3.1 Graphical representation
We begin with a definition. A Walras equilibrium (or a
competitive equilib-
rium) consists of prices (p̂ 1, p̂ 2) and an allocation (x̂ a, x̂ b) =
((x̂ a1, x̂
a
2), (x̂
b
1, x̂
b
2))
such that:
(a) the consumption bundle x̂ a maximizes ua subject to the
budget con-
straint p̂ 1 xa1 + p̂ 2 x
a
2 ≤ p̂ 1ω
a
1 + p̂ 2ω
a
2;
(b) the consumption bundle x̂ b maximizes ub subject to the
budget con-
straint p̂ 1 xb1 + p̂ 2 x
b
2 ≤ p̂ 1ω
b
1 + p̂ 2ω
b
2; and
(c) the markets for goods 1 and 2 clear:
x̂ a1 + x̂
b
1 = ω
a
1 + ω
b
1 and x̂
a
2 + x̂
b
2 = ω
a
2 + ω
b
2.
Therefore a Walras equilibrium is a pair of prices and a pair of
consumption
bundles at which each consumer maximizes her utility given her
budget con-
straint, and the total demand for each good equals its supply.
Note that the right hand side of consumer i’s budget constraint
in (a) and
(b) above represent her income which is merely the value of i’s
endowment
at the equilibrium prices, i.e.,
m
̂ i = p̂ 1ωi1 + p̂ 2ω
i
2.
Therefore (a) and (b) are an alternative way of saying that x̂ i is
the bundle
demanded by consumer i when the prices are the equilibrium
ones and her
income is m
̂ i:
x̂ i = hi(p̂ 1, p̂ 2, m
̂ i).
Before we see what happens in equilibrium, consider an
arbitrary pair of
prices (p̄ 1, p̄ 2) set by a mythical Walrasian auctioneer whose
job is to find
the equilibrium prices. In Figure 6.6, the blue budget line with
slope −p̄ 1/ p̄ 2
is shown passing through the initial endowment, ω. Viewed
from origin Oa,
this is the endowment budget6 for consumer a, while the same
line is the
endowment budget for consumer b when viewed from origin Ob.
Note that
the slope of this budget line is −p̄ 1/ p̄ 2 irrespective of whether
you view it
using Oa as your origin, or whether you turn the page upside
down and
view it with Ob as your origin.
6See section 2.3.1 and Figure 2.5.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
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IP
B
AM
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Exchange Economies 99
x1
a
x2
b
x2
a
x1
b
Oa
Ob
S1
a
D2
a
D1
b
A
B
p2
–
p1
ω
S2
b
Figure 6.6 Demand and supply at (p̄ 1, p̄ 2)
Given this budget, consumer a demands the bundle at point A.
In other
words, starting from ω, she is willing to supply Sa1 units of
good 1 (shown
by the solid magenta arrow) in exchange for Da2 units of good 2
(shown by
the dashed magenta arrow) to move to the bundle at A.
Likewise, consumer
b would like to move from ω to point B, supplying Sb2 units of
good 2 in
exchange for Db1 units of good 1. But the market for good 1
does not clear
at these prices: consumer a would like to supply Sa1 units but
consumer b
demands more, Db1. Similarly, the market for good 2 does not
clear either as
the demand for good 2, Da2, is less than its supply, S
b
2.
Assume now that the Walrasian auctioneer raises p1 which
makes con-
sumer a wish to supply more and consumer b to demand less of
good 1,
and/or lowers p2 which makes consumer a demand more of good
2 and
consumer b supply less of it. In other words, beginning with the
initial dot-
ted blue budget line in Figure 6.7, the auctioneer can raise the
relative price
ratio, p1/ p2, to find a set of prices (p̂ 1, p̂ 2) shown by the
steeper, solid blue
budget line. Note that this new budget pivots around the
endowment ω
as the relative price ratio increases, and equates Sa1 = D
b
1 for good 1, and
Sb2 = D
a
2 for good 2. Then, (p̂ 1, p̂ 2) are the Walras prices, the prices at
which
the consumers attain the Walras allocation, E = (x̂ a, x̂ b), where
each per-
son is maximizing her utility given her budget (at the Walras
prices) and the
demand for each good equals its supply.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
0 :M = ? =
0
IP
B
AM
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=
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B
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100 Chapter 6
x1
a
x2
b
x2
a
x1
b
Oa
Ob
S1
a
D2
a
D1
b
S2
b
E
—
p1
p2
ˆ
ˆ
ω
Figure 6.7 Walras equilibrium
There are three insights regarding Walras equilibria that can be
gleaned
from Figure 6.7:
(1) whenever the market for one good is in equilibrium, the
other must
also be in equilibrium;
(2) what matters for bringing about equilibrium is the relative
price ratio,
not the absolute price levels; and
(3) the Walras allocation is both individually rational and
Pareto efficient.
Insight (1) follows from the fact that in moving from the initial
endow-
ment ω to the Walras allocation E in Figure 6.7, the quantities
that each
consumer wants to buy and sell are opposite sides of a rectangle
(shown
with the solid and dashed magenta arrows). It is not possible,
for example,
for the market for good 1 to clear but not that of good 2.
Mathematically,
this follows from Walras’ Law7 which states that the value of
everyone’s
consumption expenditures must always add up to the value of
the aggre-
gate endowment. A consequence of Walras’ Law is that if there
are ℓ goods
with prices p̂ 1, p̂ 2, . . . , p̂ ℓ so that every market but one is in
equilibrium, then
that remaining market must also be in equilibrium. Since here
there are two
goods (ℓ = 2), this corollary to Walras’ Law guarantees that
finding prices
7Section 6.5.1 below presents a formal statement and proof.
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B
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Exchange Economies 101
to bring about equilibrium in one market ensures that the other
market is
automatically in equilibrium.
Insight (2) follows from the fact that in going from the initial
prices of
(p̄ 1, p̄ 2) to the Walras equilibrium prices of (p̂ 1, p̂ 2), what
equilibrates the
two markets is the steeper slope of the latter budget. If the slope
of the bud-
get at the Walras prices is −2 for example, there are infinitely
many price
combinations that give rise to this slope. Therefore, the absolute
levels of the
prices is indeterminate at a Walras equilibrium. To peg the level
of the Wal-
ras prices, we normalize the price of one good to $1; this good
is then called
the numéraire good and the prices of all other goods are
measured in terms
of this numéraire. For instance, if a pack of chewing gum is the
numéraire,
then the price of a shirt worth $30 would be priced at 30 packs
of gum —
packs of gum are the unit of account.
Finally, regarding insight (3), individual rationality holds since
each con-
sumer is on a higher indifference curve at E as compared to ω.
Indeed, since
trade is voluntary, neither consumer would wish to move to the
Walras allo-
cation from ω unless they are at least as well off as initially.
Pareto efficiency
of the Walras allocation follows from the tangency of the
consumers’ indif-
ference curves at E. This result, known as the First Welfare
Theorem, is one
of the key insights of microeconomic theory and is a precise
modern restate-
ment of the idea attributed to Adam Smith that the greatest
social good arises
when individuals follow their self-interest in free markets.
6.3.2 Algebraic derivation
Consider a two-person economy where the utilities are Cobb-
Douglas and
given by
ua = xa1 x
a
2 and u
b = (xb1)
2 xb2
and endowments are
ωa = (6, 4) and ωb = (2, 8).
Then the demand functions for each consumer (using the
formulas in equa-
tion (4.11)) are
ha(p1, p2, ma) =
!
ma
2p1
,
ma
2p2
"
and hb(p1, p2, mb) =
!
2mb
3p1
,
mb
3p2
"
,
where ma = 6p1 + 4p2 and mb = 2p1 + 8p2 are the values of
each consumer’s
endowment.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
0 :M = ? =
0
IP
B
AM
Q
7
ME
=
.
EE
B
AM
=
Chapter 6
Exchange Economies
One of the significant advances in economic theory in the 20th
century has
been the development of general equilibrium analysis which
explores the
possibility of simultaneous equilibrium in multiple markets, as
opposed to
the older partial equilibrium analysis of Alfred Marshall which
studies the
possibility of equilibrium in a single market in isolation. Today,
much of
modern macroeconomic theory is developed in a general
equilibrium frame-
work. In this chapter, we take up the simplest possible general
equilibrium
model with two consumers and two goods. Because there is no
production,
the consumers may only choose to trade the available supplies
of the goods;
ergo, such an economic environment is called a pure exchange
economy.
6.1 The Edgeworth Box
Suppose there are only two consumers, a and b, and two goods,
1 and 2. We
will use the superscript i to refer to either individual, and the
subscript j to
refer to either good. Each consumer i has a characteristic ei
which consists
of two pieces of information specific to her, namely, her
preferences and her
individual endowment. Her preferences are represented by a
utility func-
tion, ui, over the two goods; her individual endowment, ωi, is a
commodity
bundle which shows the total amounts of the two goods that she
possesses
initially, i.e., ωi = (ωi1, ω
i
2). Then i’s characteristic is written as
ei = (ui, ωi) (6.1)
88
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
0 :M = ? =
0
IP
B
AM
Q
7
ME
=
.
EE
B
AM
=
Exchange Economies 89
which summarizes all the relevant information about this
consumer. Finally,
an economy, e, is a list of the characteristics of all consumers:
e = (ea, eb) = ((ua, ωa), (ub, ωb)). (6.2)
This economy e is our prototype of a two-person private goods
pure ex-
change economy.1
5
2
8
7Oa
x2
a
x1
a
Ob
x2
b
x1
b
ωa
ωb
Figure 6.1 Characteristics of consumers a and b
To make things more concrete, suppose consumer a’s
characteristic ea is
given by a Cobb-Douglas utility ua = xa1 x
a
2 and an endowment ω
a = (5, 2),
while eb is given by a linear utility ub = 2xb1 + x
b
2 and ω
b = (7, 8). The
left panel of Figure 6.1 shows consumer a’s origin, Oa, a couple
of her or-
ange indifference curves and her endowment bundle, ωa. The
right panel
of Figure 6.1 shows b’s origin, Ob, a couple of her linear green
indifference
curves and her endowment bundle, ωb. By adding the
endowment of each
consumer, we obtain the aggregate endowment, Ω (read as
‘capital omega’),
which shows the total supply of all goods in the economy:
Ω = ωa + ωb = (5, 2) + (7, 8) = (12, 10).
Any list of consumption bundles (xa, xb) for the two consumers
is called
an allocation. Suppose the total supplies of both goods are
divided between
1A good is said to be private if one person’s consumption of a
good precludes it being
consumed by someone else, and if others can be excluded from
consuming it. See Chapter 16
for more details.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
0 :M = ? =
0
IP
B
AM
Q
7
ME
=
.
EE
B
AM
=
90 Chapter 6
x1
a
x2
b
x2
a
x1
b
Oa
Ob
5
7
8
2
ω
C
Figure 6.2 The Edgeworth box
the two consumers so that a receives the bundle x̄ a = (4, 7)
while b receives
the remainder, x̄ b = (8, 3). Then we say that the pair of
consumption bun-
dles (x̄ a, x̄ b) = ((4, 7), (8, 3)) is a feasible allocation, meaning
that this al-
location is actually possible given the total supply of the goods.
In fact any
pair (xa, xb) is a feasible allocation so long as xa + xb ≤ Ω.
