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Chapter 2
Appendix
Welfare Economics
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ISBN 0-03-033652-X
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Efficiency Resource Use
Assumptions
 2 inputs (capital and labor)
 2 outputs (food and clothing)
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Production Functions
F = F(LF,KF)
C = C(LC,KC)
Where
 F = food production
 C = clothing production
 Li = labor devoted to the production of good i
 Ki = capital devoted to the production of good i
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Constraints
L = LF + LK
K = KF + LF
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Productive Efficiency
 It is not possible to reallocate
inputs to alternative uses in
such a manner as to increase
the output of any good without
reducing the output of some
alternative good.
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Figure 2A.1 Productive Efficiency
L*C
K
LC 0'
KC
E*
Z*
K*F
C3
KF
0
D
C6 F1
LF
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C5 F3
C4
F5
F6
C1 K*
C
Z1
F
C2 4
F3
L*F
L
Efficiency Condition
MRTSFLK = MRTSCLK
 The Marginal Rate of Technical
substitution of Labor for Capital in each
good are equal
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Figure 2A.2 The Production-Possibility Curve
Food per Year
T
E1
A
E2
D
F
0
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C T'
Clothing per Year
Pareto Efficiency
Preferences on Consumption
UA = U(FA,CA)
UB = U(FB,CB)
Where
Ui = the utility of person i
Fi = food consumed by person i
Ci = clothing consumed by person i
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Constraints
F = FA + FB
C = CA + CB
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Figure 2A.3 Efficient Allocation of A Given Amount of
Food and Clothing per Year For Two Consumers
Food per Year
T
CB
CB*
F
UB1
UB3
UB4
FA*
UB7
UB6
E*
UB5
UA1
0
CA
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UA7
FB
UA6
FB*
UA5
UA3
FA
UB2
E**
D
UA4
UA2
CA*
C
Clothing per Year
T’
Efficiency Criterion on
Consumption and Production
MRSACF = MRSBCF = MRTCF
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Interpretation of Efficiency
Criterion
Suppose we say that the “price of a unit of clothing is
$1.” Then clothing is the same as “money.” We can
then say that MRSACF is A’s willingness to substitute
clothing for money, which is their marginal benefit of
clothing, MBAC. The same is true for B. If these are
equal to the MRTCF then this represents the
capability of turning money into clothing as well.
Thus it reflects the costs of production. Lastly if there
are no other people who gain from either A or B
consuming clothing or food then:
MSB = MBAC = MBBC = MSCC
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Social Welfare Functions
W = W(UA,UB)
 Where
 W is social welfare
 UA is A’s utility
 UB is B’s utility
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Efficiency and Economic
Institutions
Given the conditions for a market rendering
a Pareto Optimal outcome referred to in
Chapter 2 then if costs are:
C = PKK + PLL
then production of a particular amount of a
good is efficient if the slope of the production
function for each good is equal to the slope
of the isocost line.
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Capital
Figure 2A.4 Cost Minimization and Productive Efficiency
E
K
F = F1 per Year
0
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L
Labor
Implications of Figure 2A.4
 MRTSFLK = PL/PK
 MRTSCLK = PL/PK
 MRTSFLK = MRTSCLK = PL/PK
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Pure Market Economy and
Pareto Efficiency
Step 1
So far we know that PF = MCF and PC = MCC
from perfect competition dividing one by the
other we get
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=
PC
PF
MCC
MCF
Pure Market Economy and Pareto
Efficiency
Step 2
 MCF is the amount of other resources
that must be given up to produce more
Food. We will denote this fact by saying:
MCF = DC.
 It is the forgone clothing to produce
more Food.
 The same applies the other way around
MCC = DF.
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Pure Market Economy and
Pareto Efficiency
Step 3
Dividing these by each other we get:
MCC DF
=
MCF
DC
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Pure Market Economy and
Pareto Efficiency
Step 4
Since
DF
DC
= MRTCF
And
MRTCF =
Then
MCC
MCF
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=
PC
PF
DF
DC
= MRTCF =
PC
PF
Figure 2A.5 Consumer Choice
Food per Year
A
E
FA
UA3
UA2
UA1
0
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CA
B
Clothing per Year
Pure Market Economy and
Pareto Efficiency
Step 5
As just seen the slopes of the individual’s
indifference curves are equal to the ratio of the
prices. So
PC
A
MRSCF =
PF
B
MRSCF
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=
PC
PF
Pure Market Economy and Pareto
Efficiency
Final
A
B
MRSCF
= MRSCF
= MRTCF =
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PC
PF
Market Imperfections
 Monopoly P > MC
 Others are affected so MB = MSB or
MC = MSC
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