In order to better understand allocations, take the right panel of
Figure
6.1, rotate it counterclockwise by 180◦, and place it over the
left panel so that
the bundles ωa and ωb coincide as shown by the point ω in
Figure 6.2. The
rectangle contained between the origins Oa and Ob is known as
an Edge-
worth box named after Francis Edgeworth.2
Any point inside this box represents a feasible allocation, where
the con-
sumption bundle for individual a is read from her origin, Oa,
while that of
b is read (upside down!) from the perspective of b’s origin, Ob.
For exam-
ple, the point ω = (ωa, ωb) is the allocation ((5, 2), (7, 8)). This
is called the
initial endowment for this Edgeworth box economy; it shows
the consump-
tion bundle each person starts out with before any trade takes
place. The
allocation corresponding to Ob is ((12, 10), (0, 0)) where
individual a gets
everything while b gets nothing. Conversely, the allocation
corresponding to
Oa is ((0, 0), (12, 10)).
2It is also known as an Edgeworth-Bowley box, after the
English statistician and economist
Arthur Bowley who popularized it.
/: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0
M :E
AMMI D M :E I M EB = = M:BE : MB -= 31,
0 :M = ? =
0
IP
B
AM
Q
7
ME
=
.
EE
B
AM
=
1)
a) Show an Edgeworth box for a general case of two agents who
both have Cobb-Douglas preferences. (Make sure to label axis
and curves.)
b) Briefly explain what the contract curve is.
2) For two agents, a and b, with the following utility functions
over goods x and y
a) Determine the slope of the contract curve in the interior of an
Edgeworth box that would show this two-person two-goods
situation.
b) For initial endowments ωa=(12,7) and ωb=(9,10), what is the
Walras allocation between the two agents a and b? (Remember
that it is the relative price of the goods that matters in this
consideration. Also remember that all the units of goods that
exist here are will end up with one or the other agent; so, the
overall 21 units of x and the 17 units of y will be fully allocated
between the two. )
c) Calculate the utility level before and after trading.
3) For two agents, a and b, with the following utility functions
over goods x and y
a) Determine the slope of the contract curve in the interior of an
Edgeworth box that would show this two-person two-goods
situation.
b) For initial endowments ωa=(9,8) and ωb=(6,7), what is the
Walras allocation between the two agents a and b?
c) Calculate the utility level before and after trading.
4) For two agents, a and b, with the following utility functions
over goods x and y
a) Determine the slope of the contract curve in the interior of an
Edgeworth box that would show this two-person two-goods
situation.
b) For initial endowments ωa=(4,5) and ωb=(3,2), what is the
Walras allocation between the two agents a and b? (Remember
that it is the relative price of the goods that matters in this
consideration.)
c) Calculate the utility level before and after trading.
Imelios 33.2 (2008): 19-33
"Work Out Your Salvation":
Conduct "Worthy of the Gospel"
in a Communal Context
— Paul Hartog —
Paul Hartog Is an associate professor at Failli Baptist
Geological Semluaty In
Ankeny Iowa, where He teaches New Testament and earty
Christian studies.
He Is the authorofPoYptp WTvdlYveNewr Testamewt,
WUNT2.134
(Tubingen: Mol‫״־‬ Slebeck, 2002).
ommentators have customarily interpreted Phil 2:12 as a
reference to "working out" one's
personal salvation.! For this reason, the verse became a
flashpoint beOveen Roman Catholic
advocates who emphasized the “working out" of personal
salvation and Protestant apologists
who emphasized the "working out” of personal salvation (i.e.,
"progressive sanctification")^ On a lexi-
cal level, fire Greek verb of this phrase (κατεργάζεσθαι) can
mean "to accomplish," "to bring about," "to
subdue," "to cultivate," "to prepare," "to produce," or "to
complete" (see Rom 1:27; 2:9; 4:15; 5:3; 7:8-20;
2 Cor 4:17; 5:5; 7:10; Eph 6:13; Jas 1:3; 1 Pet 4:3).‫؛‬ "Gis does
not mean that [the Philippians] are to earn
their salvation," explains Jerry Sumney. "Rather, the sense is
similar to that expressed in 1:27, where they
are exhorted to 'live worthy of the gospel.'"! Sumney then turns
in a fresh interpretive direction:
It is significant that the verb and the reflexive pronoun that
modify σωτηρία are
plural. Gis shows that the call to live out their salvation is a call
to the Philippians as a
community and anticipates that the matters to be raised in the
following verses involve
relations within the community.‫؛‬
Sumney's additional material with its stress upon the
"community" does not address the traditional
Catholic-Protestant debate, but rather touches upon interpretive
questions raised during the last
century.
Scripture quotations are from the Holy Bible, En٥ish Standard
Version, copyright 2001 by Crossway Bibles, a“ ‫נ‬
division of Good News Publishers. Used by permission. All
rights reserved."
2 Cf. the translation “work for" in thejB and NJB (Roman
Catholic translations). By contrast, ]. Warren (an evangelical)
highlighted a passage in Strabo that describes the Roman
imperial exchequer's “working out" the Spanish silver mines, in
the
sense of operating, not acquiring (j. Warren, “Work Out Your
Salvation," EvQ 16 [1944], 125). Warren further argued that
the “out" prefix (κατά) does not refer to “exteriority" but to
“thoroughness;' as in wearing “out" a coat, tiring “out" a horse,
or
burning “out" a candle (ibid., 128).
3 BDAG; EDNT; MM; PGL; TDNT. See especially the six-fold,
consistent use in Rom 7:8-20.
4 Jerry 1. Sumney, Philippians: A Greek Students Intermediate
Reader (Peabody: Hendrickson, 2007), 53. See also
Bonnie B. Hurston and Judith M. Ryan, Philippians and
Philemon (SP; Collegeville, MN: Liturgical Press, 2005), 94.
.‫ة‬ ‫آل‬ ,snaippilihP ,yimU( ‫؟‬ ‫؛׳‬
19
'Work Out Your Salvation": Conduct "Worthy of the Gospel" in
a Communal Context
Σωτηρία as Corporate Health or Well-Being
In 1924, ]. H. Michael published an influential article that
argued drat the σωτηρία of Phil 2:12 does
not refer to personal salvation in any sense but to the corporate
"health" or "well-being" of the believing
community.‫؛‬
An effective divine energy is at work in the community and if
the Philippians only avail
themselves of its presence, cooperate with it, and permit it to
express itself in their
working, the inevitable result will be not only the willing, but
also the achieving, by
them of the salvation of the community.‫؟‬
Michael's "communal" approach was adopted by Loh and Nida,
Martin, Bonnard, Collange, Gnilka,
Hawthorne, and Bruce. For example, Ralph Martin maintained,
"There cannot be an individualistic
sense attached to salvation here since Paul has the entire Church
in view"‫؟‬ In a later work, Martin
reiterated that the "salvation" of Phil 2:12 should not be
interpreted in "personal terms," but "in regard
to the corporate life of the Philippian church."‫؟‬ Paul urged his
readers to "work at" matters "until the
spiritual health of the community, diseased by strife and bad
feeling, is restored."“
According to Ι-Jin Loh and Eugene Nida, "It is not an
exhortation to the Philippian Christians to
accomplish the personal salvation of the individual members.
Paul is rather concerned about the well-
being of their common life together in community (cf. 1.28;
2.4)."" Gerald Hawthorne concurs, "Paul is
not here concerned with the eternal welfare of the soul ofthe
individual.... Rather the context suggests
that this command is to be understood in a corporate sense.'‫؛‬
'"!he entire church, which had grown
spiritually ill (2:3-4), is charged now with taking whatever steps
are necessary to restore itself to health,
integrity and wholeness.'‫؛‬ F. F. Bruce agrees, "In this context
Paul is not urging each member of the
church to keep working at his or her personal salvation; he is
thinking of the health and well-being of
the church as a whole."“
'Ihese scholars have assembled an array of evidences for their
interpretive position. First, such a call
to corporate health is exactly what the Philippian situation
required, since apparently the church lacked
full unity (Phil 2:2-4; 2:14; 4:2-3).“
٥ F H. Michael, “Work out Your own Salvation," Expositor 12
(1924): 439-50. Michael acknowledges that he was not
the first to argue against an individualistic interpretation of Phil
2:12 (ibid., 440). For example, the year before Michael's article
was published, F H. Burn (himself borrowing from others)
argued that the interpretation of Phil 2:12 as an exhortation to
“promote earnestly the welfare of each other" deserved “more
attention" (j. H. Burn, “Philippians ii.12ExpTim 34 [1922-23],
562).
7 Michael, “Work out Your own Salvation," 23.
8 Ralph p Martin, Philippians (NCB; London: Marshall, Morgan
& Scott, 1976; repr.. Grand Rapids: Eerdmans, 1985),
102.
9 See idem, I Epistle ofPaul fo the Philippians (TNTC; Grand
Rapids: Eerdmans, 1987), 115.
“Ibid.
11 Ι-Jin Loh and Eugene A. Nida, A Translator’s Elandbook
ofPaul’s Epistle fo the Philippians (New York: United Bible
Societies, 1977), 67.
12 Gerald F. Hawthorne, Philippians (WBC; Waco: Word,
1983), 98 (italics original).
13 Gerald F. Hawthorne, Philippians (rev. and expanded by
Ralph p Martin; WBC; Waco: Word, 2004), 139.
.F. F. Bruce, Philippians (NIBCNT; Peabody: Hendrickson,
1989), 81 ‫لا‬
15 He state of the Philippian church needed Just this call'
(Martin, Philippians, 103).
Themelios
Second, the wider context of Phil 1:27-2:18 emphasizes he
communal nature of the directive.
Conduct "worthy of the gospel" includes standing firm together
in one spirit, striving for the faith of the
gospel with one mind (1:27). Such conduct entails mutual love
and concord, humility, and unselfishness
(2:2-4). Rivalry, conceit, and self-interest are to be avoided, as
well as grumbling and complaining (2:3-
4,14).
'Ihird, Phil 2:12-13 consistently uses the plural.''' Paul addresses
the άγαπητο'ι ("beloved," plural). He
entreats them that as "you [plural] have always obeyed" in the
past, so now "you [plural] work out your
[reflexive plural] salvation.'‫؟‬ Paul reminds them that God is the
one working "in/among you [plural]."!‫؟‬
"Once again," claim Hawthorne and Martin, "there is the strong
indication that the exhortation is not to
individual but to corporate action, to cooperative effort in the
common life together as community.""
Fourth, a concern for individual salvation would not be proper
after the explicit command not to
think of one's own personal interests but rather those of others
(Phil 2:4; cf 2:19-21).2٥ "Hence," explains
Hawthorne, "it is highly unlikely that he here now reverses
himself by commanding hem to focus on
their own individual salvati0n."21
Fifth, the suggestion that humans complete their own
"theological" salvation contradicts Paul's
understanding of such salvation as the divine work of God.22
Sixth, "with fear and trembling" speaks of human-ward
attitudes, as in other Pauline texts (including
1 Cor 2:3; 2 Cor 7:15; and Eph 6:5). Martin therefore renders
the import of Phil 2:12 as "let the Philippians
have a healthy respect for one another in the resolving of their
differences."23
Seventh, έν ύμίν in Phil 2:13 should be translated as "among
you" (corporately) rather than "within
you" (individually). Thus, according to Hawthorne and Martin,
"here is 'among them,' rather han
'within them,' an energizing force that is no less than God
himself."! '
Eighth, σωτηρία and σώζειν ("salvation" and "to save") are
commonly used in the FXX and the Greek
papyri to convey the ideas of health, wholeness, or weH-
being.25 'Ihese words are also used in "non-
theological" ways in some New Testament texts: Mark 3:4
(preserving physical life); Acts 4:9 and 14:9
،‫ا‬ ‫لآ‬ ‫دن‬ ‫لآن‬ Philippians, ‫ةلآ‬.
17 Bruce describes “the reflexive pronoun of the third person
being extended to do duty for the second person"
!Philippians,
18 See the discussion on έν ύμίν below.
19 Hawthorne and Martin, Philippians, 140. Michael even
claims that it woifld be “singiflarly inappropriate" for a
passage emphasizing one's personal salvation to come
immediately after 2:5-11 (Michael, “Work Out Your Own
Salvation,"
444; cf. Martin, Philippians, 103).
2" See also G. B. Caird, Paul’s Lettersfrom Prison (New
Clarendon Bible; Oxford: Oxford University Press, 1976), 125.
21 Hawthorne, Philippians, 98.
22 Loh and Nida, Translator’s Handbook, 67.
Mán, Philippians, 101 ‫لآأ‬
24 Hawthorne and Martin, Philippians, 142. Hawthorne's
original edition had “among them and within them"
(Hawthorne, Philippians, 100).
Hawthorne and Martin, Philippians, 14Ö. Cf. MM, 622;
NewDocs 1 (1981), 10, 14, 56, 57. “Salvation" in the New ‫؛‬2
Testament most commonly refers to God's rescuing sinners from
the penalty, power, and ultimately presence of sin. The
term and its cognates, however, can be used of physical healing
and physical deliverance from trouble. See Loh and Nida, A
Translator's Handbook, 41.
'Work Out Your Salvation": Conduct "Worthy of the Gospel" in
a Communal Context
(physical healing); and Acts 27:34 (physical strengthening).
'Ihese scholars contend that an application
to corporate "well-being" is the most appropriate reading in the
wider context (cf. Phil 1:19; cf. 1:28).
Σωτηρία as Individual Sanctification
Other scholars, especially Moisés Silva and Peter O'Brien, have
criticized this corporate
interpretation of Phil 2:12. Silva has dubbed the corporate view
"the new view" and the “sociological”
interpretation, and he has contrasted it with his own “strictly
theological” one."' O'Brien employs dais
same dichotomized labeling: "Numbers of writers since the late
nineteenth century... have contended
that σωτηρία is being used in a sociological rather than a
strictly theological sense to describe the
spiritual health and well-being of the entire community at
Philippi."27 O'Brien insists that the arguments
assembled for the "sociological" or "corporate" interpretation
"do not dislodge the view that V. 12 speaks
of personal salvation." " Silva concurs that the reasons for the
"new view" "utterly fail" to C0nvince.25
In fact, Silva fears that the "sociological view" easily lends
itself "to a remarkably weakened reading
of a remarkably potent text.'. He situates the text's "potency" in
its description of the human and divine
activity in the total work of personal salvation, including
personal sanctificationty He fears that the
"sociological" emphasis upon the community's well-being to the
exclusion of the personal element may
be an attempt to deny or resolve the human activity-divine grace
tensionty "'!he text itself, by its very
juxtaposition of those two emphases, cries out loudly against
any such attempts at resolution," explains
Silva. 'And the point here is not merely that both the human and
the divine are stressed, but that in one
and the same passage we have what is perhaps the strongest
biblical expression of each element." ; ;
O'Brien and Silva have assembled their own litany of
arguments, which are arranged here to parallel
the eight contrary arguments assembled above:
26 Moisés Silva, Philippians (2d ed.; Baker Exegetical
Commentary on the New Testament; Grand Rapids: Baker,
2005), 118-19 (italics added). According to Martin's revision of
Hawthorne, Silva “omits a third option, i.e., the 'ecclesiological'
reference, which is to be preferred, given the context of the
passage" (Hawthorne and Martin, Philippians, 140). Martin,
however, does not produce a sustained explanation or argument
for this "ecclesiological" view.
,ins‫؟‬YeA.‫׳‬s،‫؛‬A‫؟‬Petocl Ö tkven, I Epistle to the Philippians; A
Commentary on the Greek Text |GAG’,G1Ala ‫لآ‬
1991), 277 (italics added).
28 Ibid., 278.
11 BAva, Philippians, ATÖ.
8"Ibid.
31 Silva quotes Calvin's interpretation “that salvation is taken
to mean the entire course of our calling, and that this
term includes all things by which God accomplishes that
perfection, to which He has determined US by His free election"
(ibid.,
121). “Gott wirkt nicht nur den Anfang, sondern auch den
Fortgang im Christenleben" (Wolfgang Schräge, Die konkreten
Einzelgebote in der paalinischen Pardnese; Ein Beitrag zar
neatestamentlichen Ethik YGÜV. Güvet NeAagAiis
Mohn, 19671,72).
32 Silva, Philippians, 121; cf. also 121η4. Silva declares, “The
conceptual tension between verse 12 and verse 13 seems
unbearable—apparently, an extreme formulation of the paradox
of divine sovereignty and human responsibility" (ibid., 118).
Craddock highlights the divine grace/human activity parallel of
1 Cor 15:10: “But by the grace of God I am what I am, and his
grace toward me was not in vain. On the contrary., I worked
harder than any of them, though it was not I, but the grace of
God
that is with me" (Fred B. Craddock, Philippians [IBC; Atlanta:
John Knox, 1985], 46; cf. Frank Stagg, “The Mind in Christ
Jesus:
Philippians 1:27-2:18;' RevExp 77 [1980], 346). Eph 1:19 and
3:7 also accentuate God's power at work (edvepyeidv) in the
believer by grace.
.BAva, Philippians, ATT ‫أع‬
Themelios
First, Gospel-worthy conduct "clearly involves them in
responsibilities to one another," yet "their
responsibilities to one another or to the outside world (eg., Phil
2:15-16) are not to be confused with
the context of the eschatological salvation itself."34
Second, the context in Phil 1:27-2:18 certainly accentuates
community-oriented injunctions, "But
the contextual argument per se does not inform US of the
content of'complete your salvation."' ;‫'־‬ Rather,
"an eschatological motivation has been set before them that will
result in heir heeding the apostolic
injunction, hat is, of pursuing unity through humility and doing
everything without grumbling or
arguing.";''
'Ihird, the plurals in Phil 2:12-13 do not signify communal life,
but indicate that ”٥« the believers
at Philippi are to heed this apostolic admonition."‫؛‬ O'Brien
concludes, "έαυτών σωτηρίαν κατεργάζεσθε
is an exhortation to common action, urging the Philippians to
show forth the graces of Christ in their
lives, to make their eternal salvation fruitful in the here and
now as they fulfill their responsibilities to
one another as well as to non-Christians.'«‫؟‬
Fourth, carrying out one's personal salvation does not conflict
with the condemnation of minding
one's own interests (2:4), since "concern for one's soul" is not a
form of selfishness or self-absorption.‫؟؟‬
Fifth, although Phil 2:12 describes humans "carrying out" their
own salvation, the balanced tension
that follows in 2:13 reiterates that salvation is the sovereign and
gracious act of God.4٥
Sixth, "with fear and trembling" is directed God-ward, and
"denotes an awe and reverence in the
presence of the God who acts mightily."«
Seventh, Silva argues (based upon 2 Cor 4:12) that εν ύμίν with
the verb ένεργέομαι should be
translated as "in you" rather than "among you" in Phil 2:13 (cf.
1 Cor 12:6; Rom 7:5; Col. 1:29).« O'Brien
adds that "God's inward working in the believer is a recurrent
theme in Paul's letters."«
Eighth, O'Brien responds that Paul normally uses σωτηρία of
personal, eschatological salvation
(including, he argues, in Phil 1:19 and 1:28).« Silva also
highlights the characteristic Pauline usage of
σωτηρία: "out of nearly twenty occurrences of this noun in the
Pauline corpus, not one instance requires
the translation 'well-being'; the vast majority require-and all of
them admit-the theological sense."«
34 O'Brien, Epistle to the Philippians, 280.
.Ibid ‫؛‬3
3، Ibid.
33 Ibid.) 279.
38 Ibid.) 280.
35 Silva, Philippians, 120; cf. Gal 6:1-6. As pointed out to me
by David R. Bickel, the Apology oftheAugsburg Confession
asserts that the free reception of the forgiveness of sins is
actually a form of worship.
4” See Silva's relevant comments above.
44 O'Brien, Epistle fo the Philippians, 280.
،،1lia., Philippians,119.
43 O'Brien, Epistle fo the Philippians, 287 (cf. 1 Cor 12:6;
15:10; 2 Cor 3:5; Col 1:29; 1 Thess 2:13).
44 Ibid., 278-79.
Silva, Philippians, 119-20. Although Silva concedes that a
"nontheological" sense of "deliverance" is possible in Phil ‫؛‬4
1:19, even there an insipid “well-being" is not possible (ibid.,
120). Cf. O'Brien, Epistle to the Philippians, 278-79.
23
'Work Out Your Salvation": Conduct "Worthy of the Gospel" in
a Communal Context
The Quest for Middle Ground
Some of the leading advocates of the competing positions have,
at times, taken a step back and
have acknowledged that a false dilemma may be created in the
minds of some. For example, although
Silva contrasts a "sociological" reading and a "strictly
theological" one, he ultimately concedes that
a complete distinction between "the well-being of the
community" and "the question of individual
salvation" is simply impossible."' He adds, "... one must again
underscore that the personal salvation in
view manifests itself primarily in healthy community
relationships."^
A few scholars have attempted to mediate between the so-called
"sociological" interpretation and
the so-called "theological" interpretation. Markus Bockmuehl
maintains that "it is best not to reduce the
term salvation too readily either to the individual and spiritual
or to the corporate and social realm.""
Although "the individual concern is safeguarded," "the
corporate dimension is clear."® '"Ihree facets must
be affirmed together," insists Bockmuehl. First, the New
Testament notion of salvation "encompasses
deliverance from all forms of evil." Second, salvation "directly
addresses both individuals and the body of
Christ which together they constitute and to which they belong."
'Ihird, God's work of salvation includes
present and future aspects.5٥
Gordon Fee asserts, "There has been considerable, and probably
unnecessary, debate over whether
salvation in this passage refers to the individual believer or the
community of believers."‫!؛‬ "But that is a
false dichotomy," he ret0rts.52 Fee asserts that O'Brien and
Silva "are basically (correctly so) critiquing a
viewthatwaters down the term salvation somewhat Lo be more
sociological."'; "Unfortunately," continues
Fee, "their rebuttals tend to place more emphasis on the
individual ffian the context [in Philippians]
seems to warrant."‫!؛‬ Fee insists that this is an "ethical" text that
concerns "working or carrying out in
their corporate life the salvation that God has graciously given
them."‫؛؛‬ He concludes that the passage
«Ibid., 118-19; cf. 119η2.
47 Ibid., 120. “The translation ‘your own salvation' for verse 12
is quite proper;' acknowledges Silva, “though I would
not argue against such a rendering as ‘your common salvation,'
since there is no denying that Paul has the community, not
isolated individuals in mind" (ibid., 119η3). Silva complains
that Fee has characterized his view as “a case of'either/or' (i.e.
either
individual or community)" (ibid., 119η2). Pedersen also
concludes that since Paul does not separate the collective from
the
individual, the question is irrelevant (Sigfred Pedersen, “Mit
Furcht und Zittern;' ST 32 [1978], 29η74). Yet, when
interpretive
push comes to positional shove, Pedersen espouses the
collective understanding.
48 Markus Bockmuehl, I Epistle fo the Philippians (BNTC;
London: Black, 1998), 151.
45 Ibid.
50 Ibid.
51 Gordon D. Fee, Philippians (IVP New Testament
Commentary; Downers Grove: InterVarsity, 1999), 102-3
(italics
original). See the similar sentiments in Gordon D. Fee, Pauls
Letter fo the Philippians (NICNT; Grand Rapids: Eerdmans,
1995), 234-35.
“Ibid., 235.
Yee, Philippians, 101 Ci. Aso Yee, Paals Letters to the
Philippians, TYmTO.
.Λ Yee, Philippians, 100‫؛‬
55 Fee, Pauls Letter to the Philippians, 235. Although “people
are saved one by one to be sure;' acknowledges Fee, “they
are saved so as to become a ‘people for God’s name;"
24
Themelios
is "a call to individually workout our common salvation in our
life together.""'
Ben Witherington argues for an "eschatological reality" behind
Phil 2:12, but one that may also
include "a social dimension or implication."‫?؛‬
In short, the appeal to unity is based on what God has already
done and is doing in them
and in their midst to bring about their salvation. Working out
salvation means, among
other things, continuous strenuous effort working harmoniously
together as the body
of Christ.‫؛؟‬
Carolyn Osiek similarly contends that "salvation" "is certainly
not to be understood only in the
eschatological sense," "yet hat dimension must be included."‫؛؟‬
"Paul is speaking of their total well-being,
including their spiritual prosperity now and in the future."“ "It
is not so much individual salvation as
communal eschatological success that is envisioned. This is not
to deny the individual aspects of the
concept, but neither Paul nor his contemporaries thought
primarily in individual terms, '!he collective
good is the principal referent."“
The Apostolic Fathers
It seems that the strong points of the so-called "sociological"
view are the recurring plural verbs
and pronouns, but especially he wider communal situation and
corporate context of Phil 1:27-2:18. On
the other hand, the strengths of the so-called "theological" view
are its insistence that seeking personal
salvation is not inherendy "selfish," the divine orientation of
"fear and trembling" within the argument
of Phil 2:12-13, and especially the customary "theological"
sense of σωτηρία/σώζειν within Pauline
thought.‫?؛‬ Might it be possible to combine some of the insights
of he two views and form a coherent
understanding of Phil 2:12 within its wider context? Can the
σωτηρία/σώζειν word group be used in
ways that are both theological and community-oriented?
Although Michael, Hawthorne, and Martin cite uses of σωτηρία
and σώζειν as references to well-
being and physical health in the New Testament, the LXX, and
in the Greek papyri, they do not cite
pertinent uses of the word group in the Apostolic Fathers.‫؛؛‬
Perhaps these overlooked materials reveal
a weakness in a purely "sociological" view: a "health or
wholeness" of the community disengaged from a
a ton erofereht si sihT“ ,seunitnoc eeF .401 ,snaippilihP ,eeF ٥‫؛‬
text dealing with individual salvation but an ethical text
dealing with the outworking of salvation in the believing
community for the sake of the world. ‫لآس‬ they must comply
with this
injunction at the individual level is assumed, and that their final
salvation will be realized personally and individually is a truth
that does not need stating, because that is not at issue here. The
present concern is with their being God's people in Philippi,
as 2:15 makes certain" (ibid., 104).
57 Ben Witherington, Friendship and Finances in Philippi
(Valley Forge: Trinity Press International, 1994), 71.
“Ibid.
.Carolyn Osiek, Philippians, Philemon (ANTC; Nashville:
Abingdon, 2000), 70 ‫؛‬9
٥" Ibid.
61 Ibid.
62 “One will have a hard time defending that [sociological]
understanding of this word on the basis of Pauline usage
(as Hawthorne's resorting to some papyrus uses indicates)"
(Fee, Pauls Letter fo the Philippians, 235η23).
63 Hawthorne and Martin, Philippians, 140.
25
'Work Out Your Salvation": Conduct "Worthy of the Gospel" in
a Communal Context
"theological" understanding of "salvati0n."٥4 At times, the
Apostolic Fathers use σώζειν and its cognates
in manners that are clearly mutual/reciprocal or
corporate/communal, yet still manifestly "theological"
as well (rather than mere references to physical health or
"sociological" well-being).
A mutual/reciprocal use of σώζειν within the community of
believers is fairly common in the
Apostolic Fathers.'" This emphasis of the Apostolic Fathers
upon the mutual/reciprocal "saving"
of others and the community-orientation of σωτηρία may seem
rather foreign to Paul (or the New
Testament in general) at first glance. But a quick perusal of
Rom 11:13-14; 1 Cor 7:16; 9:22; 1 Tim 4:16;
Jas 5:19-20; and Jude 22-23 readily reveals that Paul and other
New Testament writers could speak of
a mutual/reciprocal "saving" of others. Admittedly there are
definite (and even significant) theological
differences between Paul's epistles and various Apostolic
Fathers.‫'״‬ But this (later) linguistic evidence
at least confirms that the σωτηρία/σώζειν word group could be
used in ways that were both theological
and other-oriented, at least in a mutual/reciprocal sense.
Two further examples in the Apostolic Fathers may cast
additional light upon the interpretation
of Phil 2:12. Both of these passages stress a "corporate"
application of σώζειν, …

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Theological Thinking Grading Rubric Criteria Levels of A.docx

  • 1. Theological Thinking Grading Rubric Criteria Levels of Achievement Below Expectations Basic Proficient Outstanding Summary of Exegetical Work 25% 0 to 69 % The discussion does not cover the features of the exegetical analysis, or is incomplete, or does not properly contribute to an understanding of the passage. 70 to 79 % The discussion covers features of the exegetical analysis but is not sufficiently clear and comprehensive.
  • 2. 80 to 89 % The discussion adequately covers the features of the exegetical analysis. 90 to 100 % The discussion displays depth of understanding and clearly articulates all of the features of the exegetical analysis. Summary of Schools of Thought 20% 0 to 69 % Consensus or opposing schools of thought about the theological meaning of this passage are not adequately explained or contrasted. Sources are poor and not well used in the explanation.
  • 3. 70 to 79 % Consensus or opposing schools of thought about the theological meaning of this passage are adequately explained or contrasted. Sources are adequate to poor and are used adequately in the explanation. 80 to 89 % Consensus or opposing schools of thought about the theological meaning of this passage are well explained or contrasted. Sources are good and used adequately to well in the explanation. 90 to 100 % Consensus or opposing schools of thought about the theological meaning of this passage are
  • 4. insightfully explained or contrasted. Sources are excellent and used well in the explanation. Personal Analysis 25% 0 to 69 % The theological meaning of the passage is not adequately developed. The reasoning used is poor, and sources are not adequately used or not used at all. 70 to 79 % The theological meaning of the passage is adequately developed. Adequate reasoning is employed, and sources adequately used in support. 80 to 89 % The theological meaning of the passage is clearly developed. Good reasoning is employed,
  • 5. and sources are used well in support. 90 to 100 % The theological meaning of the passage is clearly and persuasively developed. Excellent reasoning is employed, and sources are used very well in support. Contemporary Application 20% 0 to 69 % The application is not directly related to the analysis of the text and/or is not applied to a contemporary situation which clearly correlates to the text, and/or is poorly explained.
  • 6. 70 to 79 % The application relates to the analysis of the text and is applied in to a contemporary situation. However, the correlation between the text and its application is not clear and/or not clearly explained. 80 to 89 % The application is true to the analysis of the text and is appropriately applied in a contemporary situation. 90 to 100 % The application is consistent with the analysis of the intended meaning of the text and is thoughtfully and appropriately applied in a meaningful contemporary situation.
  • 7. Writing Style 10% 0 to 69 % Obvious grammatical stylistic errors that make understanding difficult are present. 70 to 79 % There are obvious grammatical/stylistic errors; and/or there are numerous typos, and/or sources are not cited. 80 to 89 % Errors are limited to a “typo” or two, Turabian style is followed adequately, and sources are cited. 90 to 100 % There are no obvious grammatical or stylistic errors, and content is well constructed and easy to follow
  • 8. and Turabian style is carefully followed. Exchange Economies 91 The length of an Edgeworth box shows the total supply of good 1, while the height shows the total supply of good 2. Given the Edgeworth box and the initial endowment, any exchange of goods between the consumers en- tails a movement to another allocation inside the box. Starting from any allocation inside the Edgeworth box — say, the center, C = ((6, 5), (6, 5)) — to an allocation to its northeast makes consumer a better off and b worse off because both consumers’ preferences are strictly monotonic. Conversely, any allocation to the southwest of the box makes b better off and a worse off. 6.2 Properties of Allocations Given the preferences of the individuals and the initial endowment, we can now discuss properties of allocations. Some allocations may be more desir- able than others. We explore two different notions of desirability.
  • 9. 6.2.1 Individually rational allocations Individual rationality embodies the idea that if two people trade voluntar- ily, that trade must leave each person at least as well off as before they trade; if trade hurts either consumer, they will have no incentive to engage in such an exchange of goods. We define an allocation (xa, xb) to be individually rational if ua(xa) ≥ ua(ωa) and ub(xb) ≥ ub(ωb), (6.3) i.e., each person’s utility at her consumption bundle xi is at least as great as her utility from her endowment ωi, where i = a, b. Thus, the movement from the endowment bundle ωa to the bundle xa leaves consumer a no worse off than initially, and similarly for consumer b. In Figure 6.3, the individually rational allocations lie in the blue lens- shaped area (labeled IR) between the indifference curves of each consumer that pass through the initial endowment. For example, in moving from ω to A, both consumers are better off than initially because A lies on a higher indifference curve for each consumer. At an allocation such as B, consumer a remains on her initial indifference curve and so remains as well off, but consumer b is on a higher indifference curve. You can verify
  • 10. this by drawing ¶b b’s indifference curve through point B. At C, consumer b is as well off as initially but a is better off. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q 7 ME = . EE B AM = 92 Chapter 6 x1
  • 11. a x2 b x2 a x1 b Oa Ob IR A B C E F D ω Figure 6.3 Individually rational allocations Note that any allocation inside the Edgeworth box but outside of the IR area places at least one consumer behind her indifference curve, signifying
  • 12. that she is worse off than at ω. For example, at D, consumer a is worse off; at E, b is worse off, and at F, both consumers are worse off. If we expect the consumers to barter and trade with each other starting at ω, the only allocations that they would agree to move to voluntarily must lie within the IR area since neither is made worse off by such a move; indeed, it is quite possible for one or even both of them to be better off. Individually rational allocations inside the Edgeworth box can be found by following the three steps summarized below. 1. Identify the initial endowment, ω, in the Edgeworth box. 2. Draw an indifference curve for consumer a that passes through ω, us- ing arrows to show the direction in which her utility is increasing. Do the same for consumer b. 3. The area between the indifference curve for consumer a and that for consumer b (including the indifference curves themselves) is the set of individually rational allocations. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? =
  • 13. 0 IP B AM Q 7 ME = . EE B AM = Exchange Economies 93 6.2.2 Pareto efficient allocations Pareto efficiency (or more traditionally, Pareto optimality) embodies the idea of non-wastefulness in allocating the total supply of goods at our dis- posal among consumers.3 Given an allocation, if it is possible to reallocate the goods so as to make at least one person happier and no one worse off, then the original allocation is wasteful in the sense that there is scope for im-
  • 14. proving on it. At a Pareto efficient allocation, it is not possible to reallocate the goods so as to make one consumer better off without hurting someone else, so it is non-wasteful. To illustrate this idea simply, suppose we have an apple and a banana to allocate between two persons. Consumer a is indifferent between an apple and a banana, but consumer b has an aversion to bananas and strictly prefers apples over bananas. Then the allocation that gives a the apple and b the banana is wasteful because it is possible to make at least one person better off without hurting the other. Simply give the banana to consumer a and the apple to b; then a is as well off, but b is better off. Giving the banana to a and the apple to b is a Pareto efficient allocation because it is not possible to reallocate the goods and make at least one person happier without hurting the other. Before we can define what a Pareto efficient allocation is formally, we need another definition. Starting from an allocation (xa, xb), the allocation (x̄ a, x̄ b) is said to be Pareto superior to (or a Pareto improvement over) (xa, xb) if nobody is worse off at (x̄ a, x̄ b) and at least one person is better off. In other words, if we started with the initial allocation (xa, xb) and moved
  • 15. to (x̄ a, x̄ b), then that would constitute an improvement because nobody is hurt and someone is happier. An allocation (x̂ a, x̂ b) is Pareto efficient if there is no other allocation that is Pareto superior to (x̂ a, x̂ b). In other words, at a Pareto efficient allocation, it is not possible to make at least one person hap- pier without hurting anyone else — any reallocation of goods either hurts somebody, or leaves everyone as well off. Graphical representation Typically an Edgeworth box will have many Pareto efficient allocations. These Pareto efficient allocations can be found by following this algorithm. 3Pareto efficiency is named after Vilfredo Pareto, an influential economist and sociologist. The phrase “non-wastefulness” was coined by Leonid Hurwicz. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q
  • 16. 7 ME = . EE B AM = 94 Chapter 6 1. Fix the utility of one consumer, say individual b, at some arbitrary level ūb inside the Edgeworth box. 2. Maximize the utility of consumer a while keeping b on the indifference curve ūb. Then the allocation reached is a Pareto efficient allocation. 3. To find other Pareto efficient allocations, repeat the process by picking a different utility level for b in step 1. To find one Pareto efficient allocation and understand how this algorithm works, arbitrarily fix b’s utility at ūb shown by the green ūb indifference curve in Figure 6.4. Maximize a’s preferences while keeping b on her green indiffer-
  • 17. ence curve, yielding the allocation A. Then A is a Pareto efficient allocation. To check this, consider the different regions of the Edgeworth box where an x1 a x2 b x2 a x1 b Oa Ob A I II III IV ub ua Figure 6.4 A Pareto efficient allocation
  • 18. alternative allocation could be picked. Any allocation in region I (which lies to the southwest of the green indifference curve) makes consumer a worse off. In regions II and III, both a and b are worse off as they are behind their indifference curves ūa and ūb. In region IV (which lies to the northeast of the orange indifference curve ūa), b is worse off. Therefore, beginning with A, there is no Pareto superior allocation in the Edgeworth box, and hence A is Pareto efficient. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q 7 ME = . EE
  • 19. B AM = Exchange Economies 95 Two remarks are in order. First, the fact that we fix the utility of b in step 1 is totally arbitrary. In other words, the same set of Pareto efficient allocations can be found by reversing the roles of a and b, namely, fixing the utility of a instead in step 1, and maximizing b’s utility while keeping a at this utility in step 2. Second, unlike individually rational allocations, Pareto efficient alloca- tions do not depend on the initial endowment as a reference point. They only depend on the consumers’ preference and the aggregate supplies of the goods, Ω. In other words, given the consumers’ preferences and the dimen- sions of the Edgeworth box, the set of Pareto efficient allocations would re- main unchanged if the initial endowment were to be some other point inside the Edgeworth box. Algebraic derivation The algorithm to find the Pareto efficient allocations
  • 20. graphically is tedious since there are infinitely many utility levels that could be picked in the first step. The alternative algebraic method presented here holds the promise of finding many, if not all, the Pareto efficient allocations in the interior of the Edgeworth box at once. The algebraic derivation is motivated by Figure 6.4 which suggests that at an interior Pareto efficient allocation, the tangency of the consumers’ in- difference curves is a necessary condition, i.e., if (x̄ a, x̄ b) is Pareto efficient, then MRSa(x̄ a) = MRSb(x̄ b). When preferences are strictly monotonic and convex, the tangency of the indifference curves is also sufficient to guaran- tee Pareto efficiency, i.e., if MRSa(x̄ a) = MRSb(x̄ b), then (x̄ a, x̄ b) is Pareto efficient. Therefore, the tangency of the indifference curves is often a way to find (interior) Pareto efficient allocations algebraically, or to verify whether a given allocation in the interior of the Edgeworth box is Pareto efficient. To find the interior Pareto efficient allocations algebraically for the econ- omy in section 6.1, set the marginal rate of substitution for a equal to that for b to obtain MRSa = xa2/x a
  • 21. 1 = MRS b = 2. Then xa2 = 2x a 1, which means that when the two consumers’ indifference curves are tangent, person a consumes twice as much of good 2 as good 1. Plot the equation xa2 = 2x a 1 in Figure 6.5 beginning from O a, joining interior Pareto efficient allocations such as R and S where the consumers’ indiffer- ence curves are tangent as shown. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q 7 ME
  • 23. PE Figure 6.5 The Pareto set or contract curve However, there are other Pareto efficient allocations in addition to the allocations that lie along the line xa2 = 2x a 1. For instance, verify by inspec-b· tion that a point like T = ((9, 10), (3, 0)) which is on the edge (and not the interior) of the Edgeworth box is also Pareto efficient. Generally, the tangency condition will not hold at Pareto efficient allocations along the edges of the Edgeworth box. For instance, at T, MRSa(9, 10) = 0.9 while MRSb(3, 0) = 2.4 The set of all Pareto efficient allocations (often called the contract curve) for this economy is labeled PE. When the contract curve consists of allocations in the interior of the Edge- worth box, it is possible to find an equation for it by following these three steps. 1. Set MRSa = MRSb. 2. From the supply constraints for the two goods, xa1 + x b 1 = Ω1 and x a
  • 24. 2 + xb2 = Ω2, derive x b 1 = Ω1 − x a 1 and x b 2 = Ω2 − x a 2. Use these to eliminate xb1 and x b 2 in the equation from step 1. 3. Solve the equation from step 2 to write xa2 as a function of x a 1. Then this is the equation for the contract curve with Oa as the origin. 4In general, at a Pareto efficient allocation that lies on the left hand or top edge of the Edgeworth box, it will be the case that MRSa ≤ MRSb; the inequality will be reversed for a Pareto efficient allocation that lies on the right hand or bottom edge of the Edgeworth box. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31,
  • 25. 0 :M = ? = 0 IP B AM Q 7 ME = . EE B AM = Exchange Economies 97 To illustrate, suppose both consumers have Cobb-Douglas preferences, where a’s utility function is ua(xa1, x a 2) = x a 1 x
  • 26. a 2 while b’s utility is u b(xb1, x b 2) = (xb1) 2 xb2. Suppose that there are 10 units of each good in this economy, i.e., Ω = (10, 10). Then from step 1, we get xa2 xa1 = 2xb2 xb1 . From step 2, xb1 = 10 − x a 1 and x b 2 = 10 − x a 2. Substituting these into the equation above and solving, we get the contract curve ¶b xa2 =
  • 27. 20xa1 10 + xa1 , where 0 ≤ xa1 ≤ 10. Finally, to end this section on Pareto efficiency, note that in moving from one Pareto efficient allocation to another, there will typically be a change in the distribution of the goods that makes one person better off at the expense of another. In other words, no Pareto efficient allocation can be Pareto supe- rior to another Pareto efficient allocation. For example, the extreme situation where consumer a gets the aggregate endowment (at the point Ob) or its polar opposite where consumer b gets everything (at the point Oa) are both Pareto efficient. Thus, the notion of Pareto efficiency is insensitive to distri- butional concerns. 6.3 Walras Equilibrium We will now consider the possibility of the two consumers trading goods 1 and 2 in markets at a per-unit price of p1 and p2. Even though there are only two consumers for now, we will assume that each takes the market prices as given and outside of their control.5 Given these prices, each consumer decides how much she wishes to buy or sell of each good. The
  • 28. markets are said to clear if the quantity demanded of good 1 by both consumers equals its supply, and likewise for good 2. Then the question that Léon Walras asked in the 1870s in the context of our Edgeworth box economy is: does there exist a price pair (p̂ 1, p̂ 2) for which both markets clear? We explore this question graphically to uncover the basic insights and then fill in the more technical details. 5This assumption would of course be more plausible if there were a very large number of consumers. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q 7 ME = .
  • 29. EE B AM = 98 Chapter 6 6.3.1 Graphical representation We begin with a definition. A Walras equilibrium (or a competitive equilib- rium) consists of prices (p̂ 1, p̂ 2) and an allocation (x̂ a, x̂ b) = ((x̂ a1, x̂ a 2), (x̂ b 1, x̂ b 2)) such that: (a) the consumption bundle x̂ a maximizes ua subject to the budget con- straint p̂ 1 xa1 + p̂ 2 x a 2 ≤ p̂ 1ω
  • 30. a 1 + p̂ 2ω a 2; (b) the consumption bundle x̂ b maximizes ub subject to the budget con- straint p̂ 1 xb1 + p̂ 2 x b 2 ≤ p̂ 1ω b 1 + p̂ 2ω b 2; and (c) the markets for goods 1 and 2 clear: x̂ a1 + x̂ b 1 = ω a 1 + ω b 1 and x̂ a 2 + x̂ b 2 = ω
  • 31. a 2 + ω b 2. Therefore a Walras equilibrium is a pair of prices and a pair of consumption bundles at which each consumer maximizes her utility given her budget con- straint, and the total demand for each good equals its supply. Note that the right hand side of consumer i’s budget constraint in (a) and (b) above represent her income which is merely the value of i’s endowment at the equilibrium prices, i.e., m ̂ i = p̂ 1ωi1 + p̂ 2ω i 2. Therefore (a) and (b) are an alternative way of saying that x̂ i is the bundle demanded by consumer i when the prices are the equilibrium ones and her income is m ̂ i: x̂ i = hi(p̂ 1, p̂ 2, m ̂ i). Before we see what happens in equilibrium, consider an arbitrary pair of prices (p̄ 1, p̄ 2) set by a mythical Walrasian auctioneer whose job is to find the equilibrium prices. In Figure 6.6, the blue budget line with
  • 32. slope −p̄ 1/ p̄ 2 is shown passing through the initial endowment, ω. Viewed from origin Oa, this is the endowment budget6 for consumer a, while the same line is the endowment budget for consumer b when viewed from origin Ob. Note that the slope of this budget line is −p̄ 1/ p̄ 2 irrespective of whether you view it using Oa as your origin, or whether you turn the page upside down and view it with Ob as your origin. 6See section 2.3.1 and Figure 2.5. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q 7 ME = . EE
  • 34. p2 – p1 ω S2 b Figure 6.6 Demand and supply at (p̄ 1, p̄ 2) Given this budget, consumer a demands the bundle at point A. In other words, starting from ω, she is willing to supply Sa1 units of good 1 (shown by the solid magenta arrow) in exchange for Da2 units of good 2 (shown by the dashed magenta arrow) to move to the bundle at A. Likewise, consumer b would like to move from ω to point B, supplying Sb2 units of good 2 in exchange for Db1 units of good 1. But the market for good 1 does not clear at these prices: consumer a would like to supply Sa1 units but consumer b demands more, Db1. Similarly, the market for good 2 does not clear either as the demand for good 2, Da2, is less than its supply, S b 2. Assume now that the Walrasian auctioneer raises p1 which makes con-
  • 35. sumer a wish to supply more and consumer b to demand less of good 1, and/or lowers p2 which makes consumer a demand more of good 2 and consumer b supply less of it. In other words, beginning with the initial dot- ted blue budget line in Figure 6.7, the auctioneer can raise the relative price ratio, p1/ p2, to find a set of prices (p̂ 1, p̂ 2) shown by the steeper, solid blue budget line. Note that this new budget pivots around the endowment ω as the relative price ratio increases, and equates Sa1 = D b 1 for good 1, and Sb2 = D a 2 for good 2. Then, (p̂ 1, p̂ 2) are the Walras prices, the prices at which the consumers attain the Walras allocation, E = (x̂ a, x̂ b), where each per- son is maximizing her utility given her budget (at the Walras prices) and the demand for each good equals its supply. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP
  • 37. Ob S1 a D2 a D1 b S2 b E — p1 p2 ˆ ˆ ω Figure 6.7 Walras equilibrium There are three insights regarding Walras equilibria that can be gleaned from Figure 6.7: (1) whenever the market for one good is in equilibrium, the other must also be in equilibrium; (2) what matters for bringing about equilibrium is the relative
  • 38. price ratio, not the absolute price levels; and (3) the Walras allocation is both individually rational and Pareto efficient. Insight (1) follows from the fact that in moving from the initial endow- ment ω to the Walras allocation E in Figure 6.7, the quantities that each consumer wants to buy and sell are opposite sides of a rectangle (shown with the solid and dashed magenta arrows). It is not possible, for example, for the market for good 1 to clear but not that of good 2. Mathematically, this follows from Walras’ Law7 which states that the value of everyone’s consumption expenditures must always add up to the value of the aggre- gate endowment. A consequence of Walras’ Law is that if there are ℓ goods with prices p̂ 1, p̂ 2, . . . , p̂ ℓ so that every market but one is in equilibrium, then that remaining market must also be in equilibrium. Since here there are two goods (ℓ = 2), this corollary to Walras’ Law guarantees that finding prices 7Section 6.5.1 below presents a formal statement and proof. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? =
  • 39. 0 IP B AM Q 7 ME = . EE B AM = Exchange Economies 101 to bring about equilibrium in one market ensures that the other market is automatically in equilibrium. Insight (2) follows from the fact that in going from the initial prices of (p̄ 1, p̄ 2) to the Walras equilibrium prices of (p̂ 1, p̂ 2), what equilibrates the two markets is the steeper slope of the latter budget. If the slope of the bud- get at the Walras prices is −2 for example, there are infinitely
  • 40. many price combinations that give rise to this slope. Therefore, the absolute levels of the prices is indeterminate at a Walras equilibrium. To peg the level of the Wal- ras prices, we normalize the price of one good to $1; this good is then called the numéraire good and the prices of all other goods are measured in terms of this numéraire. For instance, if a pack of chewing gum is the numéraire, then the price of a shirt worth $30 would be priced at 30 packs of gum — packs of gum are the unit of account. Finally, regarding insight (3), individual rationality holds since each con- sumer is on a higher indifference curve at E as compared to ω. Indeed, since trade is voluntary, neither consumer would wish to move to the Walras allo- cation from ω unless they are at least as well off as initially. Pareto efficiency of the Walras allocation follows from the tangency of the consumers’ indif- ference curves at E. This result, known as the First Welfare Theorem, is one of the key insights of microeconomic theory and is a precise modern restate- ment of the idea attributed to Adam Smith that the greatest social good arises when individuals follow their self-interest in free markets. 6.3.2 Algebraic derivation Consider a two-person economy where the utilities are Cobb-
  • 41. Douglas and given by ua = xa1 x a 2 and u b = (xb1) 2 xb2 and endowments are ωa = (6, 4) and ωb = (2, 8). Then the demand functions for each consumer (using the formulas in equa- tion (4.11)) are ha(p1, p2, ma) = ! ma 2p1 , ma 2p2 " and hb(p1, p2, mb) = ! 2mb
  • 42. 3p1 , mb 3p2 " , where ma = 6p1 + 4p2 and mb = 2p1 + 8p2 are the values of each consumer’s endowment. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q 7 ME = . EE B
  • 43. AM = Chapter 6 Exchange Economies One of the significant advances in economic theory in the 20th century has been the development of general equilibrium analysis which explores the possibility of simultaneous equilibrium in multiple markets, as opposed to the older partial equilibrium analysis of Alfred Marshall which studies the possibility of equilibrium in a single market in isolation. Today, much of modern macroeconomic theory is developed in a general equilibrium frame- work. In this chapter, we take up the simplest possible general equilibrium model with two consumers and two goods. Because there is no production, the consumers may only choose to trade the available supplies of the goods; ergo, such an economic environment is called a pure exchange economy. 6.1 The Edgeworth Box Suppose there are only two consumers, a and b, and two goods, 1 and 2. We
  • 44. will use the superscript i to refer to either individual, and the subscript j to refer to either good. Each consumer i has a characteristic ei which consists of two pieces of information specific to her, namely, her preferences and her individual endowment. Her preferences are represented by a utility func- tion, ui, over the two goods; her individual endowment, ωi, is a commodity bundle which shows the total amounts of the two goods that she possesses initially, i.e., ωi = (ωi1, ω i 2). Then i’s characteristic is written as ei = (ui, ωi) (6.1) 88 /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q 7
  • 45. ME = . EE B AM = Exchange Economies 89 which summarizes all the relevant information about this consumer. Finally, an economy, e, is a list of the characteristics of all consumers: e = (ea, eb) = ((ua, ωa), (ub, ωb)). (6.2) This economy e is our prototype of a two-person private goods pure ex- change economy.1 5 2 8 7Oa x2 a
  • 46. x1 a Ob x2 b x1 b ωa ωb Figure 6.1 Characteristics of consumers a and b To make things more concrete, suppose consumer a’s characteristic ea is given by a Cobb-Douglas utility ua = xa1 x a 2 and an endowment ω a = (5, 2), while eb is given by a linear utility ub = 2xb1 + x b 2 and ω b = (7, 8). The left panel of Figure 6.1 shows consumer a’s origin, Oa, a couple of her or- ange indifference curves and her endowment bundle, ωa. The right panel of Figure 6.1 shows b’s origin, Ob, a couple of her linear green
  • 47. indifference curves and her endowment bundle, ωb. By adding the endowment of each consumer, we obtain the aggregate endowment, Ω (read as ‘capital omega’), which shows the total supply of all goods in the economy: Ω = ωa + ωb = (5, 2) + (7, 8) = (12, 10). Any list of consumption bundles (xa, xb) for the two consumers is called an allocation. Suppose the total supplies of both goods are divided between 1A good is said to be private if one person’s consumption of a good precludes it being consumed by someone else, and if others can be excluded from consuming it. See Chapter 16 for more details. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q 7 ME
  • 49. 2 ω C Figure 6.2 The Edgeworth box the two consumers so that a receives the bundle x̄ a = (4, 7) while b receives the remainder, x̄ b = (8, 3). Then we say that the pair of consumption bun- dles (x̄ a, x̄ b) = ((4, 7), (8, 3)) is a feasible allocation, meaning that this al- location is actually possible given the total supply of the goods. In fact any pair (xa, xb) is a feasible allocation so long as xa + xb ≤ Ω. In order to better understand allocations, take the right panel of Figure 6.1, rotate it counterclockwise by 180◦, and place it over the left panel so that the bundles ωa and ωb coincide as shown by the point ω in Figure 6.2. The rectangle contained between the origins Oa and Ob is known as an Edge- worth box named after Francis Edgeworth.2 Any point inside this box represents a feasible allocation, where the con- sumption bundle for individual a is read from her origin, Oa, while that of b is read (upside down!) from the perspective of b’s origin, Ob. For exam- ple, the point ω = (ωa, ωb) is the allocation ((5, 2), (7, 8)). This is called the
  • 50. initial endowment for this Edgeworth box economy; it shows the consump- tion bundle each person starts out with before any trade takes place. The allocation corresponding to Ob is ((12, 10), (0, 0)) where individual a gets everything while b gets nothing. Conversely, the allocation corresponding to Oa is ((0, 0), (12, 10)). 2It is also known as an Edgeworth-Bowley box, after the English statistician and economist Arthur Bowley who popularized it. /: C 8: B : 3 M =B:M 4B B . 9 E / BE=B .II : A 7 ME = M 2 D 0 M :E AMMI D M :E I M EB = = M:BE : MB -= 31, 0 :M = ? = 0 IP B AM Q 7 ME = . EE B
  • 51. AM = 1) a) Show an Edgeworth box for a general case of two agents who both have Cobb-Douglas preferences. (Make sure to label axis and curves.) b) Briefly explain what the contract curve is. 2) For two agents, a and b, with the following utility functions over goods x and y a) Determine the slope of the contract curve in the interior of an Edgeworth box that would show this two-person two-goods situation. b) For initial endowments ωa=(12,7) and ωb=(9,10), what is the Walras allocation between the two agents a and b? (Remember that it is the relative price of the goods that matters in this consideration. Also remember that all the units of goods that exist here are will end up with one or the other agent; so, the overall 21 units of x and the 17 units of y will be fully allocated between the two. )
  • 52. c) Calculate the utility level before and after trading. 3) For two agents, a and b, with the following utility functions over goods x and y a) Determine the slope of the contract curve in the interior of an Edgeworth box that would show this two-person two-goods situation. b) For initial endowments ωa=(9,8) and ωb=(6,7), what is the Walras allocation between the two agents a and b? c) Calculate the utility level before and after trading. 4) For two agents, a and b, with the following utility functions over goods x and y a) Determine the slope of the contract curve in the interior of an Edgeworth box that would show this two-person two-goods situation.
  • 53. b) For initial endowments ωa=(4,5) and ωb=(3,2), what is the Walras allocation between the two agents a and b? (Remember that it is the relative price of the goods that matters in this consideration.) c) Calculate the utility level before and after trading. Imelios 33.2 (2008): 19-33 "Work Out Your Salvation": Conduct "Worthy of the Gospel" in a Communal Context — Paul Hartog — Paul Hartog Is an associate professor at Failli Baptist Geological Semluaty In Ankeny Iowa, where He teaches New Testament and earty Christian studies.
  • 54. He Is the authorofPoYptp WTvdlYveNewr Testamewt, WUNT2.134 (Tubingen: Mol‫״־‬ Slebeck, 2002). ommentators have customarily interpreted Phil 2:12 as a reference to "working out" one's personal salvation.! For this reason, the verse became a flashpoint beOveen Roman Catholic advocates who emphasized the “working out" of personal salvation and Protestant apologists who emphasized the "working out” of personal salvation (i.e., "progressive sanctification")^ On a lexi- cal level, fire Greek verb of this phrase (κατεργάζεσθαι) can mean "to accomplish," "to bring about," "to subdue," "to cultivate," "to prepare," "to produce," or "to complete" (see Rom 1:27; 2:9; 4:15; 5:3; 7:8-20; 2 Cor 4:17; 5:5; 7:10; Eph 6:13; Jas 1:3; 1 Pet 4:3).‫؛‬ "Gis does not mean that [the Philippians] are to earn their salvation," explains Jerry Sumney. "Rather, the sense is similar to that expressed in 1:27, where they are exhorted to 'live worthy of the gospel.'"! Sumney then turns in a fresh interpretive direction: It is significant that the verb and the reflexive pronoun that modify σωτηρία are plural. Gis shows that the call to live out their salvation is a call to the Philippians as a community and anticipates that the matters to be raised in the following verses involve relations within the community.‫؛‬ Sumney's additional material with its stress upon the "community" does not address the traditional Catholic-Protestant debate, but rather touches upon interpretive questions raised during the last
  • 55. century. Scripture quotations are from the Holy Bible, En٥ish Standard Version, copyright 2001 by Crossway Bibles, a“ ‫נ‬ division of Good News Publishers. Used by permission. All rights reserved." 2 Cf. the translation “work for" in thejB and NJB (Roman Catholic translations). By contrast, ]. Warren (an evangelical) highlighted a passage in Strabo that describes the Roman imperial exchequer's “working out" the Spanish silver mines, in the sense of operating, not acquiring (j. Warren, “Work Out Your Salvation," EvQ 16 [1944], 125). Warren further argued that the “out" prefix (κατά) does not refer to “exteriority" but to “thoroughness;' as in wearing “out" a coat, tiring “out" a horse, or burning “out" a candle (ibid., 128). 3 BDAG; EDNT; MM; PGL; TDNT. See especially the six-fold, consistent use in Rom 7:8-20. 4 Jerry 1. Sumney, Philippians: A Greek Students Intermediate Reader (Peabody: Hendrickson, 2007), 53. See also Bonnie B. Hurston and Judith M. Ryan, Philippians and Philemon (SP; Collegeville, MN: Liturgical Press, 2005), 94. .‫ة‬ ‫آل‬ ,snaippilihP ,yimU( ‫؟‬ ‫؛׳‬ 19 'Work Out Your Salvation": Conduct "Worthy of the Gospel" in a Communal Context Σωτηρία as Corporate Health or Well-Being
  • 56. In 1924, ]. H. Michael published an influential article that argued drat the σωτηρία of Phil 2:12 does not refer to personal salvation in any sense but to the corporate "health" or "well-being" of the believing community.‫؛‬ An effective divine energy is at work in the community and if the Philippians only avail themselves of its presence, cooperate with it, and permit it to express itself in their working, the inevitable result will be not only the willing, but also the achieving, by them of the salvation of the community.‫؟‬ Michael's "communal" approach was adopted by Loh and Nida, Martin, Bonnard, Collange, Gnilka, Hawthorne, and Bruce. For example, Ralph Martin maintained, "There cannot be an individualistic sense attached to salvation here since Paul has the entire Church in view"‫؟‬ In a later work, Martin reiterated that the "salvation" of Phil 2:12 should not be interpreted in "personal terms," but "in regard to the corporate life of the Philippian church."‫؟‬ Paul urged his readers to "work at" matters "until the spiritual health of the community, diseased by strife and bad feeling, is restored."“ According to Ι-Jin Loh and Eugene Nida, "It is not an exhortation to the Philippian Christians to accomplish the personal salvation of the individual members. Paul is rather concerned about the well- being of their common life together in community (cf. 1.28; 2.4)."" Gerald Hawthorne concurs, "Paul is not here concerned with the eternal welfare of the soul ofthe individual.... Rather the context suggests
  • 57. that this command is to be understood in a corporate sense.'‫؛‬ '"!he entire church, which had grown spiritually ill (2:3-4), is charged now with taking whatever steps are necessary to restore itself to health, integrity and wholeness.'‫؛‬ F. F. Bruce agrees, "In this context Paul is not urging each member of the church to keep working at his or her personal salvation; he is thinking of the health and well-being of the church as a whole."“ 'Ihese scholars have assembled an array of evidences for their interpretive position. First, such a call to corporate health is exactly what the Philippian situation required, since apparently the church lacked full unity (Phil 2:2-4; 2:14; 4:2-3).“ ٥ F H. Michael, “Work out Your own Salvation," Expositor 12 (1924): 439-50. Michael acknowledges that he was not the first to argue against an individualistic interpretation of Phil 2:12 (ibid., 440). For example, the year before Michael's article was published, F H. Burn (himself borrowing from others) argued that the interpretation of Phil 2:12 as an exhortation to “promote earnestly the welfare of each other" deserved “more attention" (j. H. Burn, “Philippians ii.12ExpTim 34 [1922-23], 562). 7 Michael, “Work out Your own Salvation," 23. 8 Ralph p Martin, Philippians (NCB; London: Marshall, Morgan & Scott, 1976; repr.. Grand Rapids: Eerdmans, 1985), 102. 9 See idem, I Epistle ofPaul fo the Philippians (TNTC; Grand Rapids: Eerdmans, 1987), 115. “Ibid. 11 Ι-Jin Loh and Eugene A. Nida, A Translator’s Elandbook
  • 58. ofPaul’s Epistle fo the Philippians (New York: United Bible Societies, 1977), 67. 12 Gerald F. Hawthorne, Philippians (WBC; Waco: Word, 1983), 98 (italics original). 13 Gerald F. Hawthorne, Philippians (rev. and expanded by Ralph p Martin; WBC; Waco: Word, 2004), 139. .F. F. Bruce, Philippians (NIBCNT; Peabody: Hendrickson, 1989), 81 ‫لا‬ 15 He state of the Philippian church needed Just this call' (Martin, Philippians, 103). Themelios Second, the wider context of Phil 1:27-2:18 emphasizes he communal nature of the directive. Conduct "worthy of the gospel" includes standing firm together in one spirit, striving for the faith of the gospel with one mind (1:27). Such conduct entails mutual love and concord, humility, and unselfishness (2:2-4). Rivalry, conceit, and self-interest are to be avoided, as well as grumbling and complaining (2:3- 4,14). 'Ihird, Phil 2:12-13 consistently uses the plural.''' Paul addresses the άγαπητο'ι ("beloved," plural). He entreats them that as "you [plural] have always obeyed" in the past, so now "you [plural] work out your [reflexive plural] salvation.'‫؟‬ Paul reminds them that God is the one working "in/among you [plural]."!‫؟‬ "Once again," claim Hawthorne and Martin, "there is the strong indication that the exhortation is not to individual but to corporate action, to cooperative effort in the common life together as community.""
  • 59. Fourth, a concern for individual salvation would not be proper after the explicit command not to think of one's own personal interests but rather those of others (Phil 2:4; cf 2:19-21).2٥ "Hence," explains Hawthorne, "it is highly unlikely that he here now reverses himself by commanding hem to focus on their own individual salvati0n."21 Fifth, the suggestion that humans complete their own "theological" salvation contradicts Paul's understanding of such salvation as the divine work of God.22 Sixth, "with fear and trembling" speaks of human-ward attitudes, as in other Pauline texts (including 1 Cor 2:3; 2 Cor 7:15; and Eph 6:5). Martin therefore renders the import of Phil 2:12 as "let the Philippians have a healthy respect for one another in the resolving of their differences."23 Seventh, έν ύμίν in Phil 2:13 should be translated as "among you" (corporately) rather than "within you" (individually). Thus, according to Hawthorne and Martin, "here is 'among them,' rather han 'within them,' an energizing force that is no less than God himself."! ' Eighth, σωτηρία and σώζειν ("salvation" and "to save") are commonly used in the FXX and the Greek papyri to convey the ideas of health, wholeness, or weH- being.25 'Ihese words are also used in "non- theological" ways in some New Testament texts: Mark 3:4 (preserving physical life); Acts 4:9 and 14:9 ،‫ا‬ ‫لآ‬ ‫دن‬ ‫لآن‬ Philippians, ‫ةلآ‬. 17 Bruce describes “the reflexive pronoun of the third person
  • 60. being extended to do duty for the second person" !Philippians, 18 See the discussion on έν ύμίν below. 19 Hawthorne and Martin, Philippians, 140. Michael even claims that it woifld be “singiflarly inappropriate" for a passage emphasizing one's personal salvation to come immediately after 2:5-11 (Michael, “Work Out Your Own Salvation," 444; cf. Martin, Philippians, 103). 2" See also G. B. Caird, Paul’s Lettersfrom Prison (New Clarendon Bible; Oxford: Oxford University Press, 1976), 125. 21 Hawthorne, Philippians, 98. 22 Loh and Nida, Translator’s Handbook, 67. Mán, Philippians, 101 ‫لآأ‬ 24 Hawthorne and Martin, Philippians, 142. Hawthorne's original edition had “among them and within them" (Hawthorne, Philippians, 100). Hawthorne and Martin, Philippians, 14Ö. Cf. MM, 622; NewDocs 1 (1981), 10, 14, 56, 57. “Salvation" in the New ‫؛‬2 Testament most commonly refers to God's rescuing sinners from the penalty, power, and ultimately presence of sin. The term and its cognates, however, can be used of physical healing and physical deliverance from trouble. See Loh and Nida, A Translator's Handbook, 41. 'Work Out Your Salvation": Conduct "Worthy of the Gospel" in a Communal Context (physical healing); and Acts 27:34 (physical strengthening).
  • 61. 'Ihese scholars contend that an application to corporate "well-being" is the most appropriate reading in the wider context (cf. Phil 1:19; cf. 1:28). Σωτηρία as Individual Sanctification Other scholars, especially Moisés Silva and Peter O'Brien, have criticized this corporate interpretation of Phil 2:12. Silva has dubbed the corporate view "the new view" and the “sociological” interpretation, and he has contrasted it with his own “strictly theological” one."' O'Brien employs dais same dichotomized labeling: "Numbers of writers since the late nineteenth century... have contended that σωτηρία is being used in a sociological rather than a strictly theological sense to describe the spiritual health and well-being of the entire community at Philippi."27 O'Brien insists that the arguments assembled for the "sociological" or "corporate" interpretation "do not dislodge the view that V. 12 speaks of personal salvation." " Silva concurs that the reasons for the "new view" "utterly fail" to C0nvince.25 In fact, Silva fears that the "sociological view" easily lends itself "to a remarkably weakened reading of a remarkably potent text.'. He situates the text's "potency" in its description of the human and divine activity in the total work of personal salvation, including personal sanctificationty He fears that the "sociological" emphasis upon the community's well-being to the exclusion of the personal element may be an attempt to deny or resolve the human activity-divine grace tensionty "'!he text itself, by its very juxtaposition of those two emphases, cries out loudly against any such attempts at resolution," explains Silva. 'And the point here is not merely that both the human and
  • 62. the divine are stressed, but that in one and the same passage we have what is perhaps the strongest biblical expression of each element." ; ; O'Brien and Silva have assembled their own litany of arguments, which are arranged here to parallel the eight contrary arguments assembled above: 26 Moisés Silva, Philippians (2d ed.; Baker Exegetical Commentary on the New Testament; Grand Rapids: Baker, 2005), 118-19 (italics added). According to Martin's revision of Hawthorne, Silva “omits a third option, i.e., the 'ecclesiological' reference, which is to be preferred, given the context of the passage" (Hawthorne and Martin, Philippians, 140). Martin, however, does not produce a sustained explanation or argument for this "ecclesiological" view. ,ins‫؟‬YeA.‫׳‬s،‫؛‬A‫؟‬Petocl Ö tkven, I Epistle to the Philippians; A Commentary on the Greek Text |GAG’,G1Ala ‫لآ‬ 1991), 277 (italics added). 28 Ibid., 278. 11 BAva, Philippians, ATÖ. 8"Ibid. 31 Silva quotes Calvin's interpretation “that salvation is taken to mean the entire course of our calling, and that this term includes all things by which God accomplishes that perfection, to which He has determined US by His free election" (ibid., 121). “Gott wirkt nicht nur den Anfang, sondern auch den Fortgang im Christenleben" (Wolfgang Schräge, Die konkreten Einzelgebote in der paalinischen Pardnese; Ein Beitrag zar neatestamentlichen Ethik YGÜV. Güvet NeAagAiis Mohn, 19671,72).
  • 63. 32 Silva, Philippians, 121; cf. also 121η4. Silva declares, “The conceptual tension between verse 12 and verse 13 seems unbearable—apparently, an extreme formulation of the paradox of divine sovereignty and human responsibility" (ibid., 118). Craddock highlights the divine grace/human activity parallel of 1 Cor 15:10: “But by the grace of God I am what I am, and his grace toward me was not in vain. On the contrary., I worked harder than any of them, though it was not I, but the grace of God that is with me" (Fred B. Craddock, Philippians [IBC; Atlanta: John Knox, 1985], 46; cf. Frank Stagg, “The Mind in Christ Jesus: Philippians 1:27-2:18;' RevExp 77 [1980], 346). Eph 1:19 and 3:7 also accentuate God's power at work (edvepyeidv) in the believer by grace. .BAva, Philippians, ATT ‫أع‬ Themelios First, Gospel-worthy conduct "clearly involves them in responsibilities to one another," yet "their responsibilities to one another or to the outside world (eg., Phil 2:15-16) are not to be confused with the context of the eschatological salvation itself."34 Second, the context in Phil 1:27-2:18 certainly accentuates community-oriented injunctions, "But the contextual argument per se does not inform US of the content of'complete your salvation."' ;‫'־‬ Rather, "an eschatological motivation has been set before them that will result in heir heeding the apostolic injunction, hat is, of pursuing unity through humility and doing everything without grumbling or
  • 64. arguing.";'' 'Ihird, the plurals in Phil 2:12-13 do not signify communal life, but indicate that ”٥« the believers at Philippi are to heed this apostolic admonition."‫؛‬ O'Brien concludes, "έαυτών σωτηρίαν κατεργάζεσθε is an exhortation to common action, urging the Philippians to show forth the graces of Christ in their lives, to make their eternal salvation fruitful in the here and now as they fulfill their responsibilities to one another as well as to non-Christians.'«‫؟‬ Fourth, carrying out one's personal salvation does not conflict with the condemnation of minding one's own interests (2:4), since "concern for one's soul" is not a form of selfishness or self-absorption.‫؟؟‬ Fifth, although Phil 2:12 describes humans "carrying out" their own salvation, the balanced tension that follows in 2:13 reiterates that salvation is the sovereign and gracious act of God.4٥ Sixth, "with fear and trembling" is directed God-ward, and "denotes an awe and reverence in the presence of the God who acts mightily."« Seventh, Silva argues (based upon 2 Cor 4:12) that εν ύμίν with the verb ένεργέομαι should be translated as "in you" rather than "among you" in Phil 2:13 (cf. 1 Cor 12:6; Rom 7:5; Col. 1:29).« O'Brien adds that "God's inward working in the believer is a recurrent theme in Paul's letters."« Eighth, O'Brien responds that Paul normally uses σωτηρία of personal, eschatological salvation (including, he argues, in Phil 1:19 and 1:28).« Silva also
  • 65. highlights the characteristic Pauline usage of σωτηρία: "out of nearly twenty occurrences of this noun in the Pauline corpus, not one instance requires the translation 'well-being'; the vast majority require-and all of them admit-the theological sense."« 34 O'Brien, Epistle to the Philippians, 280. .Ibid ‫؛‬3 3، Ibid. 33 Ibid.) 279. 38 Ibid.) 280. 35 Silva, Philippians, 120; cf. Gal 6:1-6. As pointed out to me by David R. Bickel, the Apology oftheAugsburg Confession asserts that the free reception of the forgiveness of sins is actually a form of worship. 4” See Silva's relevant comments above. 44 O'Brien, Epistle fo the Philippians, 280. ،،1lia., Philippians,119. 43 O'Brien, Epistle fo the Philippians, 287 (cf. 1 Cor 12:6; 15:10; 2 Cor 3:5; Col 1:29; 1 Thess 2:13). 44 Ibid., 278-79. Silva, Philippians, 119-20. Although Silva concedes that a "nontheological" sense of "deliverance" is possible in Phil ‫؛‬4 1:19, even there an insipid “well-being" is not possible (ibid., 120). Cf. O'Brien, Epistle to the Philippians, 278-79. 23 'Work Out Your Salvation": Conduct "Worthy of the Gospel" in a Communal Context The Quest for Middle Ground
  • 66. Some of the leading advocates of the competing positions have, at times, taken a step back and have acknowledged that a false dilemma may be created in the minds of some. For example, although Silva contrasts a "sociological" reading and a "strictly theological" one, he ultimately concedes that a complete distinction between "the well-being of the community" and "the question of individual salvation" is simply impossible."' He adds, "... one must again underscore that the personal salvation in view manifests itself primarily in healthy community relationships."^ A few scholars have attempted to mediate between the so-called "sociological" interpretation and the so-called "theological" interpretation. Markus Bockmuehl maintains that "it is best not to reduce the term salvation too readily either to the individual and spiritual or to the corporate and social realm."" Although "the individual concern is safeguarded," "the corporate dimension is clear."® '"Ihree facets must be affirmed together," insists Bockmuehl. First, the New Testament notion of salvation "encompasses deliverance from all forms of evil." Second, salvation "directly addresses both individuals and the body of Christ which together they constitute and to which they belong." 'Ihird, God's work of salvation includes present and future aspects.5٥ Gordon Fee asserts, "There has been considerable, and probably unnecessary, debate over whether salvation in this passage refers to the individual believer or the community of believers."‫!؛‬ "But that is a false dichotomy," he ret0rts.52 Fee asserts that O'Brien and Silva "are basically (correctly so) critiquing a
  • 67. viewthatwaters down the term salvation somewhat Lo be more sociological."'; "Unfortunately," continues Fee, "their rebuttals tend to place more emphasis on the individual ffian the context [in Philippians] seems to warrant."‫!؛‬ Fee insists that this is an "ethical" text that concerns "working or carrying out in their corporate life the salvation that God has graciously given them."‫؛؛‬ He concludes that the passage «Ibid., 118-19; cf. 119η2. 47 Ibid., 120. “The translation ‘your own salvation' for verse 12 is quite proper;' acknowledges Silva, “though I would not argue against such a rendering as ‘your common salvation,' since there is no denying that Paul has the community, not isolated individuals in mind" (ibid., 119η3). Silva complains that Fee has characterized his view as “a case of'either/or' (i.e. either individual or community)" (ibid., 119η2). Pedersen also concludes that since Paul does not separate the collective from the individual, the question is irrelevant (Sigfred Pedersen, “Mit Furcht und Zittern;' ST 32 [1978], 29η74). Yet, when interpretive push comes to positional shove, Pedersen espouses the collective understanding. 48 Markus Bockmuehl, I Epistle fo the Philippians (BNTC; London: Black, 1998), 151. 45 Ibid. 50 Ibid. 51 Gordon D. Fee, Philippians (IVP New Testament Commentary; Downers Grove: InterVarsity, 1999), 102-3 (italics original). See the similar sentiments in Gordon D. Fee, Pauls
  • 68. Letter fo the Philippians (NICNT; Grand Rapids: Eerdmans, 1995), 234-35. “Ibid., 235. Yee, Philippians, 101 Ci. Aso Yee, Paals Letters to the Philippians, TYmTO. .Λ Yee, Philippians, 100‫؛‬ 55 Fee, Pauls Letter to the Philippians, 235. Although “people are saved one by one to be sure;' acknowledges Fee, “they are saved so as to become a ‘people for God’s name;" 24 Themelios is "a call to individually workout our common salvation in our life together.""' Ben Witherington argues for an "eschatological reality" behind Phil 2:12, but one that may also include "a social dimension or implication."‫?؛‬ In short, the appeal to unity is based on what God has already done and is doing in them and in their midst to bring about their salvation. Working out salvation means, among other things, continuous strenuous effort working harmoniously together as the body of Christ.‫؛؟‬ Carolyn Osiek similarly contends that "salvation" "is certainly not to be understood only in the
  • 69. eschatological sense," "yet hat dimension must be included."‫؛؟‬ "Paul is speaking of their total well-being, including their spiritual prosperity now and in the future."“ "It is not so much individual salvation as communal eschatological success that is envisioned. This is not to deny the individual aspects of the concept, but neither Paul nor his contemporaries thought primarily in individual terms, '!he collective good is the principal referent."“ The Apostolic Fathers It seems that the strong points of the so-called "sociological" view are the recurring plural verbs and pronouns, but especially he wider communal situation and corporate context of Phil 1:27-2:18. On the other hand, the strengths of the so-called "theological" view are its insistence that seeking personal salvation is not inherendy "selfish," the divine orientation of "fear and trembling" within the argument of Phil 2:12-13, and especially the customary "theological" sense of σωτηρία/σώζειν within Pauline thought.‫?؛‬ Might it be possible to combine some of the insights of he two views and form a coherent understanding of Phil 2:12 within its wider context? Can the σωτηρία/σώζειν word group be used in ways that are both theological and community-oriented? Although Michael, Hawthorne, and Martin cite uses of σωτηρία and σώζειν as references to well- being and physical health in the New Testament, the LXX, and in the Greek papyri, they do not cite pertinent uses of the word group in the Apostolic Fathers.‫؛؛‬ Perhaps these overlooked materials reveal a weakness in a purely "sociological" view: a "health or wholeness" of the community disengaged from a
  • 70. a ton erofereht si sihT“ ,seunitnoc eeF .401 ,snaippilihP ,eeF ٥‫؛‬ text dealing with individual salvation but an ethical text dealing with the outworking of salvation in the believing community for the sake of the world. ‫لآس‬ they must comply with this injunction at the individual level is assumed, and that their final salvation will be realized personally and individually is a truth that does not need stating, because that is not at issue here. The present concern is with their being God's people in Philippi, as 2:15 makes certain" (ibid., 104). 57 Ben Witherington, Friendship and Finances in Philippi (Valley Forge: Trinity Press International, 1994), 71. “Ibid. .Carolyn Osiek, Philippians, Philemon (ANTC; Nashville: Abingdon, 2000), 70 ‫؛‬9 ٥" Ibid. 61 Ibid. 62 “One will have a hard time defending that [sociological] understanding of this word on the basis of Pauline usage (as Hawthorne's resorting to some papyrus uses indicates)" (Fee, Pauls Letter fo the Philippians, 235η23). 63 Hawthorne and Martin, Philippians, 140. 25 'Work Out Your Salvation": Conduct "Worthy of the Gospel" in a Communal Context "theological" understanding of "salvati0n."٥4 At times, the Apostolic Fathers use σώζειν and its cognates in manners that are clearly mutual/reciprocal or
  • 71. corporate/communal, yet still manifestly "theological" as well (rather than mere references to physical health or "sociological" well-being). A mutual/reciprocal use of σώζειν within the community of believers is fairly common in the Apostolic Fathers.'" This emphasis of the Apostolic Fathers upon the mutual/reciprocal "saving" of others and the community-orientation of σωτηρία may seem rather foreign to Paul (or the New Testament in general) at first glance. But a quick perusal of Rom 11:13-14; 1 Cor 7:16; 9:22; 1 Tim 4:16; Jas 5:19-20; and Jude 22-23 readily reveals that Paul and other New Testament writers could speak of a mutual/reciprocal "saving" of others. Admittedly there are definite (and even significant) theological differences between Paul's epistles and various Apostolic Fathers.‫'״‬ But this (later) linguistic evidence at least confirms that the σωτηρία/σώζειν word group could be used in ways that were both theological and other-oriented, at least in a mutual/reciprocal sense. Two further examples in the Apostolic Fathers may cast additional light upon the interpretation of Phil 2:12. Both of these passages stress a "corporate" application of σώζειν, …